# Physics Opportunities with Meson Beams for EIC

William J. Briscoe The George Washington University, Washington DC 20052, USA
Michael Döring The George Washington University, Washington DC 20052, USA
Helmut Haberzettl The George Washington University, Washington DC 20052, USA
D. Mark Manley Kent State University, Kent, OH 44242, USA  Megumi Naruki Kyoto
University, Kyoto 606-8502, Japan  Greg Smith Thomas Jefferson National
Accelerator Facility, Newport News, Virginia 23606, USA  Igor Strakovsky The
George Washington University, Washington DC 20052, USA  Eric S. Swanson
University of Pittsburgh, Pittsburgh, PA 15260, USA

###### Abstract

Abstract: Over the past two decades, meson photo- and electroproduction data
of unprecedented quality and quantity have been measured at electromagnetic
facilities worldwide. By contrast, the meson-beam data for the same hadronic
final states are mostly outdated and largely of poor quality, or even non-
existent, and thus provide inadequate input to help interpret, analyze, and
exploit the full potential of the new electromagnetic data. To reap the full
benefit of the high-precision electromagnetic data, new high-statistics data
from measurements with meson beams, with good angle and energy coverage for a
wide range of reactions, are critically needed to advance our knowledge in
baryon and meson spectroscopy and other related areas of hadron physics. To
address this situation, a state-of-the-art meson-beam facility needs to be
constructed. The present letter summarizes unresolved issues in hadron physics
and outlines the vast opportunities and advances that only become possible
with such a facility.

Introduction: The CM energy range up to 2.5 GeV is rich in opportunities for
physics with pion and kaon beams to study baryon and meson spectroscopy
questions complementary to the electromagnetic programs underway at
electromagnetic facilities. The White Paper Briscoe:2015qia  highlights some
of these opportunities and describes how facilities with high-energy and high-
intensity meson beams can contribute to a full understanding of the high-
quality data now coming from electromagnetic facilities. We emphasize that
what we advocate here is not a competing effort, but an experimental program
that provides the hadronic complement of the ongoing electromagnetic program,
to furnish the common ground for better and more reliable phenomenological and
theoretical analyses based on high-quality data. A number of the topics
mentioned in the White Paper are addressed in the summary of the recent DNP
Town Meeting on QCD and Hadron Physics Brodsky:2015aia , which notes (on page
28) that meson beams are being considered.

The physics case for our program is aligned with Reaching for the Horizon:
Long Range Plan for Nuclear Science Geesaman:2015fha : …a better understanding
of the role of strange quarks became an important priority. Knowledge of the
hyperon spectrum is an important component of this proposal. Overall, our
knowledge of the hyperon spectrum is very poor; e.g., the empirical knowledge
of the low-lying spectra of $\Lambda$ and $\Sigma$ hyperons remains very poor
in comparison with that of the nucleon and, in the case of the $\Xi$ hyperons,
extremely poor. The structure of hyperon resonances cannot be understood
without empirical determination of their pole positions and decays, which is
the goal of the proposed experiments. The determination of the strange hyperon
spectra in combination with the current measurements of the spectra of the
charm and beauty hyperons at the LHCb experiment at CERN allows for a clearer
understanding of soft QCD matter and the approach to heavy quark symmetry
Isgur:1991wq .

Opportunities with Meson Beams: Looking further down the road, we plan to take
part in the future electron-ion collider (EIC) following the recommendation of
the new Long-Range Plan Reaching for the Horizon: Long Range Plan for Nuclear
Science Geesaman:2015fha : RECOMMENDATION III: We recommend a high-energy
high-luminosity polarized EIC as the highest priority for new facility
construction following the completion of FRIB.

An EIC will likely be one of the future large accelerator facilities for high-
energy and nuclear physics AbdulKhalek:2021gbh . The creation of a state-of-
the-art hadron physics complex to study QCD at the deepest level with an EIC
would provide the unique infrastructure for a meson-beam facility to complete
our picture of the hadron spectrum of QCD at the same time. In addition, the
presence of an electron beam at an EIC facility would permit a unique
opportunity to measure the pion EM form factor directly using an electron-pion
collider, although such a facility would present tremendous technical
challenges. This is useful because the pion form factor serves as a paradigm
for nonperturbative hadronic structure and is associated with chiral dynamics,
gauge invariance, and perturbative QCD in a nontrivial fashion. Current
methods to extract the form factor rely on extrapolation to the pion
$t$-channel pole. Unfortunately, this procedure is not without ambiguity and
remains controversial to this day.

The form factor is especially relevant in light of a more recent controversy
concerning its approach to the expected perturbative QCD behavior. This issue
is of fundamental importance since it questions the existence of perturbative
QCD for exclusive processes Gorchtein:2011vf . Unfortunately, the experimental
situation is confused, with the BaBar and Belle Collaborations obtaining
results for $Q^{2}|F_{\pi}(Q^{2})|$ that appear to be in conflict
Bevan:2014iga .

Spectroscopy of Hyperon Resonances: Most of our current knowledge about the
bound states of three light quarks has come from partial-wave analyses (PWAs)
of $\pi N\to\pi N$ scattering. Measurements of $\pi N$ elastic scattering are
mandatory for determining absolute $\pi N$ branching ratios. Without such
information, it is likewise impossible to determine absolute branching ratios
for other decay channels. A summary of resonance properties (pole positions
(masses and widths), branching ratios, helicity couplings to $\gamma N$, etc.)
is provided in the Review of Particle Physics (RPP) Zyla:2020zbs .

The information on resonance properties obtained from analyses of experimental
data provides fundamental information about QCD in the nonperturbative region.
A variety of quark models have been used to interpret these results. Dyson-
Schwinger approaches provide a picture of baryons in terms of quarks and
gluons by incorporating dynamical chiral symmetry. Results from lattice gauge
theory calculations are constantly improving and are therefore becoming more
relevant to experiment.

A comparison of the experimental results and models led to the well-known
conundrum known as the “missing resonances” problem Koniuk:1979vw . Put
simply, the models (and lattice-gauge calculations) predict far more states
than are observed experimentally. These missing resonances, however, do not
appear at all in the quark-diquark model. The reason for this, it is
conjectured, is their weak coupling to the $\pi N$ channel, which supplies the
bulk of our information about baryonic resonance states. A desire to test this
hypothesis by looking for resonances in reactions that do not involve $\pi N$
in either the initial or final state was a major reason behind the
construction of Hall B and the CLAS facility at JLab.

The world data on $\pi N\to\eta N,\,K\Lambda,\,K\Sigma$ were collected and
date back to more than 20 or 30 years ago. In many cases, systematic
uncertainties were not reported (separately from statistical uncertainties),
and in many cases it is known that systematic uncertainties were
underestimated. These problems of pion-induced reaction data have led to the
emergence of many different analyses that claim a different resonance content.
While many analyses agree on the 4-star resonances that are visible in elastic
$\pi N$ scattering Arndt:2006bf , there is no conclusive agreement on
resonances that couple only weakly to the $\pi N$ channel.

Unlike in the cases described above, kaon beams are crucial to provide the
data needed to identify and characterize the properties of hyperon resonances.
The masses and widths of the lowest $\Lambda$ and $\Sigma$ baryons were
determined mainly with kaon-beam experiments in the 1970s Zyla:2020zbs . First
determinations of pole positions, for instance for $\Lambda(1520)$, were
obtained only recently Qiang:2010ve . An intense kaon beam would open a window
of opportunity not only to locate missing resonances but also to establish
properties including decay channels systematically for higher excited states.

In summary, better data from hadron-induced reactions will significantly
contribute to answer the same fundamental questions that originally motivated
the photoproduction program: the missing resonance problem, amplitudes for
comparison with ab initio calculations, and low-energy precision physics. A
program with hadron beams provides complementary information with large impact
in the extraction of the amplitudes from observables. With a more precise
knowledge of the amplitude it is expected that much-debated concepts, such as
the aforementioned multiquark hypotheses, hadronic molecules, hybrid states,
chiral symmetry restoration, chiral solitons, or string models, can be
confirmed or ruled out.

Meson Spectroscopy: Although it was light hadron spectroscopy that led the way
to the discovery of color degrees of freedom and Quantum Chromodynamics, much
of the field remains poorly understood, both theoretically and experimentally
Pennington:2014dwa . The availability of pion and kaon beams provide an
important opportunity to improve this situation. Experimentally, meson
spectroscopy can be investigated by using PWAs to determine quantum numbers
from the angular distributions of final-state particle distributions. Such
methods will be used to analyze data from future measurements at CLAS12. Pion
beams with CM energies up to 5 GeV should be adequate for a complementary
program. Such energies correspond to beam momenta of about 13 GeV/$c$. We note
that meson beam experiments may not be ideal for the study of meson
resonances; however, this approach has been taken at BNL and COMPASS and a
closely related one is being pursued by the GlueX Collaboration. We therefore
briefly review some of the open issues in light meson spectroscopy in this
section.

What is Needed for Hadron-Induced Reactions: These measurements also have the
potential to observe dozens of predicted (but heretofore unobserved) states
and to establish the quantum numbers of already observed hyperon resonances
listed in the RPP Zyla:2020zbs . Interesting puzzles exist for RPP-listed
excited hyperons that do not fit into any of the low-lying excited multiplets,
and these need to be further revisited and investigated. Excited $\Xi$s, for
instance, are very poorly known. Establishing and discovering new states is
important, in particular, for determination of the multiplet structure of
excited baryons.

Our expertise says that is doable at JLab. The use 3-10 GeV protons from pre-
booster or booster (which will be busy several minutes a day) to produce
secondary charged meson beams will increase the efficiency of the EIC
facility. One can roughly estimate that it will cost about 10% of the EIC
cost.

How it May Work: What would be required to expand the scope of the EIC to
include the production of secondary beams of pions and kaons, and what
secondary fluxes might we expect? It’s useful to recall the projects that were
proposed (both successfully and unsuccessfully) in the past to provide such
beams.

History: Back in the 1980s, there were two proposals for kaon factories that
failed to secure funding. The TRIUMF KAON factory Craddock:1986nw ; TRIUMF1 ;
TRIUMF2  proposed to add an alternating series of three storage rings and two
fast-cycling synchrotrons to the existing 150 $\mu$A, 0.5 GeV CW TRIUMF
cyclotron. It would have provided 100 $\mu$A of 30 GeV protons (3 MW) to an
experimental area with four production targets to provide a range of secondary
meson beams, as well as a dedicated line for neutrino physics, for Cdn $700M
(1986 dollars), or about $1.1 B in today’s (US) dollars. At the same time, a
competing design at LAMPF called the Advanced Hadron Facility proposed to add
a 1.2 GeV superconducting booster linac, which would have accepted 100 $\mu$A
from the existing 0.8 GeV linac. The booster linac would have fed a 2 GeV
compressor ring, followed by a 15 GeV booster ring and finally a 60 GeV main
ring. This configuration allowed extraction of a short duty-factor neutrino
beam and a high duty-factor beam for production of secondary particles. Both
of these were (planned to be) MW-scale Kaon factories. Additionally, there was
the the LAMPF II (AHF) proposal which described the 45-GeV version AHF .

BNL successfully operated kaon beam lines at the 30 GeV AGS Littenberg:1983vn
for many years. Typical proton intensities of $6\times 10^{12}$ protons per
second were achieved with a 43% duty factor (DF), corresponding to almost 100
kW of average beam power.

Today the highly successful J-PARC facility JPARC ; Sato:2010zzb ;
Takahashi:2011zzf  in Japan is the only Kaon factory in the world. It is a
several-hundred kW proton accelerator with an extensive array of secondary
kaon channels.

The EIC Booster: Several designs are under consideration for the EIC booster.
Here we consider just one of these designs Nissen:2018gdz . It envisions an 8
GeV (figure-8 shaped) booster of circumference 313.5 m producing a $\sim 1/4$
circumference, 260 ns-long spill every 2 s with a parabolic intensity
distribution (the booster synchrotron magnets take 1 s to ramp up and 1 s to
ramp down). The design intensity of $1\times 10^{12}$ protons (160 nC) per
spill corresponds to only about 0.6 kW, 2 orders of magnitude below the BNL
AGS when it was serving kaon beamlines, and 3 orders of magnitude less than
J-PARC JPARC . The time-averaged current is only 80 nA.

It seems possible to consider flattening the distribution to 840 ns, or
increasing the intensity a factor of 2-3 for modest additional investment.
Much more expensive would be to increase the intensity significantly, or to
slow-extract over (for example) 2 s every 3 s. While these changes would offer
significant advantages, we take the position for the remainder of this
manuscript that the booster parameters are frozen as described in Ref.
Nissen:2018gdz , and then look to see what would need to be done on top of the
existing design to satisfy the requirements for $\pi$ and K beams outlined
above. Since the EIC booster would only inject to the main ring a small
fraction of the time each day, we assume it could be made available for
$\pi$/K physics the rest of the time.

Stretcher: The nominal booster design has a duty factor of only 0.00005%,
which makes it completely unsuitable for the physics experiments described
earlier in this manuscript. Most experiments rely on detectors that are
limited to instantaneous rates below a few MHz, so it’s better to have the
same number of beam particles delivered with a lower instantaneous rate over a
longer period of time than all at once in a short period of time. As noted,
for example, in Ref. Arvieux , “In coincidence measurements the number of true
events is proportional to the intensity but the number of random coincidence
events (background) goes like the square of the peak current”. Without
improving the duty factor of the nominal EIC booster there is no reason to
proceed any further. Of course if the booster itself could be modified to
provide slow extraction, a possibility mentioned above, that would be the most
cost-effective solution to the duty-factor problem.

There is a solution to this seemingly fatal problem that does not involve
making changes to the nominal booster design: adding a stretcher ring (see,
for example, Ref. Tomizawa:2018koh ). The nominal 8 GeV/$c$ booster
corresponds to a magnetic rigidity of 26.67 T-m. There are many stretcher
configurations that could be used to provide nearly CW 100% duty factor beam
in this situation. The simplest and most basic would be to extract the booster
beam in a direction different than used to fill the EIC main ring, and fill
exactly one turn of a stretcher ring over the 260 ns booster spill. That
implies a booster ring with a radius of 12.3 m, and 39 one-meter-long dipole
magnets of 4.3 T (fixed field) if half the circumference of the ring consisted
of dipoles. While this is feasible, it would be more sensible to (for example)
double the stretcher diameter, fill only half its circumference every spill,
and halve the field to 2.16 T so resistive magnets could be used. In this
mode, and with some flexibility in the bunch length, the planned booster
tunnel would be about the right circumference to house the stretcher magnets.
The stretcher magnet design could be the the same or similar to that of the
booster magnets.

Either way the beam could be extracted essentially CW with a good duty factor
using the common technique of resonant slow extraction (see, for example
resonantslowextraction ) while the booster magnets are ramping up and down. In
this way, a time-average of $5\times 10^{11}$ protons/s could be slow-
extracted from the stretcher ring into a transfer line to a production target
for secondary particles ($\pi$/K) in a dedicated hadron hall. Now we look to
see what $\pi$/K fluxes might be achieved with a CW proton beam of 80 nA.

Pion and Kaon Intensities: Given the conditions just established (80 nA CW, 8
GeV/$c$ protons) we can estimate the fluxes of pions and kaons as a function
of secondary particle momentum and secondary channel production angle. We
first use the parametrizations of Sanford and Wang (SW) to estimate the number
of pions SW1  and kaons SW2  generated at the production target per GeV/$c$
per steradian per interacting proton. Then we use those results as input to
the procedure described by Yamamoto Yamamoto:1981zr , which includes the
effects of secondary particle production efficiency and nuclear absorption
cross sections of the protons on different production targets, as well as
solid angle, momentum acceptance, and decay factors for typical secondary-
particle channels. This tells us what to expect for $\pi^{\pm}$ and K± fluxes
at the end of the secondary particle beamline, again as a function of
production angle, for a given production target and secondary-particle
beamline. Yamamoto described the design of the KEK K2 channel for $1\times
10^{12}$ protons at 12 GeV, which are similar conditions to the ones we’re
considering here.

It must be noted that the SW parametrizations SW1 ; SW2  used proton data
between 10 and 30 GeV. We are outside this range for the 8 GeV case we’re
considering here, which decreases the reliability of our predictions somewhat.
For the production target and secondary beam channel we consider Yamamoto’s
design Yamamoto:1981zr  as the default: a 6 cm Pt production target, 30 m
channel with 3.125 msr and $\Delta p/p$=2%. This is a realistic design for our
situation, and also makes it easier to benchmark our calculations against his.

Figure 1 shows the predictions of $\pi^{\pm}$ and K± production on beryllium
per steradian per GeV/$c$ per interacting proton for $5\times 10^{11}$
protons/s CW at 8 GeV from the EIC booster and stretcher, based on the
phenomonological fits of SW SW1 ; SW2 . Near production angles of $0^{\circ}$,
and for $\pi$/K momenta near 3 GeV/$c$, $\pi^{\pm}$ production rates are just
under 1/sr/(GeV/$c$) per interacting proton, with K+ rates about 30 times less
than that, and K- rates another factor of 5 below that.

Figure 1: Pion and Kaon production rates on beryllium per steradian per
GeV/$c$ per interacting proton for $5\times 10^{11}$ protons/s CW at 8 GeV.
The legend denotes different assumptions for the production angle.

Much more interesting is to use this information to predict what fluxes of
secondary particles could be expected for a specific choice of production
target and realistic secondary beamline. Following the work of Yamamoto
Yamamoto:1981zr , the $\pi$K yields $Y$ can be determined from the SW rates
$d^{2}N/(d\Omega dp)=\left(1/\sigma_{a}\right)d^{2}\sigma/(d\Omega dp)$, the
proton flux $F_{i}$ on the production target, the production efficiency $\eta$
for secondary particles per incident proton, the nuclear absorption cross
section $\sigma_{a}$ associated with the protons on the production target, as
well as the secondary channel characteristics: solid angle $d\Omega$, momentum
bite $\Delta p/p$, momentum $p$, and decay factor $d$ according to

$Y=F_{i}\,\frac{\eta}{\sigma_{a}}\frac{d^{2}\sigma}{d\Omega
dp}\Delta\Omega\,(\Delta p/p)\,p\,d.$ (1)

We take an incident proton flux $F_{i}=5\times 10^{11}$ protons/s CW at 8 GeV,
a 6 cm Pt production target for which $\sigma_{a}=1798$ mb, $\eta=0.365$. We
scale $\sigma_{a}$ and $\eta$ from the SW rates that were for a Be production
target ($\sigma_{a}=227$ mb and $\eta=0.14$). The secondary channel is 30 m
long with 3.125 msr and $\Delta p/p$=2%. The decay factor $d$ is the
probability the secondary particle of mass $M$, mean life $\tau$, and momentum
$p$ survives a distance $x=30$ m:

$d(x)=\exp{\left(-Mx/(p\;c\tau)\right)}.$ (2)

Following Yamamoto Yamamoto:1981zr , we determine the production efficiency
from the absorption lengths in Ref. Denisov:1973zv  for protons, pions, and
kaons. Although the absorption cross sections tabulated in Ref. Denisov:1973zv
are at higher momenta than in our application, they are reasonably flat. This
is also apparent from the corresponding plots of total cross sections (Figs.
51.6-51.9) in the RPP Zyla:2020zbs . We determine the nuclear absorption cross
section for the protons in the production target from Ref. Denisov:1973zv  and
note that Yamamoto Yamamoto:1981zr  points out that it scales like $A^{2/3}$.
For forward-angle production, 3 GeV/$c$ pion fluxes of about 10 MHz are
possible. Similarly, K+ fluxes are an order of magnitude less, and K- fluxes
are another order of magnitude below that.

These modest kaon fluxes would not inspire rare-decay experiments; however,
they do seem well-suited to the physics program described earlier in this
manuscript. At these $\pi$/K rates, the beam can be directly counted, which
offers important benefits to experimenters working with these beams. Although
the low power associated with the proton beam (0.6 kW) is the root cause of
the lower-than-ideal $\pi$/K rates, it has a silver lining: it makes it much
easier (and less expensive) to deal with the shielding, rad-hardening of
magnets, activation issues, and cooling of the production target and
surrounding region than has been the case with higher power beams
Densham:2010fva ; Agari:2012gj ; Agari:2005zz .

Secondary particle channels have been designed (see, for example
Yamamoto:1981zr ; Pile:1992vk ; Doornbos:2000hb ) at a number of different
facilities that would serve the application described here as well. They
employ one, usually two Wien filters Ieiri:2013cpa  (crossed E and B field
regions) to select either $\pi$ or K beams.

Figure 2: Pion and Kaon rates that could be expected at the end of a 30 m-long
channel with a solid angle of 3.125 msr and a momentum bite of 2% $\Delta
p/p$. The production target is assumed to be 6 cm Pt. Decay along the length
of the channel, as well as secondary particle production efficiency and
nuclear absorption cross sections of the protons on the Pt target are also
factored in to this prediction. The legend denotes different assumptions for
the production angle.

Summary: The goals of current EM facilities would benefit greatly from having
hadron-beam data of a quality similar to that of EM data. To this end, it is
commonly recognized that a vigorous U.S. program in hadronic physics requires
a modern facility with pion and kaon beams. A pion beam and a facility in
which $\pi N$ elastic scattering and the reactions $\pi^{-}p\to K^{0}\Lambda$,
$\pi^{-}p\to K^{0}\Sigma^{0}$, $\pi^{-}p\to K^{+}\Sigma^{-}$, and $\pi^{+}p\to
K^{+}\Sigma^{+}$ can be measured in a complete experiment with high precision
would be very useful. Full solid angle coverage is required to study inelastic
reactions such as $\pi^{-}p\to\eta n$, $\pi^{+}p\to\pi^{0}\pi^{+}p$, or
strangeness production (among many other reactions). Such a facility ideally
should be able to allow baryon spectroscopy measurements up to center-of-mass
energies $W$ of about 2.5 GeV, which would require pion beams with momenta up
to about 2.85 GeV/$c$. The 2 GeV/$c$ pion beam at J-PARC will allow baryon
spectroscopy measurements up to $W\approx 2150$ MeV.

The White Paper Briscoe:2015qia  outlined some of the physics programs that
could be advanced with a hadron-beam facility. These include studies of baryon
spectroscopy, particularly the search for “missing resonances” with hadronic
beam data that would be analyzed together with photo- and electroproduction
data using modern coupled-channel analysis methods. A hadron beam facility
would also advance hyperon spectroscopy and the study of strangeness in
nuclear and hadronic physics.

At the end of the White Paper Briscoe:2015qia , there is a list of endorsers
who have expressed support for the initiative described herein: 135
researchers from 77 institutes representing 20 countries around the world.

Acknowledgment: We thank the numerous colleagues who have contributed either
directly or indirectly to this work. This material is based upon work
supported by the U.S. Department of Energy, Office of Science, Office of
Nuclear Physics under Contracts No. DE–SC0016583, DE–SC0016582, and
DE–SC0014323.

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