pure Pomeron exchange and of a Pomeron-like representation of the Pauli repulsion.
The other difficulty was  small LS splittings in the $\Lambda$ hypernuclei
which are characterized by the LS potential of ($V_{SLS}-V_{ALS}$) type.
In conventional OBE model, ALS becomes smaller compared with SLS which leads the large LS splitting in the $\Lambda$ hypernuclei.
In this model, in order to reproduce the small LS splitting, some prescriptions have been performed such as meson pair exchange of the axial-vector pairs.
These treatments of the ALS force should be tested with the Polarization (is equal to the Analyzing power) of the $\Lambda p$ scattering
where the ALS and SLS should make a sizable contribution.

* Quark cluster model

In the quark cluster model <cit.>, the interaction Hamiltonian for quarks consists of the phenomenological confinement potential, the color Fermi-Breit interaction
with explicit flavor-symmetry breaking, and the effective-meson exchange potentials of pseudoscalar, scalar and vector mesons.
The six quarks are put in the Gauss potential which is characterized by a size parameter $b$.
These six quarks are imposed to be anti-symmetric under the exchange between any quark combination.
The fermion nature of quark is taken into account and its effect is characterized by the size parameter $b$.
Large repulsive nature in the (10) and (8$_{s}$) multiplets in the SU(3) representation can be naturally predicted by the Pauli effect in the quark level.
The color Fermi-Brit interaction between quarks gives another source of ALS, SLS and tensor forces in addition to the contribution from meson exchange potential.
They predict the sizable ALS comparable to SLS and explain the small $\Lambda$ hypernuclear LS splitting.

* Chiral Effective Field Theory (Chiral EFT)

Chiral EFT has turned out to be a  powerful tool for the derivation of nuclear forces.
Its most notable feature is that there is an underlying power counting which allows one to improve calculations systematically by going to
higher orders in a perturbative expansion.
In addition, it is possible to derive two- and three- nucleon forces in a consistent way.
This method is applied for the YN interaction and the $\Lambda N$ and $\Sigma N$ interactions are obtained at next-to-leading order where
contributions from one- and two-pseudoscalar meson exchange diagrams and from four-baryon contact terms are considered <cit.>.
The chiral YN potential contains meson exchanges and a series of contact interactions with an increasing number of derivatives.
For the former meson exchange, contributions from the pseudoscalar octet ($\pi, K, \eta$) are taken into account.
The latter represent the short-range part of the interaction and are parametrized by low-energy constants (LEC), which need to be fixed by a fit to data.
The present Chiral EFT framework is constrained  from SU(3) symmetry in order to reduce the number of free parameter
and there are five, eight and ten independent LECs for the $S$-waves at LO, the $S$-waves and $S$-$D$ transition at NLO and for the $P$-waves at NLO.

The present YN scattering data are insufficient to determine the LEC parameters higher than the next-leading order.
One of the the most important experimental tasks is to provide higher precision data for the YN channels to impose the constraint to determine these parameters at NLO more accurately.
Because the existing YN experimental cross sections are concentrated on the lower energy where the $S$-wave contribution is dominant,
the experimental constraints for the P-wave parameters are quite weak.
Therefore the differential cross sections and the polarization observables above $p_{\Lambda} > 400$ MeV/$c$ are essential even for determining the LEC at NLO.
At the NNLO, the number of LEC does not increase for the two-body interaction <cit.>.
Therefore, accumulation of YN scattering data can contribute to extend Chiral EFT to  NNLO.

[]Differential cross sections calculated by theoretical models for the momentum range between 0.4 and 0.85 GeV/$c$.
Two types of Nijmegen models (NSC97f and ESC16 <cit.>) and Jülich model <cit.> are presented as the typical example of the boson exchange picture.
The two results by chiral EFT (chiral EFT13 and 19) <cit.> are calculated with the different sets of the LEC parameters both of which reasonably reproduce the YN scattering cross section.

Figure <ref> shows the differential cross sections calculated by each model for the momentum range between 0.4 and 0.85 GeV/$c$.
Two types of Nijmegen models (NSC97f and ESC16 <cit.>) and Jülich model <cit.> are presented as the typical example of the boson exchange picture.
Two results by chiral EFT (chiral EFT13 <cit.> and 19 <cit.> )  are calculated with the different sets of the LEC parameters both of which reasonably reproduce the YN scattering cross section.
However, the strength of the $\Lambda N$-$\Sigma N$ coupling potential, which is closely related to the attraction in $\Lambda N$ interaction in $\Lambda$ hypernuclei, in chiral EFT13 is much larger than that in chiral EFT19.
As for the total cross section, there are experimental data even for these momentum regions and the each model's parameters were determined to reproduce the existing total cross section.
However the differential cross section in each model shows quite different angular distribution due to the lack of the experimental input for the angular dependence.

It is true that there were no experimental inputs to impose any constraint on such contributions.
For this purpose, the accurate differential cross section data in the $P$-wave region are essential.
The polarization measurements are also essential to determine the LS contribution which were never determined from the YN scattering data.
Figure <ref> shows the Analyzing power (Left) and the Depolarization (Right) for the polarized $\Lambda$ beam <cit.>.
In the lower momentum around 0.4 GeV/$c$ where the $P$-wave contribution is less significant, there is no large model difference.
However, the model difference appears clearly in the higher momentum region, where the $P$- and higher waves contribute in the reaction.
Especially, the difference in the $\Sigma N$ threshold (0.633 GeV/$c$ for $\Sigma^{+} n$ and 0.642 GeV/$c$ for $\Sigma^{0} p$) becomes significant
due to the different treatments of tensor force ($^{3}S_{1}-^{3}D_{1}$ transition) and ALS ($^{3}P_{1}-^{1}P_{1}$ transition).
Such effect should be reflected in all measurements, that is, the differential cross section, Analyzing power and  Depolarization.

In present, the experimental situation is changing.
The J-PARC E40 experiment successfully detected the $\Sigma^{+} p$, $\Sigma^{-} p$ elastic scatterings and the $\Sigma^{-} p \to \Lambda n$ reaction
in the momentum range between 0.4 and 0.8 GeV/$c$.
The differential cross sections for these channels will be derived in near future <cit.>.
Such data are the first experimental inputs to impose the remarkable constraint on the theoretical models.
As shown in Table <ref>, the $\Lambda N$ and $\Sigma N$ channels are related with each other through the flavor SU(3) representation.
Because we measured both the $\Sigma^{+} p (I=3/2)$, $\Sigma^{-} p$ (superposition of $I=1/2, 3/2$) elastic scatterings,
the knowledge for all multiplets not included in the $NN$ channels will be updated.
Then, the theoretical prediction for the $\Lambda N$ channel should become less uncertain compared with the present situation.
It is worth comparing the experimental results of the $\Lambda p$ scattering with the updated theoretical calculations to test the theoretical framework with the flavor SU(3) symmetry.

Theoretical calculation of the Analyzing power ($A_{y}$) (left) and the Depolarization ($D_{y}^{y}$) (right) for the polarized $\Lambda$ beam.
The each colored line is same with figure <ref>

§.§.§ Impact on the neutron star physics

Hypernuclear physics are studied based on the two-body $\Lambda N$ interaction, especially the Nijmegen models are widely used to study the hypernuclear structure.
Due to the lack of the YN scattering data, such two-body models are partially tuned to reproduce the hypernuclear phenomena such as level splittings of $\Lambda$ hypernuclei and
$\Sigma$ nuclear potential.
In the last section, we have reviewed that there is a large disagreement among models even for the $\Lambda N$ interaction which is intensively studied from $\Lambda$ hypernuclei.
The present urgent issue to be solved is the so-called "hyperon puzzle" in neutron star.
This is the unsolved question how one can reconcile the softening of the equation of state (EOS) due to the appearance of hyperons with the observed two-solar-mass neutron star.
Because $\Lambda$ hyperon plays an essential role for the softening of the EOS, the understanding of the $\Lambda$ potential in the high density region is indispensable.
Currently, the importance of the three-body interaction including hyperon such as $\Lambda NN$ is widely discussed.

Yamamoto et al. pointed out that such $\Lambda NN$ three-body effect appears in the $\Lambda$ binding energies in heavy $\Lambda$ hypernuclei <cit.>.
Two-body $\Lambda N$ potential in the nuclei obtained by the G-matrix calculation from the Nijmegen ESC model was used.
The three-body interaction, composed of the multipomeron exchange repulsive potential (MPP) and the phenomenological three-body attraction (TBA), is added as the density dependent potential.
These three-body interaction's parameters were adjusted to reproduce the angular distribution of $^{16}$O $+$ $^{16}$O elastic scattering at $E/A = 70$ MeV
with use of the G-matrix folding potential, and values of the saturation density and the energy per nucleon there in nuclear matter.
One of the possible scenarios to explain two-solar-mass neutron star is that such density dependent three-body repulsion (MPP) contributes additional repulsive force to support the gravity of the neutron star.
Such three-body interaction should give a sizable contribution to the energy spectra of $\Lambda$ hypernuclei.
They calculated it systematically for wide mass number $\Lambda$ hypernuclei ($^{13}_{\Lambda}$C, $^{16}_{\Lambda}$O, $^{28}_{\Lambda}$Si, $^{51}_{\Lambda}$V, $^{89}_{\Lambda}$Y,
$^{139}_{\Lambda}$La, $^{208}_{\Lambda}$Pb) in the framework of  the latest Nijmegen model (ESC16)  with and without the three-body force as shown in Figure <ref> where
its energy spectra is reproduced well by including the three-body force <cit.>.
They concluded that the density dependent three-body force works to reproduce better energy spectra of heavy system.
In the high-density region, this three-body term dominated by MPP is expected to lead the stiff EOS of the hyperon-mixed neutron-star matter.

Energy spectra of  $^{13}_{\Lambda}$C, $^{16}_{\Lambda}$O, $^{28}_{\Lambda}$Si, $^{51}_{\Lambda}$V, $^{89}_{\Lambda}$Y,
$^{139}_{\Lambda}$La, $^{208}_{\Lambda}$Pb as a function of $A^{-2/3}$ calculated with the ESC16 model <cit.>.
Solid and dashed lines show calculated value by the $G$-matrix folding model derived from ESC16 with and without the three-body interaction, respectively.
Open circles and error bars denote the experimental values.

Isaka et al. also analyzed the $\Lambda$ binding energies with the various Nijmegen two-body interaction models with AMD framework <cit.>.
They pointed out that the three-body force strength reproducing the $\Lambda$ binding energies depends on the two-body interaction model and
there are considerable difference even within various ESC and NSC models.
Such difference comes due to the potential of $P$-state contribution.
Figure <ref> shows the density dependence of the $S$- and $P$-state contributions to $\Lambda$ potential as a function of $k_{F}$ <cit.>.
In case of ESC14 which is similar to ESC16, the $P$-state contributions are small.
On the other hand, in case of ESC12 and NSC96f, the $P$-state contributions are substantially repulsive.
Therefore, in the former model,  the $\Lambda$ binding energies are well reproduced by adding the strong MPP repulsion which can support the two-solar mass neutron star.
However, in the later model, the $P$-state repulsive contribution can reasonably work to reproduce the $\Lambda$ binding energy and there is no room to introduce the strong MPP repulsion.
The difference in the $P$-wave contribution even within the same Nijmegen framework is quite reasonable
because these models predict the different behavior in differential cross section as shown in Figure <ref>.
In the NSC97f, the larger $P$-wave contribution might make the differential cross section larger than that in ESC16.

$S-$state (left) and $P-$state (right)  contributions to $U_{\Lambda}$ as a function of $k_{F}$ taken from ref. <cit.>.
Red solid, blue dashed, black dotted, and black dot-sashed curves are for ESC14, ESC12, ESC08a, and ESC08b, respectively.
The latest ESC16 is similar to ESC14.

We believe that comparison between the high-resolution experimental data of the $\Lambda$ binding energy and the Nijmegen model calculation with the three-body interaction
is a crucial way to derive the $\Lambda NN$ three-body interaction.
In order to reinforce such the strategy, the accurate $\Lambda p$ scattering data are really awaited.
In the $NN$ sector, the realistic model of the nuclear force is established by updating the theoretical frameworks so as to reproduce a plenty of two-body scattering observables.
Now, we also have to construct the realistic $YN$ interaction model and both of theoretical and experimental efforts are necessary.
For the experimental side, various scattering observables as many as possible with a reasonable precision should be measured as the basic information for constructing a real bridge to the many-body system.

Chiral EFT is a promising theoretical framework to describe the nuclei and neutron matter.
One of the biggest advantages of this model is that the three-body forces appear naturally and automatically in a consistent implementation of the framework.
In the power counting in the present YN Chiral EFT, such three-body forces arise first at next-to-next-to-leading order (N$^{2}$LO) in the chiral expansion <cit.>.
If the decuplet baryons are included as explicit degrees of freedom, the three-body forces with decuplet excitation appear already at NLO.
In this calculation, two types of B-M-B$^{*}$  and B$^{*}$-B-B-B couplings appear  where B, M and B$^{*}$ represent octet baryons, pseudo scalar mesons and decuplet baryons, respectively.
The LECs in the B-M-B$^{*}$ coupling can be estimated through decuplet saturation  <cit.>.
The two-pion-exchange $\Lambda NN$ <cit.> and $\Lambda NN$-$\Sigma NN$ <cit.> forces  are already applied to study a density-dependent effective potential for the BB interactions by integrating one nucleon degree of freedom in the medium.
The repulsive effect of the $\Lambda NN$ interaction is calculated to be about 5 MeV at normal density ($\rho_{0}$) and about 20 MeV at 2$\rho_{0}$ in symmetric nuclear matter <cit.>.
A similar repulsive contribution is also obtained in pure neutron matter.
The $\Lambda NN$-$\Sigma NN$ coupling effect works to cancel the repulsive effect of the $\Lambda NN$ interaction at normal density in symmetric nuclear matter.
However, in the higher densities, the cancellation is incomplete and the net three-body force contribution is repulsive.
In pure neutron matter, the effect of the $\Lambda NN$-$\Sigma NN$ coupling effect is very small and, therefore, does not weaken the repulsion from $\Lambda NN$ force<cit.>.
In the present calculation, the three-body forces with B$^{*}$-B-B-B couplings is not included yet, because there are two LECs which should be determined from experimental data.
However, the number of LECs are limited.
These parameters can be fixed from the $0^{+}$ and $1^{+}$ states of $^{4}_{\Lambda}$He<cit.>.
A $\Lambda$-deuteron scattering experiment, which is also possible in future at J-PARC, can also contribute to fix these LECs.
In general, such $\Lambda$-deuteron or $\Lambda$-$\alpha$ scattering measurement includes rich information to fix these LECs compared with the binding energy of a few-body hypernuclei.
The structure of single-$\Lambda$ hypernuclei is studied using the chiral EFT up to NLO by Jülich-Bonn-Munich group <cit.>, where the three-body interaction is not included yet.
A qualitatively good agreement with data is obtained for the chiral EFT19 interaction over a fairly large range of mass number values.
This shows the potential of the chiral EFT model and it is worth providing scattering observables experimentally to update the chiral EFT model.

§.§.§ $\Lambda p$ scattering experiment at the K1.1 beam line

Experimental setup for the proposed $\Lambda p$ scattering experiment.
The schematic drawing of how to identify $K^{0}_{S}$ and $\Lambda p$ scattering is also shown.

We propose a new experiment for a  $\Lambda p$ scattering by using a momentum-tagged $\Lambda$ beam produced by the $\pi^{-} p \to K^{0}_{S} \Lambda$ reaction at the K1.1 beam line.
Figure <ref> shows the experimental setup.
Experimental concept is almost the same with the E40 experiment for the $\Sigma p$  scattering.
1.05 GeV/$c$ $\pi^{-}$ beam is irradiated to the liquid hydrogen (LH$_{2}$) target with 30 cm thickness.
We design experiment to use 30 M/spill $\pi^{-}$ beam which is 1.5 times higher intensity than that in E40 in order to accumulate as much $\Lambda$ beam as possible.
The SKS spectrometer was used as a forward spectrometer to detect $\pi^{+}$ <cit.>.
Because the momentum resolution of SKS is expected to be $\Delta p/p=10^{-3}$ (FWHM) which is more than 10 times better than that of KURAMA,
the missing mass resolution for $\Lambda$ will be improved and this also results in the improvement of the S/N ratio for $\Lambda$ identification.
In order to detect the $\Lambda p$ scattering and $\pi^{-}$ from $K^{0}_{S}$ decay,
CATCH, which consists of a cylindrical fiber tracker, BGO calorimeter and PiID,  is used as shown in enlarged figure in Figure <ref>.
CATCH surrounds the LH$_{2}$ target and detect recoil proton and scattered $\Lambda$ by detecting the $\pi^{-}p$ decay.

* Advantage of the $\pi^{-}p \to K^{0} \Lambda$  at $p_{\pi} = 1.05$ GeV/$c$

(Left) Momentum dependence of the total cross section of the $\pi^{-}p\to K^{0}\Lambda$ reaction. (Right) Differential cross section around $p$=1.05 GeV/$c$.<cit.>

In order to realize the high-statistics $\Lambda p$ scattering experiment,
it is the very important to accumulate as much $\Lambda$ beam as possible.
Therefore, the $\Lambda$ production cross section is one of the most important experimental parameters.
Figure <ref> (left) shows beam momentum dependence of the total cross section.
The total cross section becomes maximum around $\sim$900 $\mu$b at 1.05 GeV/$c$.
Figure <ref> (right) shows the differential cross section.
There are two measurements that are not consistent with each other, but the measurement by R.D. Baker et al. <cit.> seems to be more reliable.
In this simulation study, we have assumed that the $\Lambda$ production cross section is 900 $\mu$b and the angular distribution by R.D. Baker et al. are used.

Second important characteristics of this $\Lambda$ production around 1.05 GeV/$c$ is that $\Lambda$ particles are produced with almost 100% polarization
for the ($\pi^{-}, K^{0}$) production plane.
Figure <ref> shows the $\Lambda$ polarization in the momentum range of $0.931 \le p$ (GeV/$c$) $ \le 1.334$
measured by R.D. Baker et al.<cit.> .
This polarization can be measured by the angular dependence of the proton from the $\Lambda$ decay.
As shown in this figure, the $\Lambda$ polarization is sufficiently high to measure the spin observables.

The $K^{0}$ angle can be covered from 1 to 0 in $\cos \theta_{CM}$, where $\theta_{CM}$ is the scattering angle of $K^{0}$ in the CM frame.
Therefore almost 100% polarized $\Lambda$ can be used as hyperon beam automatically.
The production of the polarized $\Lambda$ beam enables us to measure not only the differential cross section but also the spin observables such as Analyzing power ($A_{y}$) and
depolarization ($D_{y}^{y}$).

Induced polarization of the $\Lambda$  by the $\pi^{-} p \to K^{0} \Lambda$ reaction for the momentum of  $0.931 \le p$ (GeV/$c$) $ \le 1.334$.
Horizontal axis show the $\cos \theta_{CM}$, where $\theta_{CM}$ is the scattering angle of $K^{0}$ in the CM frame.
High polarization can be obtained for all momentum ranges.

§.§.§ Goal of $\Lambda p$ scattering experiment at K1.1

The $\Lambda p$ scattering event is identified by the CATCH detector system, which was developed for the $\Sigma p$ scattering experiment,
by detecting the scattered $\Lambda$ and recoil proton.
In this experiment, $\pi^{-}$ from $K^{0}$ decay is also detected by CATCH as shown in the enlarged figure in Figure <ref>.
Experimental method is basically the same with one developed for the $\Sigma p$ scattering.
A liquid hydrogen target is used as the $\Lambda$ production and $\Lambda p$ scattering targets and the $\Lambda p$ scattering events are kinematically identified
by detecting particles in the final state without any imaging information.
High intensity $\pi^{-}$ beam of 30 M/spill will be used to accumulate high intensity $\Lambda$ beam.
In this experiment, we want to accumulate 100 M $\Lambda$ beam in total with separated two periods.
We request 34-days beam time including 29-days production run and 5-days commissioning and calibration runs as first stage to measure the differential cross section and the Analyzing power of the $\Lambda p$ scattering by accumulating 50M momentum-tagged $\Lambda$ beam.
As second stage, we request additional 34-days beam time including the production and commissioning/calibration runs with the same ratio to measure the depolarization and to improve the accuracy of measurements of the differential cross section and Analyzing power.
Here, we assume that spill structure is 5.2 s cycle with a beam duration of 2 s and the $\pi^{-}$ beam intensity is 30 M/spill.
The experimental and analysis details are written in reference <cit.>.

The differential cross section is derived at least for four different momentum ranges (100 MeV/$c$ momentum step)  for 50M $\Lambda$ beam as shown in Figure <ref>.
The statistical error for angular region of 0 $<$ $\cos \theta$ $<$ 0.1 as a typical angular bin is expected to be 10%.
In this simulation, $\Lambda p$ total cross sections for each momentum are assumed to be 15, 10, 20 and 12 mb, respectively, based on the past experimental data and theoretical calculation.
The angular dependence is simply assumed to be flat for checking easily whether the analysis procedure works well or not.
In the present analysis, we request two protons in the final state to suppress the background due to the background contamination in the $\Lambda$ production identification.
The angular acceptance for the differential cross section is limited due to this cut.
We hope the angular acceptance becomes much wider by loosing the two-proton cut by improving the $\Lambda$ identification method in future study.
In this proposal, we are showing conservative but assured result in present study.

As shown in Figure <ref> for 50 M $\Lambda$ beam, we can select best theoretical picture among the Nijmegen model (NSC97f and ESC16), Jülich boson-exchange model and chiral EFT(13 and 19) very clearly.
In present, we are requested to select better model within the same theoretical framework (for example selection between chiral EFT13 and 19 or selection among NSC97f and ESC16 and other ESC versions).
Selection of better model in the same theoretical framework could be possible even for 50 M $\Lambda$ beam depending on the difference in the theoretical prediction.
However, differential cross section measurement with narrower momentum step is quite effective to discriminate the better framework in the same theoretical model,
because the momentum dependence of the differential cross section becomes quite large as shown in Figure <ref> toward the $\Lambda$ beam momentum of the $\Sigma N$ threshold ($\sim$630 MeV/$c$) due to the tensor $^{3}S_{1}$-$^{3}D_{1}$ coupling.
Therefore, the differential cross section measurement with narrower momentum range of  50 MeV/$c$ momentum step is very important to measure this momentum dependence.
By accumulating 100M $\Lambda$ beam in total, we will measure differential cross sections with  10% statistical error for each 50 MeV/$c$ $\Lambda$ beam momentum step from 0.4 to 0.8 GeV/$c$ as shown in Figure <ref>.
As mentioned in later,  we need also 100M $\Lambda$ beam for the $D_{y}^{y}$ measurement.

Simulated results for the differential cross section measurement of the $\Lambda p$ scattering in the momentum range from 0.4 to 0.8 GeV/$c$ with 0.1 GeV/$c$ momentum interval for 50M $\Lambda$ beam.
Theoretical calculations are also presented.

Simulated results for the differential cross section measurement of the $\Lambda p$ scattering in the momentum range from 0.4 to 0.8 GeV/$c$ with 0.05 GeV/$c$ momentum interval with 100M $\Lambda$ beam.
Theoretical calculations are also presented.

Simulated results for $A_{y}$ measurement of the $\Lambda p$ scattering in the momentum range from 0.4 to 0.8 GeV/$c$ with 0.1 GeV/$c$ momentum interval for 100M $\Lambda$ beam.
Theoretical calculations are also presented.

Expected $D^{y}_{y}$ accuracy for 100M $\Lambda$ beam.
In this simulation,  no spin transfer ($D_{y}^{y}=0$) and no induced polarization ($P=0$) in the $\Lambda p$ scattering are assumed for simplicity.
The beam polarization of $P_{\Lambda} = 1$ is also assumed based on the past measurement.
Theoretical calculations are also shown together.
Due to the limitation of the statistics, errors in the high momentum region (0.7-0.8 GeV/$c$) are still large.
However,  in the middle momentum region (0.5 to 0.7 GeV/$c$) model difference between the chiral EFT and Nijmegen models can be clearly separated.

Figure <ref> shows the sensitivity of Analyzing power ($A_{y}$) which were obtained from the left-right asymmetry for the $\Lambda p$ scattering for 100M $\Lambda$ beam.
The expected statistical error is 8% for angular step of $d\cos \theta = 0.2$.
In this simulation,  $A_{y} = 0$ is assumed to check the experimental validity easily.
The normal technique used in the $NN$ case where the beam polarization is flipped and the number of the scattered particle are counted with a single detector setup or
the identical two detectors  were placed in the left-right symmetric position, can not be used,
because the $\Lambda$ beam is produced  in the tilted direction for the CATCH detector.
Therefore the differential cross sections for the left scattered case and the right scattered case were derived and
$A_{y}$ is derived from these left- and right-differential cross sections.
We confirmed that $A_{y}$ values were reasonably obtained by such analysis method in the simulation.
In the momentum range higher than 0.5 GeV/$c$, there are large differences among three theoretical models.
In order to discriminate these models, 10% accuracy is necessary and
such new data are quite important to improve the theoretical models because sizable difference can appear in spin observables even thought the difference in the differential cross section is small.
For example, there is large difference in $A_{y}$ at 0.65 GeV/$c$ between chiral EFT13 and 19, whereas there is very small difference in the differential cross section.
$A_{y}$ is sensitive for the anti-symmetric LS force (ALS).
In the calculation by chiral EFT13, $A_{y}$  values can be varied by adding ALS with a difference of 0.1 - 0.2 depending on the size of ALS <cit.>.
Therefore the present accuracy of less than 10% is also necessary to constrain the ALS force from the $A_{y}$ measurement.

Figure <ref> shows the simulated results for the depolarization ($D_{y}^{y}$) measurement for 100M $\Lambda$ beam.
For this measurement, the polarization of the scattered $\Lambda$  has to be measured from the up-down asymmetry of the decay proton from $\Lambda$ with respect to the scattering plane.
The up-down symmetry in CATCH is rather better compared to the left-right symmetry because CATCH has the symmetric acceptance with respect to the central axis of the system.
However, there are some detector asymmetry depending on the scattering vertex position and scattering angle.
Such systematic effect due to the asymmetry in CATCH is also studied in this simulation.
In this simulation, $D_{y}^{y}=1$ which means no spin flip occurred in the scattering is assumed for the simplicity.
We have confirmed the $D_{y}^{y}$ can be reproduced reasonably by using the up-down asymmetry technique although there are some deviations due to the asymmetric effect.
This is the first trial to measure the polarizations in both initial and final states and this is an important step to measure further measurements such as rotation parameters.
As mentioned in Section <ref>,  $D_{y}^{y}$ is also the mixed combination of several spin-dependent and spin-independent amplitudes.
However, $D_{y}^{y}$ is expected to be closely related to the tensor force.
Although the accuracy is limited (15% level), the discrimination of theoretical models is possible for momentum range from 0.5 to 0.7 GeV/$c$ as shown in Figure <ref> .
These data can also impose constraint on theories from different aspects.
Accumulation of these spin observables and differential cross section are essential to improve these theoretical models and to establish the realistic YN interaction model in future.

§.§.§ International situation and future prospect at J-PARC

Recently, femtoscopic measurements are widely applied to baryon pairs produced in $pp$ and heavier ion collisions at LHC and RHIC <cit.>.
These measurements are very strong method to deduce the scattering length and effective range of the BB interactions including multi-strangeness systems.
Because the femtoscopy is applied for the baryon pairs with small relative momentum, the $S$-wave information will be updated from these studies.
In the proposed setup at J-PARC, measurement of  the low energy YN scattering is rather difficult due to the difficulty in detection of low energy protons.
However, in the present experiment, we can measure the differential information for higher momentum region.
Therefore, these experiments are complemental relation.
It should also be stressed that the differential information is quite awaited from theoretical side.

CLAS collaboration also has a potential to measure YN scattering from the re-scattering of hyperons produced by the photo-induced reaction <cit.>.
In their analysis, the $\Lambda$ momentum region is higher than 1 GeV/$c$.
Therefore, relation between CLAS and this experiment is also complemental.
However, CLAS is a potential competitor.

In J-PARC, Honda et al. <cit.> are considering a $\Lambda p$ scattering experiment at the High-p beam line in the secondary-particle mode.
In the experiment at the High-p beam line,  a wide momentum range (0.4 $<$ $p$(GeV/$c$) $<$ 2.0) of $\Lambda$ particle can be identified as $\Lambda$ beam thanks to a large acceptance of the forward spectrometer and higher incident $\pi^{-}$ beam momentum.
This experiment is also important to measure the energy dependence of the $\Lambda N$ cross section up to high momentum range (2 GeV/$c$), because the cross section at high energy is related to the short range interaction which becomes important at high density environment like the inner region of neutron star.
Although there is an overlap  in the $\Lambda$ beam momentum region with the present experiment, there are unique features in both experiments.

* K1.1 : spin observable measurement around $\Sigma N$ threshold region is a unique feature at the K1.1 beam line

* High-p : wide $\Lambda$ momentum range up to 2 GeV/$c$ and high statistics are unique feature at the High-p beam line

Therefore, both experiments can contribute the understanding of the YN two-body interaction.

In the proposed experiment at the K1.1 beam line, by accumulating several scattering observables,
the data points ($d\sigma / d \Omega$, $A_{y}$ and $D_{y}^{y}$) become comparable with the number of phase shift values up to $F$ or $G$ waves.
There is a possibility to derive the phase shift value from the global fit of all scattering observables like the $NN$ case.
In future, we should also consider this possibility for the construction of the realistic BB interaction model.

Once the two-body $\Lambda N$ interaction is established, we should also measure the $\Lambda d$ scattering to study the $\Lambda NN$ three-body force.
Experimentally, the $\Lambda d$ scattering experiment can be performed by exchanging the liquid hydrogen target to a liquid deuterium target.
Such data are essential input to fix the LECs for the chiral three-body force.

§.§ Other Experiments Planned at K1.1

§.§.§ $\gamma$-ray spectroscopy of $\Lambda$ hypernuclei

$\gamma$-ray spectroscopy with germanium (Ge) detectors provides us
with precise excitation energies and
level scheme data in accuracy of the order of 1 keV.
We performed a series of experiments at KEK-PS, BNL-AGS, and J-PARC
with dedicated Ge detector arrays (Hyperball, Hyperball-2, and Hyperball-J)
and revealed level structure of $^4_\Lambda$He,
$^4_\Lambda$Li,  $^9_\Lambda$Be,
$^{11}_\Lambda$B,  $^{12}_\Lambda$C,  $^{15}_\Lambda$N,
$^{16}_\Lambda$O, and  $^{19}_\Lambda$F
by observing and assigning 25 $\gamma$ transitions <cit.>.
With these data, the strengths of the $\Lambda$$N$
spin-spin, spin-orbit, and tensor interactions
have been determined well <cit.>, and the charge symmetry breaking (CSB)
effect in the $A=4$ hypernuclei <cit.>
as well as hypernuclear shrinking effect in $^7_\Lambda$Li <cit.>
were also discovered.

At the K1.1 beam line, $\gamma$-spectroscopy experiments will be continued particularly
for the purposes of

(1) Study of $\Lambda$$N$$N$ three-body force via $^3_\Lambda$H excited states,

(2) Further studies of CSB effects using $p$-shell $\Lambda$ hypernuclei,

(3) Study of density dependence of $\Lambda$ binding energies from $s_\Lambda$ $\to$
$p_\Lambda$ transitions, and

(4) Study of baryon modification in nuclear matter via $\Lambda$'s $B(M1)$ measurement

In addition, $\gamma$-ray spectroscopy experiments
are also necessary for the precise determination of
$\Lambda$'s single-particle energies in the ($\pi^+,K^+$) reaction spectroscopy experiments
to be carried out at HIHR.
The $\Lambda$'s single-particle level is split into spin-doublet states as well as several core-excited states
with level spacings of the order of a few 100 keV.
The $\gamma$-ray experiments will unveil level schemes of those hypernuclei studied at HIHR,
which allows precise extraction of the $\Lambda$'s single-particle energies.

(1) Study of $\Lambda$$N$$N$ three-body force via $^3_\Lambda$H excited states

In our studies of the $\Lambda$$N$$N$ 3BF and
the $\Lambda$$N$-$\Sigma$$N$ coupling, which are the main problems for neutron star EOS,
the excited states of $^3_\Lambda$H would provide decisive information if they are observed.

Figure <ref> shows the expected level scheme of $A=3$ $\Lambda$ hypernuclei.
We hope to study the $3/2^+;T=0$ state, the spin-doublet partner of the ground state ($1/2^+;T=0$) of $^3_\Lambda$H.
It is expected to be excited by a few 100 keV to 1 MeV from the ground state.
If the energy of this state is lower than or slightly above the $d+\Lambda$ threshold,
we will be able to observe the $3/2^+ \to 1/2^+$ transition.

We also hope to observe transitions from the isospin 1 ground state ($1/2^+;T=1$)
which is expected to be located around $\sim$2 MeV excitation from the $^3_\Lambda$H ground state. Although this state should be located above the $d+\Lambda$ threshold
but the strong decay to $d+\Lambda$ is greatly suppressed due to isospin conservation.
Therefore, if the energy of the $1/2^+;T=1$ state is lower than or slightly higher than
the $p+n+\Lambda$ threshold, $\gamma$ transitions to the ground state ($T=0$) doublet
are expected to be observed.
If the $^3_\Lambda n$ hyeprnucleus ($nn\Lambda$ state) is bound as reported by
the HypHI experiment <cit.>, these transitions will be observed and the precise energy of the $^3_\Lambda$H $T=1$ state will be deduced. It would provide invaluable information
on the $T=1$ $\Lambda$$N$$N$ three-body force.

In the experiment we employ the $^7$Li($K^-,\pi^-$)$^7_\Lambda$Li$^*(3/2^+)$,
$^7_\Lambda$Li$^*(3/2^+) \to ^3_\Lambda$H$^*$ +$^4$He reaction at $p_K \sim 1$ GeV/$c$.
Since the $^7_\Lambda$Li$^*(3/2^+)$ state is so-called a substitutional state having
a huge production cross section,
observation of $\gamma$-rays from these $^3_\Lambda$H excited states
may be possible even if these states are particle unbound
and the $\gamma$-ray yields are quite small, thanks to
the intense kaon beam at the K1.1 beam line and the large acceptance ($\sim$ 100 msr)
of the SKS spectrometer

Expected level scheme of $A=3$ $\Lambda$ hypernuclei.

(2) Further studies of CSB effects using $p$-shell
$\Lambda$ hypernuclei <cit.>

Even after our confirmation of a large CSB effect in $A=4$ hypernuclei <cit.>,
the origin of this effect has not been understood yet.
It is expected that the CSB effect for heavier ($p$-shell) $\Lambda$ hypernuclei
will provide a clue to understand its mechanism.
By using the $(\pi^-,K^0$) reaction, which will be used in the proposed $\Lambda$$p$ scattering
experiment, we can produce mirror $\Lambda$ hypernuclei with respect to the hypernuclei already
well studied via $(K^-,\pi^-)$ and/or $(\pi^+,K^+)$ reactions with $\gamma$-ray spectroscopy.
We will study $^7_\Lambda$He, $^{12}_\Lambda$B, $^{16}_\Lambda$N, etc.,
and compare them with
$^7_\Lambda$Li ($T=1$), $^{12}_\Lambda$C  and $^{16}_\Lambda$O data.
Because of a lower detector efficiency for $(\pi^-,K^0$) reaction, we need to occupy
an intense pion beam line for several months.
The K1.1 line + SKS spectrometer is ideal apparatus for these experiments.

(3) Study of density dependence of $\Lambda$ binding energies
from $p_\Lambda \to s_\Lambda$ transitions

In the precise $(\pi^+,K^+)$ spectroscopy at HIHR, we aim at
measuring density dependent effects
of the $B_\Lambda$ values for the $s_\Lambda$, $p_\Lambda$, $d_\Lambda$, $f_\Lambda$ orbits
in a wide variety of $\Lambda$ hypernuclei.
In the $\gamma$-ray spectroscopy,
we can obtain extremely precise (a few keV accuracy) data of
the $p_\Lambda$-$s_\Lambda$ energy spacings via $E1$($p_\Lambda \to s_\Lambda$)
transitions. In heavy hypernuclei such as
$^{139}_\Lambda$La and $^{208}_\Lambda$Pb,
both $p_\Lambda$ and $s_\Lambda$ wave functions are confined
in the center of the nucleus with a density of $\sim \rho_0$, while in lighter hypernuclei such as
$^{28}_\Lambda$Si and $^{40}_\Lambda$Ca
the $p_\Lambda$ orbit partly overlaps with less dense part near the nuclear surface.
Thus, $A$-dependence of the $p_\Lambda$-$s_\Lambda$ spacing is expected to provide
information on the density dependence of the $\Lambda$$N$ interaction that can be described by the $\Lambda$$N$$N$ 3BF. The measured $\gamma$-ray spectra will be also used to
determine the low-lying level schemes of the hypernuclei,
which is necessary to precisely extract the
single-particle $\Lambda$ binding energies from the high precision ($\pi^+,K^+$) spectra taken at HIHR.

(4) Study of baryon modification in nuclear matter via $\Lambda$'s $B(M1)$

In the approved experiment E63 <cit.>,
we plan to measure the $\Lambda$-spin-flip
M1 transition probability $B(M1)$ in $^7_\Lambda$Li,
in order to investigate possible change of the magnetic moment of a $\Lambda$ in nuclear medium
due to a possible modification of baryon structure as well as baryon mixing effects.
The experiment employs the $(K^-,\pi^-)$ reaction at the K1.1 beam line.
If a deviation of the $\Lambda$'s $g$-factor from the free space value
is observed, further studies are necessary with different hypernuclei to clarify its origin
by investigating nuclear density dependence and isospin dependence of the deviation.
Since a measurement for each hypernucleus requires a beam time more than one month,
the independent K1.1 beam line is necessary.

§.§.§ Weak decays of $\Lambda$ hypernuclei

Weak decays of $\Lambda$ hypernuclei were mainly
studied at KEK-PS and DA$\Phi$NE.
Experimental data on the lifetime and the $n$/$p$-induced rates of the
nonmesonic weak decay (NMWD) ($\Lambda$$n$, $\Lambda$$p$ $\to$ $n$$n$, $n$$p$)
confirmed a short-range nature of NMWD described by heavy meson exchanges <cit.>.
However, the three-body non-mesonic decay, $\Lambda$$N$$N$$\to$ $N$$N$$N$,
is not clearly understood, and the stage-2 approved experiment (E18) will be carried
out when the K1.1 line is available.
In addition, the following experiments are planned at K1.1.

(1) Mesonic and nonmesonic weak decays via  $(\pi^-,K^0)$
and $(\pi^+,K^+)$ reactions

The $(\pi^-,K^0$) reaction method will allow us to extend hypernuclear weak decay studies
to the neutron-rich side <cit.>, as is also planned for $\gamma$-ray spectroscopy.
Using this reaction, a test of the $\Delta I=1/2$ rule in NMWD,
which has been considered to be quite important but
not successful due to experimental difficulties,
will become feasible.
The $\Delta I=1/2$ rule is a long-standing problem
to be solved from low-energy QCD dynamics.
Some theories suggest that this rule does not hold in NMWD.
To test it we need to measure the $p$-induced NMWD rate ($\Gamma_p$) in $^4_\Lambda$H as well as
the $n$-induced NMWD rate ($\Gamma_n$) in $^4_\Lambda$He
By using intense pion beams at K1.1 and the $(\pi^-,K^0)$ reaction technique,
the $^4_\Lambda$H measurement will be feasible
in a rather short beam time.
This method is also useful in precise determination of the $^3_\Lambda$H lifetime
of which experimental data are in a puzzling situation at present <cit.>.

At the K1.1 beam line, weak decay studies
of various hypernuclei ($^3_\Lambda$H, $^4_\Lambda$H, and
neutron-rich $p$-shell hypernuclei) via $(\pi^-,K^0)$ reaction
are proposed <cit.>.
The pion spectra in the mesonic weak decay will be used
for spin-parity assignment of hypernuclear ground states,
as was confirmed by the FINUDA experiments at DA$\Phi$NE <cit.>.
In addition, coincidence measurement of weak decay particles
and $\gamma$ rays will provide a new method to study the spin-flip $\Lambda$'s B(M1)
values of heavy hypernuclei <cit.>.

(2) Beta decay of $\Lambda$ hypernuclei <cit.>

Weak decay of $\Lambda$ in a nucleus is a unique probe to investigate
possible modification of baryon structure in nuclear medium.
To avoid strong interaction effects in the final state,
measurement of the $\Lambda$'s beta decay, $\Lambda \to p e^- \bar{\nu}$, is desirable.
Because the $u$ quark distribution of a $\Lambda$ hyperon
is expected to be more spread
than the $s$ quark distribution in nuclear matter, the beta-decay rate is expected to be
significantly reduced due to a smaller overlap between $s$ and $u$ quarks
in nuclear matter than in the free space.
An experiment is planned at K1.1 to measure
the lifetime and the branching ratio of $^5_\Lambda$He hypernucleus
and to obtain the beta-decay rate precisely <cit.>.
The hypernuclei are produced by $^6$Li$(\pi^+,K^+)$ reaction with the SKS spectrometer,
and beta-decay electrons are detected by a 4$\pi$ calorimeter around the target.
Since the beta-decay branching ratio of a $\Lambda$ is small ($8.3 \times 10^{-4}$),
reduction of huge background from the main weak decay modes (mesonic and nonmesonic decays)
is a key of the measurement. A recent simulation study shows that the background can be
sufficiently reduced,
and the beta-decay rate can be measured in a statistical accuracy of $\sim$4%
in two months of beam time.

Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

journaltitleNucl. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. Lett.

journaltitleJ. High Energy Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev.

journaltitlePhys. Rev.

journaltitlePhys. Rev. C

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitleAIP Conf. Proc.

journaltitleJPS Conf. Proc.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. Lett.

journaltitleProg. Part. Nucl. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Lett.

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Lett.

journaltitleAIP Conf. Proc.

journaltitleProg. Theor. Exp. Phys.

journaltitleJPS Conf. Proc.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev.

journaltitleJ. Radioanal. Nucl. Chem.

journaltitleJPS Conf. Proc.

family=The CLAS Collaboration,

journaltitleProg. in Part. and Nucl. Phys.

journaltitleKEK/J-PARC-PAC 2014-4

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Lett. B

journaltitlePhys. Lett. B

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Lett. B

journaltitleJ. High Energy Phys.

journaltitleJ. Phys. Conf. Ser.

journaltitleThe Astrophysical Journal

journaltitlePhys. Rev. Lett.

journaltitleAnn. Rev. Nucl. Part. Sci.

journaltitlePhys. Rev. C

journaltitleProg. Part. Nucl. Phys.

journaltitleRev. Mod. Phys.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleNature Astronomy

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Phys.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitleRev. Mod. Phys.

journaltitleRev. Mod. Phys.

journaltitleThe Astrophysical Journal

journaltitleRept. Prog. Phys.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev.
volumeC 38

journaltitleNucl. Phys. A

journaltitlePhys. Lett. B

journaltitleEur. Phys. J. A

journaltitlePhys. Rev. Lett.

journaltitleEur. Phys. J. A

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Exp. Phys.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Phys.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitlepresentation at JLab Hypernuclear workshop

journaltitlePhys. Rev. C

journaltitlePhys. Lett. B

journaltitleProg. Theor. Phys. Suppl.

<http://lambda.phys.tohoku.ac.jp/ miwa9/E40/doc/Lp_scat_proposal.pdf>
journaltitleProposal for J-PARC: Measurement of the differential cross section and spin observables of the $\Lambda$$p$ scattering with a polarized $\Lambda$ beam

journaltitleLetter of Intent for J-PARC PAC: Measurement of cross section of the $\Lambda$$p$ scattering

journaltitlePhys. Rev. Lett.

journaltitleEur. Phys. J. A

<http://lambda.phys.tohoku.ac.jp/ nue/HIHR/2021HIHR-proposal.pdf>
journaltitleProposal for J-PARC: High precision spectroscopy of $\Lambda$ hypernuclei with the ($\pi^+,K^+$) reaction at the High Intensity High Resolution beamline

journaltitleNucl. Instrum. and Meth.

journaltitleNucl. Instrum. and Meth.
volumeB 126

journaltitleNucl. Instrum. and Meth.
volumeA 422

journaltitleJLab PAC35 Proposal

journaltitlePhys. Lett. B

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitleNucl. Phys. A

journaltitlePhys. Rev. C

journaltitleNucl. Instrum. Meth. A

journaltitleBNL-AGS Proposal

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Phys. Suppl.

journaltitleJPS Conf. Proc.

journaltitleSov. Astron.
volumeAJ 4

journaltitleAstrophys. J.

journaltitleEurophys. Lett.

journaltitleAstron. Astrophys.

addendumErratum: Phys. Rev. C 90, 019904 (2014)
journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleNucl. Phys.
volumeA 747

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitleJ-PARC E40 experiment.

journaltitlePhys. Rev. C

journaltitleEur. Phys. J.
volumeA 50

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitleProg. Theor. Phys. Suppl.

journaltitleNucl. Phys. A

journaltitlePhys. Rev. C

journaltitleProg. Theor. Phys.

journaltitleProc. Jpn. Acad.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. C

journaltitleProg. Part. Nucl. Phys.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleNucl. Phys. A

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleFew Body Syst.

journaltitleJ. Phys. G

journaltitleNucl. Phys. A

journaltitlePhys. Rev. C

journaltitleEur. Phys. J. A

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleNucl. Phys. A

journaltitleAIP Conf. Proc.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitlePhys. Rev.
volumeC 103

journaltitleSpecial talk at the JPS Meeting

journaltitlePhys. Rev. C

journaltitleKEK Report

journaltitleNucl. Phys. A

journaltitlePhys. Rev. C

journaltitle Proceedings of International Symposium on Medium Energy Physics

journaltitleAnn. Rev. Nucl. Part. Sci.

journaltitleProg. Theor. Exp. Phys.

journaltitleBNL internal reports
volumeNos. 11299 and 11479

journaltitlePhys. Rev. Lett.

journaltitleHIHR/K1.1 workshop

journaltitlepresentation at International workshop on the project for the extended hadron experimental facility of J-PARC, March 27, 2018

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitleFew Body Syst.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. Lett.

journaltitleNucl. Phys. A

journaltitleNucl. Phys. A

journaltitleCzech. J. Phys.

journaltitlePhys. Lett.

journaltitleNucle. Phys. A

journaltitleProg. Theor. Phys. Suppl.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitleLetter of Intent for J-PARC: Search for tetraneutron by pion double charge exchange reaction on $^4$He

journaltitleNucl. Phys. A

journaltitleProg. Part. Nucl. Phys.

journaltitleNucl. Phys. A

journaltitleEPJ Web of Conf.

journaltitlePhys. Rev.

journaltitlePhys. Rev.

journaltitleNucl. Phys. B

journaltitleNucl. Phys. B

journaltitlePhys. Lett.

journaltitlePhys. Lett. B

journaltitlePh.D. thesis

journaltitleNucl. Phys. A

journaltitleNucl. Phys. A

journaltitleProg. Theor. Phys. Suppl.

journaltitleJ. Phys. : Conf. Ser.

journaltitlePhys. Rev. C

journaltitlePhys. Lett. B

journaltitleJps. J. Appl. Phys.

journaltitleprivate communication

journaltitleprivate communication

journaltitleNucl. Phys. A

journaltitleEur. Phys. J. A

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. D

journaltitlePhys. Rev.

journaltitleNucl. Phys. B

journaltitleAIP Conf. Proc.

journaltitlePhys. Rev. Lett.

Springer Berlin Heidelberg

booktitleTopics in Strangeness Nuclear Physics
titleHypernuclear Gamma-Ray Spectroscopy and the Structure of p-shell Nuclei and Hypernuclei

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitleNucl. Phys. A

<https://lambda.phys.tohoku.ac.jp/ tamura/beta-decay_LOI.pdf>
journaltitleLetter of Intent for J-PARC: Modification of baryon structure in nuclear matter studied from beta-decay rate of a $\Lambda$ hypernucleus

journaltitleAIP Conf. Proc.

addendumand references therein.
journaltitleNucl. Phys. A

journaltitleRept. Prog. Phys.

journaltitleNucl. Phys. A

journaltitleProg. Theor. Exp. Phys.

journaltitleProg. Theor. Phys.

journaltitleProg. Part. Nucl. Phys.

journaltitleNucl. Phys. B

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. D

journaltitleProg. Theor. Phys.

journaltitleRept. Prog. Phys.

journaltitleProg. Theor. Phys.

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitleprivate communication

journaltitleProceedings of 4th International Conference on Baryon Resonances

journaltitlePhys. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. D

journaltitleNucl. Phys. A

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Rev. D

journaltitlePhys. Lett. B

journaltitleJ. High Energy Phys.
family=N. Suzuki, B. Juliá-Díaz, H. Kamano, T. S. H. Lee, A. Matsuyama and T. Sato,

journaltitlePhys. Rev. Lett.

journaltitleRev. Mod. Phys.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Lett. B

journaltitlePhys. Rev. D

journaltitlePhys. Rev. C

journaltitleNucl. Instrum. Meth. A
titleOptical design of beam lines at the KEK PS new experimental hall

journaltitleELPH annual report, Tohoku University

journaltitleELPH annual report, Tohoku University

journaltitleRCNP annual report, Osaka University

journaltitleProposal for the ELPH experiment
titlePerformance evaluation of the next generation DAQ system with high-rate detectors for the J-PARC E50 experiment

journaltitleProg. Theor. Exp. Phys.
titleContinuous timing measurement using data streaming DAQ system
pagesin press

journaltitleNucl. Instrum. Meth. A

journaltitlePhys. Rev. C

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. C

journaltitlePhys. Rev. C

journaltitleAnn. Phys.

journaltitleNucl. Phys. B

journaltitleComput. Phys. Commun.

journaltitleNucl. Phys. B

journaltitleNucl. Phys. B

journaltitleNucl. Phys. B

journaltitleNucl. Phys. B

journaltitleNucl. Phys. B

journaltitlePhys. Rev. D

journaltitlePhys. Rept.

journaltitleRev. Mod. Phys.

journaltitlePhys. Rev. Lett.

journaltitlePhys. Rev. D

journaltitlePhys. Lett. B

collaborationJ-PARC E14 Collaboration
titleProposal for $K_L \rightarrow \pi^0 \nu \overline{\nu}$ Experiment at J-PARC

journaltitleJ. Phys. Conf. Ser.

journaltitleNucl. Instrum. Meth. A

journaltitleNucl. Instrum. Meth. A

journaltitleNucl. Instrum. Meth. A

journaltitleJ. Phys. Conf. Ser.

collaborationKOPIO Project
titleKOPIO Conceptual Design Report

journaltitleNucl. Instr. Meth. Phys. Res. A

journaltitleNucl. Instr. Meth. A
Physics objectives at the K10 beam line

§ PHYSICS OBJECTIVES AT $\PI20$ AND K10 BEAM LINES

K. Aoki, Y. Hidaka, A. Hosaka, N. Ishii, T. Ishikawa, Y. Komatsu,

Y. Morino, M. Naruki, H. Nemura, H. Noumi, H. Ohnishi, K. Ozawa,

F. Sakuma, T. Sekihara, S. I. Shim, K. Shirotori, H. Takahashi,

S. Takeuchi, and M. Takizawa

Hadrons are composite particles of quarks interacting with gluons.
Hence the goal of hadron physics is to answer the question
“how quarks build hadrons".
By this we should be able to explain various properties of observed hadrons,
to predict new phenomena, and to tell how best to look for.
The resulting knowledge can be used as the basis
of various extended studies where hadrons appear such as dense
hadronic matter.
Furthermore, QCD is the only gauge theory that shows non-perturbative nature of dynamics and can be accessible by experiments. Thus the exploring QCD should be helpful to
understand what happens in various other physics systems, which can be described by the quantum field theories with the strong couplings.

Spectroscopy of hadrons (in the following this is referred to as “hadron spectroscopy")
has been carried out
for many years,
mostly driven by experimental discoveries of new states <cit.>.
Recent lattice QCD calculations have been making crucial contributions to establish
that QCD is indeed the theory of the strong interaction for hadrons,
and opened a way even to nuclear systems from QCD.
Nevertheless, there are still unsolved or unsettled issues.
They are important not only for their own sake but also due to their wide
application to related fields.
For instance, the question of the high density hadronic matter
has been considered to be one of the most challenging problems in
the strong interaction physics, QCD.

At five times or more than the normal nuclear matter densities, the nuclear matter
is expected to turn into the quark matter where exotic structure such as color superconductivity
could be formed.
Such a change in the matter structure should affect the properties of the neutron stars that have
the high density region in the core part.
As illustrated in Fig. <ref>, at such densities the core parts of the nucleon
start to overlap, where the dynamics of the quarks and their correlations (of primary importance is the diquarks) becomes relevant.
We then expect that such properties could be learned by baryon spectroscopy.
Although the information that can be obtained by the spectroscopy (at zero density)
is not exactly relevant, it provides the information
at the initial point that extrapolates to finite density regions.

In the project at the $\pi20$ and K10 beam lines,
we will perform
high statistics baryon spectroscopy
with keeping these scopes.

Schematic picture for the isolated nucleon, nuclear matter,
and quark matter.

§.§ What We Know About Baryons

Let us start with looking at a simple example of atoms
that are built by electrons (and a nucleus).
An obvious fact is that the mass of the electron
is much larger than the energies that are relevant
to various atomic phenomena, the binding energies
and excitation energies of electrons.
Thus the creation of electron and anti-electron (positron)
pair is suppressed,
and therefore, the electrons inside an atom are essentially the same
as isolated electrons, enabling the electrons
as good building blocks,
an “ordinary path" of how electrons build atoms.
A similar situation occurs in nuclear systems.

The situation changes drastically for hadrons.
the current $u, d$ quarks in the QCD Lagrangian are
far lighter than the proton <cit.>.
This makes it very difficult to draw an ordinary path
with the current quarks used as good building blocks.
If we want to create the mass of the proton about 940 MeV
from the current $u,d$-quark masses
of order a few MeV,
we need additional steps of many $q \bar q$ creations.
Obviously such a process leads to enormous complications.
If so, is the resulting hadron spectrum
In fact, the data seem very systematic
in the region of excitation energies up to around 1 GeV,
as shown in Fig. <ref>.
This implies the emergence of effective degrees of freedom
that build the observed hadrons in a rather simple manner.

Excitation energies of various baryon states.
Plots for $u, d, s$ flavors are from Ref. <cit.>,
with  heavy baryon data are added.

This is the place where the non-perturbative dynamics of QCD comes in.
It is known that the QCD vacuum $|0\rangle$ is populated by the non-zero
expectation value of the quark condensate for the light $q = u, d, s$ quarks,
$\langle 0 | \bar q q | 0 \rangle \neq 0$.
Consequently chiral symmetry is spontaneously broken and the
light quarks acquire a finite mass of order

of several hundred MeV,

constituent quarks emerge as quasi-particles.
The constituent quarks may interact effectively by exchanging gluons,
which is often treated one gluon exchange.
Furthermore, light pions are generated as the Nambu-Goldstone bosons
formed by $u, d$ quarks and their antiquarks.
Kaons of $s, u$ (or $d$) quark content are also regarded as the Nambu-Goldstone bosons
whose masses are however significantly heavier than the masses of the pions
due to heavier mass of the $s$ quark [
The current quark masses are $m_u \sim 2$ MeV, $m_d \sim 5$ MeV and $m_s \sim 100$ MeV.
Consequently, the mass of the pion is $\sim$ 140 MeV while the mass of the kaon $\sim$
500 MeV. <cit.>].
As we will discuss in Section <ref>,

the difference in the $u,d$ and $s$ quarks
and hence in the pions and kaons affects significantly the properties of baryons of different flavor contents.

One of possible mechanisms of causing the non-trivial vacuum
is the instanton scenario <cit.>.
The instanton is a topological object of gluons as a classical solution of
the SU(3) color gauge theory.
The presence of such an object leads to the zero modes of quarks
that leads to the finite quark condensate as explained by the Banks-Casher
relation <cit.>.
The instanton also induces the $U_A(1)$ breaking interaction
for quarks <cit.>.
Such an interaction explains well the
$\eta$-$\eta^\prime$ mass difference <cit.>,
one of the phenomenological consequences of the $U_A(1)$ anomaly.
The interaction may be also effective for quarks in baryons.
However, the role of such an interaction for baryons is not fully explored.
We will discuss this issue in Section <ref>.

In view of the above discussions,  the constituent quarks and pions can be
building blocks of baryons.
The quarks are confined in
the “quark core" region with its radius smaller than $\sim$ 0.5 fm,
and the pion forms the “meson cloud" around it for baryons containing $u,d$ quarks
as illustrated in the left of Fig. <ref>.
The pion cloud may be suppressed when $s$ or heavy $c, b$ quarks replace the $u,d$ quarks inside the quark core.
The constituent quarks may interact each other by the effective interactions
due to the non-perturbative effect of QCD.

They may be modeled by a form of one gluon exchange (OGE), instanton induced (III),
and even meson exchange type interactions.
These interactions generate yet an important quasi-particle degrees of freedom
through their spin-dependent components, that is the diquark.

An attractive correlation is expected for flavor-anti-symmetric quark pairs of $ud$, $us$, $ds$, etc.
Due to its spin dependent nature the correlation is  strong for the above light quark
pairs, and weakened
for heavier quark pairs.
Though the diquarks are utilized in many discussions of hadron physics, their precise correlation nature is not yet established, which however will be an important
inputs for the physics of the hadronic matter.

Discussions on the spin dependent interactions are given in Section <ref>.
These interactions are primarily two-body, and

play the main role
when discussing the baryon spectroscopy.
It is noted, however, that three-body interactions are also possible
which is a further interesting subject of spectroscopy in this project.

§.§ What We Will Explore at $\pi20$ and K10

Based on the above general descriptions,
there are several important aspects in hadron physics.
First,  different favor combinations of  quarks with different masses would cause
non-trivial flavor dependent dynamics, although
the fundamental interaction of quarks and gluons are flavor blind.
The quarks are classified into light $u, d, s$ quarks and heavy
$c, b$ quarks as their masses are compared with the QCD scale parameter $\Lambda_{\rm QCD}$.
The position of the $s$ quark is a bit subtle, as it is not as light as the $u,d$ quarks and neither
as heavy as the $c$ quarks,
which causes interesting observations in hadrons containing

the $s$ quarks.

Second,  large spin-dependent forces exist.
This contrasts with, for example, atomic systems dictated by electromagnetic interaction.
As anticipated in the previous section,
the sufficiently attractive spin-spin forces cause
strong correlation in pairs of quarks, diquarks, in its spin and flavor anti-symmetric channels
in orbitally ground state that plays a crucial role not only
in spectroscopy but also in high density hadronic matter.
In the sufficiently high density region, the color super-conducting phase
is expected to be formed that governs various matter properties <cit.>.
For spectroscopy, we consider also internal structure of the diquarks with orbital excitation.

Different flavor combinations, in particular those of $u, d, s$ quarks
may results in different properties.
Strongly correlated diquarks are also considered to be important
for exotic hadrons of multiquark contents.
Hence the detailed knowledge of the spin dependent interaction for $u, d, s$ quarks
is a very important issue that can be studied at $\pi 20$ and K10.

Spin-orbit ($LS$) force is another issue in hadron spectroscopy.
In the light flavor sector the $LS$ force is suppressed
as indicated by the mass difference of the  nucleon excited states
$N(1535)$ of spin-parity $J^P = 1/2^-$ and $N(1520)$ of $3/2^-$.
In contrast, for the heavy baryon sector, as the pair of $\Lambda_c(2595)1/2^-$-$\Lambda_c(2625)3/2^-$ and
that of $\Lambda_b(5912)1/2^-$-$\Lambda_b(5920)3/2^-$ implies the importance of the $LS$ force.
The amounts of the splittings that decrease as the mass increases, as well as their ordering
for $1/2^-$ and $3/2^-$ states
seem to be consistent with what we expect from the OGE and III.
Because the spin-dependent force is one of the central issue of this project, we discuss it
in some detail in Section <ref>

Physics studies at $\pi 20$ and K10 can cover much part of the above issues.
The main object is the baryon spectroscopy.
Hence in Fig. <ref> we have shown baryons which we can study
at $\pi 20$ and K10 at J-PARC ($Qqq$ plot on the left panel) [
In fact, there are more baryons whose flavor contents are all different such as $usc$. ].
In the figure
the $s$ quark is shown to be  different from the $u,d$ quarks, although
it is classified as a light quark.
As shown in there,

at K10 we can study $\Xi$ and $\Omega$ baryons, while
at $\pi 20$ (singly) charmed baryons are studied.

Left: various $Qqq$ baryons indicating what we can study at $\pi 20$ and K10 at J-PARC.
Right: Character changes of the $\lambda$ and $\rho$ modes for $Qcc$, $Qss$ and $Qud$ baryons
as functions of the mass of the $Q$-quark, $m_Q$.

On the right panel of Fig. <ref> typical behavior of the two internal modes,
$\lambda$ and $\rho$ modes, of baryons are shown for the three cases, $Qcc$, $Qss$ and $Qud$.
Here the $\lambda$ mode is the relative motion between $Q$ and the other pair of quarks, and
the $\rho$ mode is the internal excitation of the pair of quarks.  The behaviors of the  $\lambda$ and $\rho$ modes are discussed  furthermore in the cases of $Qqq$ $(Qud)$ and $Qss$ in Sections <ref> and <ref>.
They show up in orbital excitations which generate large structure of energy levels.
Then fine structure due to the spin-dependent forces may follow.
The different combinations of quark flavors results in qualitatively different
behaviors of the excitation energies $\Delta E$ of the $\lambda$ and $\rho$ modes.
As discussed in some detail in the next subsections, for charmed baryons of such as $cud$
the $\lambda$ mode is lower than the $\rho$ mode, while for $\Xi$ baryons of such as $uss$
the ordering changes.
Such separation of the $\lambda$ and $\rho$ modes puts constraints in spin configurations of the diquarks,
which can be efficiently used to extract the information of spin-dependent forces.

In fact, this is the one of the main purposes of the $\pi 20$ project.
In K10 from the $\Xi$-spectroscopy we expect also to extract the properties
of the diquarks containing a strange quark, $su$ and $ds$ diquarks.

$\Omega$ baryons are unique in that all quarks are the same, $sss$.
The symmetry in flavor structure can impose constraints
in spin and orbital motion that suppresses some spin-dependent forces.
Furthermore, the $sss$ structure suppreses the pion cloud unlike
the protons and neutrons [
An intuitive picture, for instance, of the neutron which contains a virtual component of
the proton and negatively charged pion can explain consistently the negative charge radius
of the neutron <cit.>.].
Such a simplification of the $\Omega$ with suppression of spin-dependent forces and pion cloud
may enable us to access directly to the dynamics of the quark core region of baryons.

To summarize we will study charmed baryons, $\Lambda_c$ and $\Sigma_c$,
at $\pi 20$ and $\Xi$ and $\Omega$ baryons at K10.
Using the QCD effective theories and lattice simulations we
will establish a framework that explains
observed spectrum consistently from the light to heavy flavored hadrons.
The results will be useful not only for further studies of hadron spectroscopy
but also for other related fields, in particular for physics of high density hadronic matter.
In this way the $\pi 20$  and K10 will contribute to  the grand challenge of
the J-PARC extension project.

§.§.§ Spectroscopy of charmed baryons

Since the charm ($c$) quark is much heavier than $u$ and $d$ quarks,
in baryons with one $c$ quark, internal motions of $ud$ quarks can be distinguished from that of the $c$ quark.
One can find that the orbital excitation energy of a $ud$ pair to $c$  ($\lambda$ mode)
is lower than that between $u$ and $d$ ($\rho$ mode),
as shown in the bottom of the right panel of Fig. <ref>.
This is a kinematical effect under the confinement potential known as the isotope shift.
In addition, the spin-spin interaction with the heavy charm quark $c$ is suppressed,
as the color magnetic interaction between two quarks is proportional
to the inverse of the relevant quark masses.
The spin-singlet $ud$ state is of particular interest since its interaction is attractive.
Hence, the $ud$ diquark correlation is developed.
Therefore, baryons with a charm quark provide a good opportunity to study the $ud$ diquark correlation.
We also expect to decompose the origin of the quark interactions by
analyzing the high statistics data in terms of QCD based effective theories.

Concerning the $U_A(1)$ anomaly, an interesting scenario was proposed in Ref. <cit.>
where the $\lambda$-$\rho$ inversion was pointed out
for the negative parity $\Xi_c$ baryons
($\Xi_c(\rho)$ is lighter than $\Xi_c(\lambda)$).
For this inversion mechanism, the $0^- (^3P_0)$ $us$ (or $ds$) diquark plays an essential role.
The corresponding $ud$ $0^-$ diquark forms a $\rho$-mode $\Lambda_c$ baryon of
$J^P = 1/2^-$.
This state has a unique feature that the decay into $\pi \Sigma_c$ is forbidden
due to the selection rule associated with the conservation of spin and parity <cit.>.
If so, there is a good chance to observe such a $\Lambda_c$ state because of
its narrow width [
Mixing with different states might cause a narrow decay width.].

Comparison of $\Lambda_c$ baryon masses from experiments <cit.>,
lattice simulations <cit.> and non-relativistic quark model <cit.>.
Orange shaded is the region of orbital excitations by the quark model.

In Fig. <ref> masses of $\Lambda_c$ charmed baryons are shown and compared among
those of  experiments,
lattice simulations <cit.> and non-relativistic quark model <cit.>.

The quark model calculations show the lower excited states corresponding to the $\lambda$ modes
expected by the kinematical effect.
Then, large splitting between the $\lambda$ and $\rho$ modes is expected to appear,
which makes a major structure in the mass spectrum.
However, identification of higher lying states of various spins and parities is not clear,
except for the first negative parity pair of $1/2^-, 3/2^-$, though the quark model
does not reproduce sufficient $LS$ splitting (see the discussion below).
To fill these gaps is the primary goal of the study of charmed baryon spectroscopy.

We have proposed charmed baryon spectroscopy at the J-PARC high-momentum beam line ($\pi$20), as approved as E50 <cit.>.
To produce charmed baryons,
missing-mass technique is employed via the $\pi^-p\rightarrow D^{*-}Y_c^{*+}$ reaction, where $Y_c^{*+}$ represent excited charmed baryons with a $c$ quark. A series of the $Y_c^{*+}$ states will be observed in the missing mass spectrum, as shown in Fig. <ref> in Section <ref>. The production rates of the excited states are expected to depend on their internal configurations of spins and orbital angular momenta (parity).
In the $\pi^-p\rightarrow D^{*-}Y_c^{*+}$ reaction, a $u$ quark in the proton is converted into a $c$ quark in the charmed baryon $Y_c^{*+}$,
that we call one quark process here, is expected to
takes place dominantly <cit.>. In the one quark process,
the angular momentum will be introduced between $c$ and $ud$,
as shown in Fig. <ref> (a).
Thus, the $\lambda$-mode excited states are favored to be populated
in the one quark process.
The reaction cross section is estimated by calculating the so-called sticking probability of $c$ to $ud$, written as

\propto\left(q/\alpha\right)^{2L}\exp{(-q^2/\alpha^2)},$$

where $\varphi_{i(f)}$, $L$, $q$, and $\alpha$ represent an initial $u$ (a final $c$) wave function,
the angular momentum introduced in the charmed baryons, the momentum transfer
of the reaction, and a typical size parameter of baryon ($\sim$0.4 GeV/$c$), respectively.
Here, $\sigma_-$ is a spin operator required in the case of a vector meson exchange in the reaction.
In the right-hand side of the above equation, the wave functions of the initial and final states for harmonic oscillator potential are employed for analytic calculations.
Since the reaction involves a large momentum transfer of $q\sim$1.4 GeV/$c$,
the sticking probability, thus the cross section, becomes very small due to
the exponential factor.
On the other hand, taking the ratio of the cross section of the excited state with $L$ to that of the ground state, the exponential factor is almost cancelled, and the ratio do not go down owing to the factor of $\left(q/\alpha\right)^{2L}$.
The intense pion beam provided by the $\pi$20 beam line compensates the small cross sections.
In the end, relatively high possibility to populate the higher excited states with a finite $L$ is rather advantageous.

We expect two-quark involved process, as shown in the right panel of
Fig <ref> (b) <cit.>.
In the two-quark process, the momentum transfer will be shared by $c$ and $u$ or $d$ in the final baryon.
Then, both $\lambda$- and $\rho$-mode states are populated.
Though the magnitude of the two-quark process is of interest to understand
the reaction mechanism,
the production ratio of $\Lambda$ to $\Sigma$, which is about 2 to 1 <cit.>,
may give a good reference for the ratio of the one-quark process to
the two-quark one, which is to be about 5 to 1 in charm sector.
We expect to populate finite magnitude of the $\rho$-mode states as well.

Reaction diagrams of the $\pi^-p\rightarrow D^{*-}Y_c^{*+}$ reaction.
(a) one-quark process: a meson with a (3-)momentum transfer of $\boldsymbol{q}$ is exchanged in the $t$ channel.
The meson is coupled to $u$ in the proton and $c$ in the charmed baryon and
introduces an angular momentum $L$ between $ud$ and $c$.
(b) two-quark process: after the meson exchange, introduced $L$ is shared among 3 quarks in the final state.

As an example, let us consider
$\Lambda_c(2625)$ and $\Lambda_c(2595)$ states, which are well established as 3 stars in PDG rating. Their spin-parities are assigned as 3/2$^-$ and 1/2$^-$ as they are believed to be so-called $LS$ partners with having an orbital angular momentum of $L=1$ between $c$ and $ud$ and the $ud$ spin-parity of 0$^+$ with isospin 0 (flavor anti-symmetric state). The production rates of
$\Lambda_c(2625)$ and $\Lambda_c(2595)$ should be $L+1:L=2:1$, respectively <cit.>. By measuring the production rates, we could determine their spin-parities and settled that they are indeed the $LS$ partners of the $\lambda$ mode with having a spin-singlet $ud$ state.

The theoretical calculation suggests good separation of the $\lambda$ and $\rho$ modes in $\Lambda_c$ <cit.>.
We will be able to confirm it by measuring the production ratios of the spin doublets in the expected $\lambda$-mode excited states, which are  described by the relative motion of a $c$ quark to the $ud$ diquark. As we discussed above, the production cross section is described by the overlap integral of the initial ($p$) and final ($\Lambda_c$) wave functions at the momentum transfer ($q$) of the relevant reaction. Thus, the total cross sections of the $\lambda$-mode states with having different orbital angular momenta $L$'s would provide detailed information on the
motion of the $ud$ diquark.

The $\rho$-mode states have not yet been identified clearly. As we discussed above, the $\Lambda_c$ state of $J^P=1/2^-$ having $ud$ diquark of $0^-$ is a good target to observe. Its mass and width provide how the $U_A(1)$ anomaly works in baryons <cit.>.

The decay branching ratios also carry information on internal motions of $ud$ quarks.

In particular, the $\lambda$ mode excitation with the $ud$ diquark, is expected to favor a decay into a $D$ meson and a nucleon ($N$) compared with decays into a pion and a low-lying charmed baryon ($Y_c^{*\prime}$) if the decay channel is open.
We will measure their decay branching ratios (decay partial widths) by detecting decay particles in coincidence with $Y_c^{*+}$ produced by the $\pi^-p\rightarrow D^{*-}Y_c^{*-}$ reactions.

Once $\lambda$-mode is confirmed for a $\Lambda_c^*$ baryon in the production process,
we expect that the decay partial width of the $\Lambda_c^*\rightarrow D^0p$ process would tell us how the $ud$-diquark correlation is formed firmly in the $\Lambda_c^*$.
Moreover, considering a similar quark line structure for the vertices of the decay and production reaction
such as $\Lambda_c^*\leftrightarrow D^0p$, one would expect that the production and decay rates
are related by the transition form factor of different momenta, $\vec q$ and $\vec q^\prime$, entering the vertices,
as shown in Fig. <ref>.
We could investigate the wave functions of the $\lambda$-mode $\Lambda_c^*$ state in the production and decay processes at a large and small transfer momenta, respectively.

Similar vertex structures appearing in the production and decay reactions.

§.§.§ Spectroscopy of $\Xi$ baryons

The high intensity kaon beam produces abundantly $\Xi$ baryons from the ground state
up to 1-GeV excitations and even higher, as demonstrated in Fig. <ref> in Section <ref>.
Currently ten excited states are listed in PDG <cit.>,
while only two states are known with established spin and parity.
In Fig. <ref>, states of masses lower than 2.1 GeV are plotted,
where $\Xi(1530)$ is rated as four-star, $\Xi(1620)$ one-star, and the others three-star.
In comparison with the lattice and quark model  results, the nature of the observed states
is  uncertain.
However, as shown in Fig. <ref>,
the $\rho$ mode, the relative motion of the two strange quarks, is expected to be lowered
which can be used efficiently for the study of $\Xi$ baryons [
For $\Xi$ baryons of $uss$ or $dss$ content, the $\lambda$ mode is defined
to be the relative motion between the $ss$ pair and $u$ (or $d$) quark, and
the $\rho$ mode the relative motion between the two $ss$ quarks as shown in the left of
Fig. <ref>.].
Furthermore, from the production experimental point of view,
two light quarks in the protons are to be converted to two strange quarks
in $\Xi^*$; namely, a two quark-process is needed unlike the singly charmed baryon productions
where only one light quark is converted into the charm quark.
The two-quark process

can populate both $\rho$ and $\lambda$ modes, as illustrated in Fig. <ref>.

Comparison of $\Xi$ baryon masses from experiments <cit.>,
lattice simulations <cit.> and non-relativistic quark model <cit.>.
Orange shaded is the region of orbital excitations by the quark model.

Reaction diagrams of the $K^-p\rightarrow K^{*0}\Xi^{*0}$ reaction.
The two quarks are involved in the $u$-channel reaction, and angular momenta between two $s$ quarks and $s$ and $u$ are introduced in the final state.

Now, following the quark model we would expect the lowest excitation
is the $P$-wave excitation of the $\rho$ mode.
Due to the Pauli principle, the spin of the $ss$ pair is zero and hence
the total spin of the $\Xi$ is expected to form a spin doublet
$J^P = 1/2^-, 3/2^-$ together with the spin 1/2
of the other $u$ or $d$ quark.
However, the current experimental data indicates only the state of $3/2^-$.
There must be the other partner of $1/2^-$.

Its location is expected to be close to the $3/2^-$ state if we naively apply the empirical
fact of the small $LS$ force from the nucleon excitations, for instance
$N(1520)$ of $3/2^-$ and $N(1535)$ of $1/2^-$.

In the lowest $\rho$-mode excitations, the $ss$ pair carries the orbital angular momentum of 1,
and the spin of the $ss$ pair is 0 because of the Pauli principle.
In this case, the two-body $LS$ force vanishes, and thus does not contribute to the energy splitting between the doublet states (Fig. <ref>(a)).
Naively, one would expect the widths for the $1/2^-$ state is wider than that of the $3/2^-$ state, when we consider
their decays into a $J^P=0^-$ meson and a $1/2^-$ baryon because of the partial wave nature of the decaying particles.
Experimentally the overlapping two peaks could be identified with sufficient statistics.
This would be true if the $s$ quark is very heavy when the $us$ or $ds$ diquark correlation is neglected.
In reality with a finite $s$ quark mass
the spin-antisymmetric $us$ (or $ds$) diquark may become non-negligibly correlated,
the $LS$ splitting may be finite through $\lambda^\prime$ orbital excitation,
as shown in Fig. <ref>(b).
Here, the relation between the two Jacobi coordinates is employed as

\begin{pmatrix}
\lambda\\
\rho\\
\end{pmatrix}
\begin{pmatrix}
\sqrt{3}/2&1/2\\
\end{pmatrix}
\begin{pmatrix}
\lambda^\prime\\
\rho^\prime
\end{pmatrix}.

$\rho$-mode excited state of $\Xi$ ($P$-wave). (a) In the case of weakly-correlated $sq$ ($q=u, d$), the orbital angular momentum of 1 is carried between the spin-antisymmetric $ss$ pair and hence it does not contribute to the $LS$ splitting. (b) In the case of strongly-correlated $sq$, the orbital angular momentum of 1 is partly carried between the correlated $sq$ and the other $s$, and thus the finite $LS$ splitting is expected.

As discussed in Section <ref>, the $LS$ splitting depends on the masses of the quarks and hence
the location of the $1/2^-$ state carries important information on the nature or the origin
of the $LS$ force.
Furthermore, the decay widths carries dynamical information of excitations.
The width of the $1/2^-$ state would be wide
if it belongs to the flavor octet <cit.>.
This could be the reason that the state has not been yet recognized.

The identification of the $1/2^-$ state is one of the important issue.
The problem of the missing $1/2^-$ state exists also in the $\Omega$ baryons,
where we will come back to the problem in more detail.

Not only the interests in the spectroscopy, the $\Xi$ baryons can provides a platform
for the study of diquark correlations of the $ds$ and $su$ diquarks.
The ground state splitting between the octet and decuplet $\Xi$'s already carries
much information.
In addition, the $\rho$ mode excitation of the $ss$ pair leaves the relative motion between
the $s$ and $u$ (or $d$) quarks in $S$-wave,
from which we study some detailed properties of the diquark correlation.

To summarize shortly, we will study masses and widths of various $\Xi$ baryons with the determination of
spins and parities.
How the spin and parity are determined is discussed in Section <ref>.
Moreover, high lying $\Xi$ excited states such as $\Xi(2370)$ or higher will be used as
a doorway to produce $\Omega$ baryons [
There is a report that $\Xi(2370)$  has a significant amount of branching ratio of $9\%\pm4$%
decaying into $\Omega\;\bar{K}$ <cit.>.].

§.§.§ Spectroscopy of $\Omega$ baryons

The $\Omega$ baryon is a system of three strange quarks, $sss$.

In flavor SU(3) symmetry group it is assigned as a member of the decuplet representation,
which was realized by the quark model whose building blocks are the $u, d$ and $s$ quarks.

Historically nine short-lived baryons of the spin $3/2^+$ were known, four $\Delta$'s, three $\Sigma^*$'s and
two $\Xi$'s fitting into the decuplet members, and the last piece $\Omega$ was predicted
in the quark model <cit.>.
The confirmation of $\Omega^-$ particle  in
1964 <cit.>

supported the validity of the quark model
based on the SU(3) flavor symmetry.

In reality, the SU(3) symmetry is broken by the mass of the $s$ quark, which is heavier
than the almost equal masses of $u, d$ quarks.
The pattern of SU(3) breaking could predict the mass of $\Omega$ under the equal mass spacing
between the decuplet members.
The broken SU(3) also leads to the obvious mass difference of the pion ($m_\pi \sim 140$ MeV)
and kaon ($m_K \sim 500$ MeV).
This difference together with the singly flavored nature leads to the unique features of the $\Omega$ baryons.

Comparison of $\Omega$ baryon masses from experiments <cit.>,
lattice simulations <cit.> and non-relativistic quark model <cit.>.
Orange shaded is the region of orbital excitations by the quark model.

The current status $\Omega$ baryon spectroscopy is shown in Fig. <ref>.
Indeed the experimental status is poor, and so it is not yet the stage of comparison between data and theory.
Nevertheless, we would like to discuss the $\Omega$ spectroscopy in some detail.
First the $sss$ combination put some restrictions on the wave function due to the Pauli's exclusion principle.
For example, the fact that spin of the ground state $\Omega$ is 3/2 rather than 1/2 is precisely from that requirement.
Similar restrictions apply to excited states.
Some consequences from the restrictions may manifest in the fine structures of excited states.
This will be discussed in Section <ref>(A).

Second is associated with the heavier mass of the kaon than that of the pion.
In fact, the pion is very light as it is the NG boson, and therefore, it in many cases
plays a role of radiation like a photon with the axial-vector nature.

On the other hand, the kaon when coupled to excited states, it plays not only
a role of radiation but also a role of a constituent forming hadronic molecule.
This could be the reason that the $\Lambda(1405)$ can develop the molecular
structure of $\bar K N$.
A similar situation may occur in excited states of $\Omega$'s, which is also
the subject in Section <ref>(B).

Third, the $\Omega$ baryons do not couple to the pion due to isospin symmetry.
Therefore, without the meson cloud which exists in the light baryon structure,
we may be able to directly access to the quark core region of the baryons.
Furthermore, we may expect that an $\Omega$ baryon is
smaller in spatial extension as compared to the light flavored baryons
which is surrounded by meson cloud.
We will discuss a related topic in Section <ref>(C).
A possible experimental study to access baryon size from scattering cross sections is discussed in Section <ref>.

§.§.§ (A) 1$P$ states – quark orbital excitation

The confined constituent quarks can be excited orbitally.
The lowest excited state is expected to be in $P$-wave with an orbital angular momentum $L = 1$.
In the spin-flavor SU(6) classification they form the 70-dimensional representation
that are decomposed into spin-flavor multiplets $^{2S+1}{\bf N} = \ ^2 8, ^2 10, ^4 8$ and $^2 1$.
Here $S$ is the total intrinsic spin of the three quarks,
$S = 1/2, 3/2$, and ${\bf N}$ the dimension of the flavor representation.
Among them, $^2 8$ and $^4 8$ are assigned to $N$,
$\Lambda$, $\Sigma$ and $\Xi$ baryons,
and $^2 1$ to $\Lambda(1405)$ and $\Lambda(1520)$.
Then the $^2 10$ representation includes the $P$-wave $\Omega$
together with $\Delta, \Sigma$ and $\Xi$ excited states.
Because of their intrinsic spin $S=1/2$, they form the spin doublet,
$J = S + L = 1/2, 3/2$, and their parity is negative due to the $P$-wave.
It is emphasized that in the standard picture, there must be
$2S+1$ or $2L+1$ fold degeneracies depending on whether  $S < L$ or $S > L$, respectively.

The $\Omega(2012)$ which has been recently reported from Belle is a candidate of
one of the multiples <cit.>.
The mass 2012 MeV is about 500 MeV above the expected ground state when possible spin-spin interaction contribution is removed.
Therefore, the state is expected to be one of doublets of $^2 10$.
Its decay width is as narrow as $6.4^{+2.5}_{-2.0} \pm1.6$ MeV.
The decay $\Omega(2012) \to \Xi \bar K $ was studied in the quark model,
resulted in a decay width about 12 MeV for $J^P = 1/2^-$ and about 6 MeV for $J^P = 3/2^-$.
The width of the $J^P = 3/2^-$ state is narrower due to its $D$-wave nature of the decaying
two-body channel in the final state.
Therefore, the quark model seems to prefer $3/2^-$ state.

Assuming a two-body $LS$ interaction, we need both $L = 1$ and $S = 1$,
where $L$ and $S$ are the orbital angular momentum and spin of an $ss$ pair.
However, such a combination is not allowed due to the Pauli principle,
when spin, flavor,  orbital and color wave functions are combined.
Therefore, we expect that the $LS$ splitting of $1/2^-$ and $3/2^-$ is suppressed
for these $\Omega$ states.

As explained in Section <ref>
the two-body spin-orbit interaction is derived from the OGE and III interactions.
In many cases they contribute with opposite signs, while in others
only the OGE survive due to flavor anti-symmetric nature of III and its suppression
for heavy quarks systems.
Such relations are summarized in Table <ref> for various baryon states,
where expectation not only for $P$-wave but also for $D$-wave excitations,
where in the latter the OGE from the III may exclusively contribute to the $\Omega$'s.
In Ref. <cit.>, a phenomenological $LS$ interaction was introduced
resulting in significant splittings.
One possible origin of such an interaction would be three-body nature.
The clarification of the $LS$ splitting is crucial to the systematic understanding
for the baryon spectroscopy.

Expected contributions of $LS$ interaction to various baryons.
In the second line $P$ and $D$ denote the total orbital angular momentum of quarks
inside baryons.
Positive values $A$ and $B$ represent matrix elements of the $LS$ interaction
which depend on baryon states, and their
computations were performed, for instance, in Ref. <cit.>.
The symbol “?" indicates that there is no experimental data.

2c$N^*$    2c$\Lambda^*$     2c$\Lambda^*_c$

Orbit     $P$     $D$     $P$     $D$     $P$     $D$     $P$     $D$

OGE     –     $+A$     $+A$     $+A$     $+A$     $+A$     $+A$     $+A$

III          –     –         $-B$     $-B$     $-B$     $-B$     –     –

Sum     0     $+A$     $\sim 0$     $\sim 0$     small     small     $+A$     $+A$

Exp (MeV)      ?     ?     $\sim 0$     $\sim 0$     36     ?     34     ?

§.§.§ (B) 1$P$ states – moleculars

Another interpretation has been proposed for $\Omega(2012)$;
since its mass is located approximately 10 MeV below the $\Xi^*\bar{K}$ threshold, it could be a $\Xi^*\bar{K}$ molecular state <cit.>.
The formation of such a molecular state is expected near the threshold region of two or more
particles with some heavy mass.
The $\Xi^*$ and $\bar{K}$ would be such.
Though the kaon is heavier than the pion, it also shares the properties of the
NG boson when the chiral interaction is effective.
In this regards, the system shows an interesting feature;
the direct interaction for $\Xi^*\bar{K}$ is absent, but the offdiagonal interaction to the coupling
to $\Omega\eta$  with higher mass can drive an attraction.
The decay width was also estimated by chiral counting, expecting values consistent with
the data <cit.>.
The mechanism itself is interesting, and deserves study.
A caveat in this picture is that $1/2^-$ state is not easy to be explained.

To establish the nature of $\Omega(2012)$ is an urgent issue in the present project.
The determination of basic properties of such as spin and parity, decay width, and also a search of spin partner provides an important information to explore the $\Omega$ spectroscopy.

§.§.§ (C) 2$S$ states, physics of the Roper-like states

Baryon resonances possessing the same spin-parity as that of the ground states are of special interest.
By now many such states are observed in a wide range of flavor contents;
$N(1440) 1/2^+$, $\Lambda(1600) 1/2^+$, $\Sigma(1660) 1/2^+$, $\Delta(1600) 3/2^+$ and $\Xi_c(2970) 1/2^+$.
The nucleon resonance $N(1440)$ has been known for long time as the Roper resonance, while $\Xi_c(2970)$ has been established only recently <cit.>.
Furthermore, $\Lambda_c(2765)$
and newly found $\Lambda_b(6072)$ <cit.> are also expected to be their siblings.
Interestingly all of their masses are about 500 MeV above their corresponding ground states
as shown clearly in Fig. <ref>.

In the nucleon sector the problem has been known as too low mass of the Roper resonance.
In the quark model the $1/2^+$ state is realized as a radial (nodal) excitation
whose mass appears at around 1800 MeV which is obviously too high
as compared to the observed one of 1440 MeV.
Related to this the quark model predicts the wrong mass ordering;
the Roper resonance appears higher than the negative parity state,
for instance $N(1535) 1/2^-$. A lowering mechanism has been proposed
due to the meson cloud around the quark core of $u$, $d$ quarks <cit.>.
Turning to the heavy quark sector, due to the lowering of the $\lambda$-mode,
the observed states of positive and negative parities appear
as in the expected order with their mass values qualitatively
consistent with the quark model predictions.
Thus another option to explain the equal excitation masses is
flavor dependent mechanism so as to cancel the natural flavor dependence
in the quark model.
These two interpretations for the Roper resonance and siblings must be converged.

To answer this question, information of $\Xi$ and $\Omega$ resonances are useful.
The mass of the strange quark is between those of light and heavy quarks, and therefore more strange baryons interpolate the light and heavy flavor dynamics, filling the missing link between the two.
As anticipated, with the suppression of the meson cloud
the $\Omega$ baryons provide an ideal platform to extract the dynamics of the constituent quarks.
This is particularly expected in the study of various transitions such
as radiative decays $\Omega^* \to \Omega \gamma$ and
kaon decays $\Omega^* \to \Xi \bar K$ since the decay rates are sensitive to the forms of the wave functions.

The decay of the Roper-like state through one kaon emission
$\Omega^* \to \Xi \bar K$ may contain interesting  physics.
The decay occurs by the chiral interaction between the NG kaon and quarks,

\begin{eqnarray}
{\cal L}_{\phi qq} = \frac{g_A^q}{f_\pi} \
\bar q \gamma_\mu \gamma_5 \lambda_a q \ \partial^\mu\phi^a
\end{eqnarray}

where $\phi^a$ is the flavor SU(3) NG boson field and
$g_A^q \sim 1$ <cit.>  the axial coupling constant of the quark.
In the previous publications, the Lagrangian was expanded non-relativistically and
took up to the first order in the velocity $v \sim p/m$ of the quarks
where $p$ is the momentum of a quark inside the baryon,

\begin{eqnarray}
{\cal L}_{\pi qq} \sim  \ \frac{g_A^q}{f_\pi}
\left( \vec \sigma \cdot \vec q
+ \frac{\omega_\pi}{2m_q}(\vec \sigma\cdot \vec q - 2 \vec \sigma \cdot \vec p)
\right)
\end{eqnarray}

The problem of the truncation up to this order is in the fact that
the leading term of order $v^0$ vanishes exactly due to the operator structure of
$\vec \sigma \cdot \vec q$ where $\vec q$ is the momentum carried by the kaon,
and the orthogonality between the wave functions of the radially excited and ground states
in the long wave length limit.
Such a kind of forbidden process was originally pointed out in the
radiative decay of the nucleon Roper resonance <cit.>.
The next to leading order term of $v^1$ also turns out to be small.
Actual computation shows that these terms (and similar studies)
predicted only small decay widths
which contradicts the observed data <cit.>.

Thus next-next to leading order term of $v^2$ is important.

\begin{eqnarray}
{\cal L} \sim \frac{g_A^q}{f_\pi}
\left(
\frac{m_\pi^2}{8m_q^2}\vec \sigma \cdot \vec q +
\frac{1}{4m_q^2}
\vec \sigma\cdot (\vec q - 2 {\vec p}) \times
(\vec q \times {\vec p})
\right)
\end{eqnarray}

The second term is the dominant term which results in the transition matrix element
as proportional to $\langle p^2 \rangle \sim 1/ \langle r^2 \rangle$,
which survives in the long-wave length limit with no forbidden selection rule applies.
Physically, we can interpret that the transition rate is dictated by the Fermi motion of the confined quarks
and hence the inversely proportional to the size of the quark core of baryons.
It was shown that such higher order term
contributed significantly to the decay width of the heavy baryons
and improved the agreement with the data <cit.>.
A preliminary calculation show the decay width of the Roper-like $\Omega$
is around 100 MeV after the inclusion of the $v^2$ contributions, while the terms
of order $v^0$ and $v^1$ give only around 20 MeV.
The small value in the lower order terms is qualitatively consistent with the previous studies.

After discussing this much about the Roper-like $\Omega$, it is very important to observe
the state and to measure the width.
The width is interesting in that it carries the information of the internal motion of
constituent quarks in the core region which is related to the size of that region.

§.§ High-Momentum Secondary Beam Line — $\pi$20

Since early 2020, the High-p beam line (B line) has been operated for an experimental study on spectral changes of light vector mesons in nuclei, E16, with a primary beam branched from the existing slow-extraction beam line (A line).

As we have discussed, baryon spectroscopy with various flavors is vital to reveal the non-trivial flavor dependent dynamics in baryons. The charmed baryon spectroscopy is important and closely related to the spectroscopy of multi-strangeness baryons, $\Xi$'s and $\Omega$'s at K10, as we review characteristic natures of baryons with a charm quark and those with two strange quarks in Sections <ref>, <ref>, and <ref> as well as Sections <ref> and <ref>.
We have already proposed a spectroscopic study of charmed baryons (E50) <cit.> and received a stage-1 approval. E50 needs a high-intensity pion beam at 20 GeV$/c$ at the $\pi$20 beam line.

The B line is designed so that the secondary beams produced at the branching point in the A line can be transported without major modification of the beam-line configuration (Fig. <ref>), except that the most upstream part around the primary target and additional structure/equipment required for radiation safety have yet to be provided.
The beam envelope calculated by the TRANSPORT code <cit.> is shown in Fig. <ref>.
The secondary beam with a negative charge produced at zero degree at the production target is departed from the primary beam course (A line) to the $\pi20$ beam line by using the so-called beam swinger optics <cit.>, as illustrated in Fig. <ref>.
For a negative secondary beam, the primary beam trajectory is swung by two dipole magnets (h07 and bs0A) to the left hand side before the target and swung back by another two dipole magnets (bs0B and h13) to the A line after the target. The layout is optimized so that the negative secondary beam of 20 GeV/$c$ produced at zero degree is extracted to the $\pi20$ beam line.

The secondary beam is collected by the first doublet of quadrupole magnets in the $\pi20$ beam line and focused at a collimator placed 50 m downstream from the production target to define the beam image at the production target. After the collimator, the beam is focused again at the dispersive focal plane with a large dispersion of 1.170 %/cm.
Here, 4 sextupole magnets are employed to eliminate/minimize major geometric and chromatic aberrations to the second order.
A correlation of horizontal position ($x$) to momentum (dispersion $dp/p$(%)) of beam particles at the dispersive focal plane is calcualted by TURTLE <cit.>, as shown in Fig. <ref>. The figure demonstrates that a momentum resolution as good as 0.1% can be realized with a spatial resolution of 1 mm for a beam particle.
A beam profile estimated by TURTLE at the experimental target is shown in Fig. <ref>.
Figure <ref> shows expected intensities of negative pions, kaons, and antiprotons per spill (5.2-second spill cycle) as functions of their momenta in the case of 30-kW primary protons on a 60-mm-long Platinum target (15-kW loss) estimated by Sangford and Wang's formula <cit.>.

At the present hadron experimental facility, no secondary charged beams greater than 2 GeV/$c$ are available. The upgrade of the B line to utilize high-momentum secondary beams is strongly desired.

Plan view of the $\pi20$ beam line (top) and schematic illustration of the beam line configuration (bottom).

Beam envelope calculated by the TRANSPORT beam optics code to the second order for the $\pi20$ beam line.

Proposed layout at the production target for the $\pi20$ beam line. For a negative secondary beam, the primary beam trajectory is swung by two dipole magnets (h07 and bs0A) to the left hand side before the target and swung back by another two dipole magnets (bs0B and h13) to the A line after the target. The layout is optimized so that the negative secondary beam of 20 GeV/$c$ produced at zero degree is extracted to the $\pi20$ beam line. This is the so-called beam swinger optics <cit.>.

Correlation of horizontal position ($x$) to momentum (dispersion $dp/p(\%)$ of beam particles at the dispersive focal plane.

Beam profile estimated by TURTLE at the experimental target.

Expected intensities of negative pions, kaons, and antiprotons per spill (5.2-second spill cycle) as functions of their momenta in the case of 30-kW primary protons on a 60-mm-long Platinum target (15-kW loss) estimated by Sangford and Wang's formula <cit.>.

§.§ Conceptual Design for the K10 Beam Line

High-intensity high-momentum negative kaon beam with high purity
is a crucial ingredient for the proposed experiment. Therefore, the K10 beam line under discussion in the project "Hadron hall extension" is the only place where the proposed experiment can be performed.

Two options are under consideration for the particle separation at
the K10 beam line;
an ordinary electrostatic (ES)-separator option and an RF-separator option.
The ES-separator option can be applied up to $4 \sim 6$ GeV/$c$.
In contrast, the RF-separator option is suitable for higher momentum.
By making a common design at the front-end section
of both options of the beam line,
we can switch the separation method without accessing the high-radiation area.
The production angle of secondary beams is chosen to be 3 degrees,
which is smaller than those of the K1.8 and K1.1 beam lines,
because the production cross-sections of $K^-$ and $\bar{p}$
at 3 degrees are about five times larger than those at 6 degrees,
according to the empirical formula by Sanford and Wang<cit.>.

Since the separation by an ordinary ES separator is proportional to $1/p^3$,
the separation is much difficult for the momentum higher than
4 GeV/$c$ ($K^-$) or 6 GeV/$c$ ($\bar{p}$).
Therefore, we need RF separators to handle such a high-momentum region, which is essential for the proposed experiment.

The principle of the particle separation using two RF cavities.

The principle of the particle separation by using RF cavities
is schematically shown in Fig.<ref>.
In this method, two RF cavities (RF1 and RF2) are located in the beam line,
and the optics between the two cavities are set so that
the transport matrix is equal to “$-I$”.
If the RF amplitude of the two cavities are the same,
the sum of the beam deflection from the two cavities is

\begin{eqnarray}
D &=& -A \sin\left(\omega t\right) + A \sin\left(\omega t + \Delta \phi\right) \\
&=& 2A \sin\frac{\Delta \phi}{2} \cos\left(\omega t + \frac{\Delta \phi}{2}\right),
\end{eqnarray}

where $\omega t$ is the phase at the first cavity,
and $\Delta \phi$ the phase difference between the two cavities.
The minus sign in the first line comes from the “$-I$” optics
between the two cavities.
The amplitude $A$ is given by

\begin{equation}
A = \frac{eEl}{pc\beta},
\end{equation}

where $e$, $p$, and $\beta$ are the charge, momentum, and velocity
of the particle, respectively, and $E$ and $l$ denote
the field gradient and the effective length of the cavity, respectively.
When the phase at the second cavity is set to be same as
that of the first cavity for an unwanted particle, namely $\pi$,
the deflection of the particle is canceled
in whichever phase it passes the first cavity,
and it is absorbed with a central stopper downstream.
On the other hand, the phase of the second cavity for particles
with the other mass and velocity ($K^-$ or $\bar{p}$) differs by

\begin{eqnarray}
\Delta \phi^u_w &=& \frac{2 \pi f L}{c}\left(\frac{1}{\beta_w} - \frac{1}{\beta_u}\right) \\
&\sim& \frac{\pi f L}{c} \frac{m^2_w - m^2_u}{p^2 c^2},
\end{eqnarray}

they are deflected by $2 A \sin \frac{\Delta \phi^u_w}{2}$ in maximum
depending on the phase at the first cavity,
and pass outside of the central stopper.
Here, $f$ is the RF frequency, $L$ the distance between the two cavities,
$p$ the momentum, and $\beta_w$/$\beta_u$ and $m_w$/$m_u$ are
the velocities and masses of the wanted/unwanted particles, respectively.

Momentum dependence of the deflection amplitude
for $K^-$ (blue) and $\bar{p}$ (red) in the case that
the RF phase of the two cavities are same for $\pi^-$.
Since the deflection for $\pi^-$ is always canceled,
usable is the momentum region in which
the deflection for $K^-$ or $\bar{p}$ is large.

For example, assuming $\pi^-$ as an unwanted particle,
the momentum dependence of the deflection amplitude for $K^-$ and $\bar{p}$
in the case of $f = 2.857$ GHz and $L = 16.8$ m is plotted
in Fig.<ref>.
The deflection for the wanted particle is also canceled
in the momentum range corresponding to

\begin{equation}
\Delta \phi^u_w = 2 n \pi \,\,\, (n = 1, 2, 3, ...),
\end{equation}

whereas the deflection get maximum in the range satisfying

\begin{equation}
\Delta \phi^u_w = (2 n - 1) \pi \,\,\, (n = 1, 2, 3, ...).
\end{equation}

Another operation mode can be considered where
the phase of the second cavity is tuned to be same as that of the first cavity
for a wanted particle ($K^-$ or $\bar{p}$).
Then the deflection of the wanted particle is always canceled,
while the unwanted particle ($\pi^-$) is deflected
depending on the phase difference and is eliminated with a slit.

Layout of the RF option of the K10 beam line.

First-order beam envelope of the RF option of the K10 beam line.The upper and lower show the vertical and horizontal directions, respectively. The dash line indicate the horizontal dispersion.

The layout of the RF-separator option of the K10 beam line is
presented in Fig.<ref>, and
the beam envelope calculated with the TRANSPORT code<cit.>
is shown in Fig.<ref>.

The total length of the beam line is $80.7 \sim 81.2$ m
depending on the configuration of the beam spectrometer.
The RF frequency and the distance between the cavities are
set to 2.857 GHz and 16.8 m, respectively.
The effective length of the cavities is 2.25 m.

The beam line consists of three sections; the front-end section,
the separation section, and the analyzing section.
In the front-end section, secondary beams generated at the production target
are extracted from the primary beam line,
and focused vertically at the intermediate (IF) slit
to reduce so-called “cloud $\pi$”.
The optics are also tuned to make beams almost achromatic at the IF slit.
In the separation section, the optics is tuned to obtain
a parallel and narrow beam at the RF cavity, and
the transport matrix of “$-I$” is realized between the cavities
by using four quadrupoles with same field gradient.
After analyzed with a beam spectrometer,
the beam is focused to an experimental target
both in horizontal and vertical directions.

As for the beam spectrometer, we have two types of the configuration.
Type I consists of two dipole magnets and three quadrupoles
with the order of QDDQQ, as shown in Fig. <ref>.
In the transport matrix of the section from VO to VI,
the condition of the point-to-point focus is satisfied
in the horizontal direction ($R_{12}=0$),
and the magnification ($R_{11}$) and the dispersion ($R_{16}$)
are $-1.627$ and $-0.635$ cm/%, respectively.
By assuming the position resolution of tracking devices located at VO and VI
is $\sigma_x = 300$ $\mu$m, the expected momentum resolution is
$\sigma_p = \frac{\sqrt{1+R_{11}^2}}{|R_{16}|} \sigma_x = 0.090$ %.

Same as Fig.<ref> but for Type II of the beam spectrometer.

Another design, Type II, has a QQDDQ configuration (Fig. <ref>).
It also realizes the point-to-point focus ($R_{12}=0$) from VO to VI,
and has the magnification of $R_{11} = -0.228$ and
the dispersion of $R_{16} = -0.354$ cm/%.
The expected momentum resolution, therefore, is 0.087 %.

Compared with Type II, the vertical beam size
in the analysing section in Type I is so large that
it causes a transmission problem when the phase of the second cavity
is tuned to $\pi^-$'s ($\pi$-tuned mode).
Type I spectrometer, therefore, can be used only with a slit
in a $K$-tuned or a $\bar{p}$-tuned mode.
On the other hand, Type II can be operated with a central stopper
in a $\pi$-tuned mode as well as a slit in a $K$- or $\bar{p}$-tuned mode.

Expected $K^-$ intensity per spill and purity ($K^-$:$\pi^-$) of
the RF option of the K10 beam line.
The beam loss of 25 kW at the production target and
the spill repetition of 5.2 s were assumed.
The production cross-section was calculated
by using Sanford and Wang formula.
Decay muons and so-called “cloud-$\pi$” were not included.
Slit conditions were varied to achieve a moderate purity
for each case.
The field gradient of RF cavities was also varied
in the range from 5 to 9 MV/m.

Type I (QDDQQ)     Type II (QQDDQ)     Type II (QQDDQ)

$K$-tuned mode     $\pi$-tuned mode     $K$-tuned mode
5 GeV/$c$     $3.9 \times 10^6$ (1:7.0)     $5.4 \times 10^6$ (1:3.5)     $6.1 \times 10^6$ (1:7.8)

6 GeV/$c$     $5.2 \times 10^6$ (1:5.0)     $7.3 \times 10^6$ (1:2.6)     $8.4 \times 10^6$ (1:5.4)

7 GeV/$c$     $6.0 \times 10^6$ (1:4.8)     $8.3 \times 10^6$ (1:2.1)     $9.4 \times 10^6$ (1:5.1)

8 GeV/$c$     $5.8 \times 10^6$ (1:5.7)     $7.9 \times 10^6$ (1:2.1)     $9.1 \times 10^6$ (1:6.1)

9 GeV/$c$     $4.9 \times 10^6$ (1:7.3)     $6.7 \times 10^6$ (1:2.1)     $8.0 \times 10^6$ (1:7.6)

10 GeV/$c$     $4.0 \times 10^6$ (1:9.4)     $4.7 \times 10^6$ (1:2.5)     $6.4 \times 10^6$ (1:10.0)

Type I ($K$-tuned mode)     Type II ($\pi$-tuned mode)     Type II ($K$-tuned mode)

Expected beam profile at the final focusing point for each type of
the beam spectrometer and the operation mode.

Table <ref> lists the result of
the beam simulation using DecayTURTLE<cit.>
for each type of the beam spectrometer and the operation mode,
assuming the beam loss of 25 kW at the production target and
the spill repetition of 5.2 s.
The horizontal and vertical beam profiles are shown
in Fig. <ref>.
Type II has an advantage in terms of intensity and purity,
whereas Type I provides a much smaller beam spot size
at the experimental target.

§.§.§ ES-separator option for K10 beam line

The layout of the ES-separator option of the K10 beam line is
presented in Fig.<ref>, and
the beam envelope calculated with the TRANSPORT code
is shown in Fig.<ref>.
The total length of the beam line is 82.8 m,
which is almost same as that of the RF option.

The front-end section from the production target to the IF is completely same
as that in the RF option.
The separation of the secondary particles is performed
by using three ES separators.
Each of the ES separators have the effective length of 9 m,
the electrode gap of 10 cm, and the electrostatic field of 75 kV/cm.
In the separation section, parallel beams are made
in both the horizontal and vertical directions
to pass through such long ES separators,
and then the beams are focused vertically at the mass slit (MS).
They are analyzed with the beam spectrometer in the analyzing section,
and finally focused both horizontally and vertically at an experimental target.
In addition, there are two horizontal focal points in the beam line (HF1, HF2),
where slits are located to determine the momentum bite and
to increase the beam purity.

The beam intensity and purity of the beam line was estimated
by using a lay-tracing code DecayTURTLE.
The assumption for the beam loss and spill repetition is
same as that for the RF option.
The result is summarized in Table <ref>.

Layout of the ES option of the K10 beam line.

First-order beam envelope of the ES option of the K10 beam line.
The upper and lower show the vertical and horizontal directions,
The dash line indicate the horizontal dispersion.

The expected intensity and purity of the ES option
of the K10 beam line.
Assumed condition of the primary protons is same as Table <ref>.

4 GeV/$c$ $K^-$     4 GeV/$c$ $\bar{p}$     6 GeV/$c$ $\bar{p}$
acceptance [msr-%]     0.33     1.2     0.55

intensity [/spill]     $1.6 \times 10^6$     $1.5 \times 10^7$     $7.5 \times 10^6

purity ($K^-:\pi^-$ or $\bar{p}:\pi^-$)     1.1:1     81:1     1:3.4

§.§ Baryon-Spectroscopy Experiment at $\pi$20 and K10

At the High-p ($\pi 20$) and K10 beam lines,
we conduct spectroscopy of $\Lambda_c$ and $\Sigma_c$ baryons (charmed baryons)
as well as that of $\Xi$ and $\Omega$ baryons (multi-strangeness hyperons).
At $\pi 20$, excited $\Lambda_c$ ($\Sigma_c$) baryons, $\Lambda_c^*$'s ($\Sigma_c^*$'s),
are produced in the two-body $\pi^-\;p\to D^{*-}\; \Lambda_c^{*+}$
($\pi^-\;p\to D^{*-}\; \Sigma_c^{*+}$) reaction,
and they are identified from the $p\left(\pi^-, D^{*-}\right)$ missing mass[
The reaction of interest is often denoted by $T(I,S)R$
for scattering experiments in Nuclear Physics,
where $I$, $T$, $S$, and $R$ stand for the incident, target, scattering,
and recoil particles, respectively.
We use this notation also in Hadron Physics
by using $S$ for a set of detected particles, and $R$ a set of undetected particles.
When $R$ is comprised of a single particle,
its mass can be calculated from four-momenta $p$ of $I$, $T$, and $S$:
m_R^2 = p_R^2 = \left(p_I+p_T-p_S\right)^2
We call $m_R$  the $T(I,S)$ missing mass.
Similarly, excited $\Xi$ baryons, $\Xi^*$'s, are produced in $K^-\;p\to K^{(*)}\; \Xi^{*}$,
and they are identified from the $p\left(K^-, K^{(*)}\right)$ missing mass.
Only low-lying $\Xi^*$'s are studied at $\pi20$
owing to the limited kaon beam intensity, and highly-excited $\Xi^*$'s will be investigated at K10.
At K10, we additionally explore excited $\Omega$ baryons, $\Omega^*$'s,
in terms of $p(K^-,K^+\;K^{(*)0})$ for $K^-\;p \to \Omega^{*-}\; K^+\; K^{(*)0}$.

A spectrometer system was originally designed for the J-PARC E50 experiment
at $\pi20$ aiming at spectroscopy of $\Lambda_c^*$'s and $\Sigma_c^*$'s <cit.>.
This spectrometer was expected to have a wide angular coverage with high
and high particle-identification power in a wide momentum range
up to $\sim 20$ GeV$/c$ for particles emitted in experiments at $\pi 20$.
The spectrometer shows high performance not only for spectroscopy of $\Xi^*$'s,
but also for that of $\Omega^*$'s.
The configuration of the spectrometer is described in sub-subsection <ref>.
Expected $p\left(\pi^-, D^{*-}\right)$ missing-mass spectra for $\Lambda_c^*$ and $\Sigma_c^*$ production
are shown in subsubsections <ref>.
The $p\left(K^-, K^{(*)}\right)$ and $p(K^-,K^+\;K^{(*)0})$ spectra appear
in sub-subsections <ref> and <ref>
for $\Xi^*$ and $\Omega^*$ production, respectively.
Since $\pi^-$-induced $\Omega^*$ production requires more than two final-state particles,
the relevant analyses are more complicated than that for $\Lambda_c^*$'s, $\Sigma_c^*$'s, or $\Xi^*$'s.
The details of the $\Omega^*$-related performance of the spectrometer
are described in sub-subsections <ref>,
<ref>, and <ref> as supplemental information.

§.§.§ Spectrometer system

The spectrometer for the E50 physics program <cit.> (E50 spectrometer)
satisfies requirements of all the planned spectroscopy experiments at $\pi$20 and K10.
Figure <ref> shows the schematic view of the E50 spectrometer.
In the E50 experiment, charmed baryons ($Y^{*+}_c$'s: a generic term of $\Lambda_c^*$'s and
$\Sigma_c^*$'s) are produced in the $\pi^{-}\;p \rightarrow D^{*-}\;Y^{*+}_c$ reaction.
The $Y^{*+}_c$ mass is determined from the $p(\pi^-,D^{*-})$ missing mass
by detecting the final-sate $K^+\;\pi^-\;\pi^-$ particles from the $D^{*-}$ decay.
The daughter particles from the $Y^{*+}_c$ decay are also planned to be detected.
The E50 spectrometer is designed for detecting all the charged particles
produced in the $\pi^{-}\;p \rightarrow D^{*-}\;Y^{*+}_c$ reaction at an incident pion momentum of 20 GeV/$c$.
Emitted at forward angles are high-momentum particles from the $D^{*-}\to\bar{D}^0\pi^-$ decay
followed by $\bar{D}^0\to K^+\;\pi^-$ as well as daughter particles from the $Y^{*+}_c$ decay.
The momenta of the emitted particles range from 0.2 to 16 GeV$/c$.
The E50 spectrometer has been designed as a multi-purpose system at $\pi20$,
and it can be be also used  for spectroscopy of  $\Xi^*$'s and $\Omega^*$'s at K10.

Schematic view of the spectrometer to be constructed for the E50 experiment at the $\pi20$ beam line.
It consists of a large dipole magnet, tracking detectors, time-of-flight detectors, and particle-identification detectors.
Some of tracking detectors and time-of-flight detectors are placed inside the gap of the magnet (internal detectors).
The liquid hydrogen target is placed just in front of the entrance of the dipole magnet.

The E50 spectrometer consists of a large dipole magnet,
tracking detectors, time-of-flight detectors, and particle-identification detectors.
The stationary target (liquid hydrogen) is placed just in front of the entrance of the dipole magnet.
To determine the $Y_c^{*+}$ mass from the $p(\pi^-,D^{*-})$ missing mass,
it is necessary to measure the four-momenta of the final-sate $K^+\;\pi^-\;\pi^-$ particles.
Since high-momentum $K^+$ and $\pi^-$ from the $\bar{D^0}$ decay are emitted at forward angles,
placed are scintillating-fiber hodoscopes <cit.>
behind the target, several drift chambers (DC's), and ring-imaging Cherenkov detector (RICH)
for the trajectory determination (momentum analysis),
time-of-flight (TOF) measurement, and particle identification, respectively.
Additional tracking and time-of-flight detectors are placed inside the gap of the magnet (internal detectors)
to detect the slow $\pi^-$'s emitted at forward angles from the $D^{*-}$ decay (not from the $\bar{D}^0$ decay)
and daughter particles from the $Y^{*+}_c$ decay.
These detectors should have a wide angular coverage
since the slow $\pi^-$'s cannot reach the exit of the dipole magnet and since the daughter particles are emitted in a wide angle range.
Placed in front of the magnet yokes are the barrel-shaped DC's and high time-resolution
TOF detector wall consisting of resistive-plate chambers (PRCs)
for detecting the slow $\pi^-$'s and horizontally-emitted daughter particles from the $Y^{*+}_c$ decay.
The RPC's are also placed on the pole pieces for detecting vertically-emitted $Y^{*+}_c$ daughter particles.
The scintillating-fiber hodoscopes and DC's located behind the target are used
not only for high-momentum $K^+\;\pi^-$ particles at forward angles but also for all the other produced particles.
To get high-counting-rate capability, the scintillating-fiber
hodoscopes are planned to be used just behind the target.
They are also placed at upstream of the target for measuring the incident momentum and profile, or $(x,y)$ intensity map.
To get the reference timing for all the detectors, a fine-segmented acrylic Cherenkov counter (time-zero counter) <cit.>
is placed just in front of the target.
Another RICH counter, Beam RICH <cit.>, is used for identifying
incident particles in the secondary beam located at most upstream.
The details of the E50 spectrometer are described elsewhere <cit.>.

We plan to use a trigger-less streaming data acquisition (DAQ) system <cit.>,
which selects the events corresponding to the reaction of interest
without any hardware trigger (trigger-less).
All the detector signals are digitized in front-end electronics,
and the digitized data fragments are continuously transferred (streaming) to a personal computers (PCs).
The events of interest are selected using software on PC's by combining the streaming data fragments.
In a streaming DAQ system,
a complicated hardware trigger system is not necessary,
which makes a busy time for processing an event corresponding to a trigger.
We are developing a streaming DAQ system primarily for the E50 experiment
as well as special time-to-digital converters (TDC's)
for a continuous time measurement without any external trigger.
We have tested and successfully demonstrated a prototype streaming DAQ system <cit.>
using high-intensity electrons and positrons converted from a bremsstrahlung photon beam
at the Research Center for Electron Photon Science, Tohoku University <cit.>.
The streaming DAQ system allows us to make the DAQ efficiency close to 100% without any trigger bias.

§.§.§ Requirements for observing $\Xi^*$'s and $\Omega^*$'s

In spectroscopy of $\Xi^*$'s and $\Omega^*$'s,
we have to primarily measure the excitation spectrum of $\Xi^{(*)}$'s and $\Omega^{(*)}$'s,
and determine the angular distribution of a daughter particle from their decay.
$\Xi^{(*)}$'s and $\Omega^{(*)}$'s are produced
in the $K^{-}\;p \rightarrow K^{(*)}\; \Xi^{(*)}$[
Note that $K^{*}\;\Xi^{(*)}$ includes
$K^{(*)0}\;\Xi^{(*)0}$ and $K^{(*)+}\;\Xi^{(*)-}$.
and $K^{-}\;p \rightarrow \Omega^{(*)-}\;K^+\;K^{(*)0}$ reactions
at incident kaon momenta ranging from 5 to 8 GeV$/c$ and 7 to 10 GeV$/c$, respectively.
Since the $\Xi^{(*)}$- and $\Omega^{(*)}$-produced
events are identified by the $p(K^-, K^{(*)})$ and the $p(K^-, K^+K^{(*)0})$ missing mass, respectively.
For detecting the emitted particles
in association with the hyperon of interest,
high acceptance is required for detecting the final-state $K^+$ and $K^{*0}$,
$K^+\;K^{*0}$ and $K^+\;K^0$, where
$K^{*0}$ and $K^{0}$ are identified from the $K^+\;\pi^-$ and $\pi^+\;\pi^-$ decays.
Additionally, high momentum-resolution is necessary
for each of the emitted particles to get enough high $\Xi^*$- and
$\Omega^*$-mass-resolution (5–7 MeV in $\sigma$)
for observing $\Xi^*$'s and $\Omega^*$'s separately,
and determining their widths directly from the mass spectra.
The daughter particles from the $\Xi^*$ and $\Omega^*$ decays should be detected
in a wide angular coverage for determining the spin-parities
of $\Xi^*$'s and $\Omega^*$'s.

High-intensity high-momentum $K^-$ beam is necessary to produce $\Xi^{(*)}$'s and $\Omega^{(*)}$'s effectively.
At such incident kaon momenta,
high-momentum particles are likely to be emitted at forward angles in the laboratory frame when we use a stationary target.
A spectrometer system with a dipole magnet covering the forward direction is suitable
to detect these particles to get high mass-resolutions for $\Xi^{(*)}$'s and $\Omega^{(*)}$'s.
The requirements for the spectrometer system are as follows:

* wide angular coverage of polar angles up to $30^\circ$ for detecting the final-state $K^+$, $K^+\;\pi^-$, $K^+\;K^+\;\pi^-$ and $K^+\;\pi^+\;\pi^-$ particles,

* wide angular coverage of polar angles up to $45^\circ$ for detecting the daughter particles from the $\Xi^*$ and $\Omega^*$ decays,

* high momentum-resolution of a few $10^{-3}$ ($\sigma$),

* multi-layer tracking system to detect multiple particles, and

* high particle-identification power (the efficiency is higher than 97%, and mis-identification fraction is lower than 1% for 0.2–8.0 GeV/$c$ particles).

Those requirements for spectroscopy of $\Xi^*$'s and $\Omega^*$'s are satisfied by
the E50 spectrometer.
It is thus a possible candidate of a spectrometer at K10.

§.§.§ Charmed baryons ($Y_c^*$: $\Lambda_c^*$ and $\Sigma_c^*$)

At the $\pi 20$ beam line,
we investigate primarily the masses and decays of excited charmed baryons
($Y^{*+}_c$'s: a generic term of $\Lambda_c^*$'s and $\Sigma_c^*$'s)
in the $\pi^-\; p \to D^{*-}\; Y_c^{*+}$ reaction at an incident pion momentum of 20 GeV/$c$.
Figure <ref> shows
the schematic view of the production mechanisms of $Y_c^*$'s in the $\pi^-\; p$ reaction, and their decay.
The decay chain of the $D^{*-}$ meson, $D^{*-} \rightarrow \bar{D}^0\;\pi^{-}$ (branching ratio: 67.7%)
and $\bar{D}^0 \rightarrow K^{+}\;\pi^{-}$ (branching ratio: 3.95%),
is used for determining the mass of the produced $Y_c^*$'s.
Detected with the E50 spectrometer are $K^{+}$'s and $\pi^{-}$'s with momenta
from 2 to 16 GeV/$c$ from the $\bar{D}^0$ decay
and $\pi^{-}$'s with momenta from 0.5 to 1.7 GeV/$c$ from the $D^{*-}$ decay.
The $Y_c^*$ mass is determined from the $p\left(\pi^-, D^{*-}\right)$ missing mass (production measurement).
The daughter particles from the $Y^{*+}_c$ decay are also planned to be detected
(decay measurement)
in the
$Y^{*+}_c \rightarrow \Sigma_c^{0}\;\pi^{+}$,
$Y^{*+}_c \rightarrow \Sigma_c^{++}\;\pi^{-}$,
and $Y^{*+}_c \rightarrow p \;D^{0}$ channels.
The four momentum of the produced $Y^{*+}_c$ is known after it is identified
by using the $p(\pi^-, D^{*-})$ missing mass.
The masses of the daughter particles,
and $D^{0}$,
from the $Y_c^{*+}$ decay can be obtained by the
$p(\pi^-, D^{*-}\pi^+)$,
$p(\pi^-, D^{*-}\pi^-)$, and
$p(\pi^-, D^{*-}p)$  missing masses, respectively.
Thus, required is only
detection of $\pi^\pm$ or $p$
from the
$Y^{*+}_c \rightarrow \Sigma_c^{0}\;\pi^{+}$,
$Y^{*+}_c \rightarrow \Sigma_c^{++}\;\pi^{-}$,
or $Y^{*+}_c \rightarrow p \;D^{0}$ decay
with momenta ranging from 0.2 to 4.0 GeV/$c$.

Schematic view of the production mechanisms of $Y_c^*$'s in the $\pi^-\;p$ reaction, and their decay.
The solid lines represent the initial- and final-state particles to be directly detected.
The dotted lines show unstable particles to be reconstructed from kinematic variables of the detected particles.
$Y_c^*$'s are expected to decay into
(left), and $p\;D^{0}$ (right).

In the proposal for the E50 experiment <cit.>,
we show the expected $Y_c^{*+}$-mass spectra estimated by a Monte-Carlo simulation
based on Geant4 with the E50 spectrometer configuration.
Here, the conditions and results of this simulation are described briefly
since the conditions are common except for the production cross sections of $Y_c^{*+}$'s.
The  estimated cross section of $Y_c^{*+}$ production
is 10$^{-4}$ smaller in the $\pi^-\; p \to D^{*-}\; Y_c^{*+}$ reaction
than that of hyperon ($Y^*$) production (10–100 $\mu$b for  $\pi^{-}\;p \rightarrow K^{*}\;Y^{*}$).
To estimate the  $Y_c^{*+}$ yield,
we assumed 1 nb for the cross section of the ground-state $\Lambda_c^{+}$ baryon,
6.0$\times$10$^7$/spill for the beam intensity,
and 4 g/cm$^2$  (57 cm) for the thickness of the liquid hydrogen target.
The acceptance for detecting the daughter particles from the $D^{*-}$ decay
was found to be 60%–70% for the excitation energy up to 1 GeV
by assuming the angular distribution of $D^{*-}$ emission corresponding to the $t$-channel process.
The momentum resolution of 0.2%($\sigma$) was obtained at 5 GeV/$c$,
giving the invariant-mass resolution of 5.5 MeV($\sigma$) and 0.6 MeV($\sigma$)
for reconstructing $\bar{D}^0$ and $D^{*-}$, respectively.
The mass resolution for the ground-state $\Lambda_c^+$ was  8.3 MeV($\sigma$).
A better mass-resolution is expected for the higher-mass $Y_c^{*+}$'s
since the momenta of the $K^+\;\pi^-\;\pi^-$ particles from the $D^{*-}$ decay are lower for these $Y_c^{*+}$'s.
In the decay measurement, a wide angular coverage of $\pi$ emission
is expected $\cos\theta_{\pi} \ge -0.9$