$\tilde{\mathbf{G}}\to\mathbf{G}$ is finite and central. By Schur’s lemma and
irreducibility, $\mathbf{N}$ thus acts on $V_{\mathbb{C}}$ by scalar
multiplication by roots of unity. Therefore, there exists $n\in\mathbb{N}$
such that $\mathbf{N}$ acts trivially on
$V_{\mathbb{C}}^{\otimes_{\mathbb{C}}n}$. Since the representation of
$\tilde{\mathbf{G}}$ on $V_{\mathbb{C}}^{\otimes_{\mathbb{C}}n}$ is defined
over $\mathbb{R}$, we deduce that it induces a real algebraic representation
of $G$ on $V^{\otimes_{k}n}=V^{\otimes_{\mathbb{R}}n}$.

In case (2),
$\rho_{\mathbb{C}}\colon\mathfrak{g}_{\mathbb{C}}\to\mathfrak{gl}(V)$ lifts to
an irreducible algebraic representation
$\tilde{\mathbf{G}}\to\operatorname{GL}(V)$. By the same argument as in the
first case, for some $n\in\mathbb{N}$ the kernel $\mathbf{N}$ of the covering
map acts trivially on $V^{\otimes_{\mathbb{C}}n}$. Hence, the action of
$\tilde{\mathbf{G}}$ on $V^{\otimes_{k}n}=V^{\otimes_{\mathbb{C}}n}$ factors
through an algebraic representation of $\mathbf{G}$. By restriction of
scalars, we can view $\mathbf{G}$ and
$\operatorname{GL}(V^{\otimes_{\mathbb{C}}n})$ as groups of real points of
algebraic groups defined over $\mathbb{R}$. Composing the map $G\to\mathbf{G}$
with the representation of $\mathbf{G}$ on $V^{\otimes_{\mathbb{C}}n}$ we
obtain the desired lift of $\rho^{\otimes_{k}n}$. ∎

###### Proof of Proposition A.3.

By Lemma A.5, $\mathfrak{f}=\operatorname{Lie}(F)$ is an epimorphic subalgebra
of $\mathfrak{g}=\operatorname{Lie}(G)$. Then Lemma A.4 implies that
$F^{\circ}$ is epimorphic in $G^{\circ}$ in the sense of Definition A.2(ii). ∎

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# The REDTOP experiment

C. Gatto
On Behalf of REDTOP Collaboration

###### Abstract

The $\eta$ and $\eta^{\prime}$ mesons are almost unique in the particle
universe since they are Goldstone and the dynamics of their decays are
strongly constrained. Because the $\eta$ has no charge, decays that violate
conservation laws can occur without interfering with a corresponding current.
The integrated $\eta$-meson samples collected in earlier experiments amount to
$\sim 10^{9}$ events, dominated by the WASA-at-Cosy experiment. A new
experiment, REDTOP (Rare Eta Decays with a TPC for Optical Photons), is being
proposed, either at the proton Delivery Ring of Fermilab or at the Proton
Synchrotron of CERN, with the intent of collecting in excess of 1012 $\eta$/yr
(1010 $\eta^{\prime}$/year) for studying rare decays. Such statistics are
sufficient for investigating several symmetry violations, and for searching
particles beyond the Standard Model. Recent studies have indicated that REDTOP
has very good sensitivity to processes that couple the Standard Model to new
physics through three of the so-called _portals_ : the vector, the scalar and
the axion portal. An upgraded version of the detector will be proposed, at a
later stage, for a run at the PIP-II accelerator complex, where the $\eta$
mesons will be produced in tagged mode. The physics program, the accelerator
systems and the detector for REDTOP are discussed.

NFN Sezione di Napoli, via Cinthia, 80126 Napoli, Italy
also, Northern Illinois University, De Kalb (IL)

> _Talk presented at the 2019 Meeting of the Division of Particles and Fields
> of the American Physical Society (DPF2019), July 29–August 2, 2019,
> Northeastern University, Boston, C1907293_.

##  1 Introduction

In the last few years, the evidence that the Standard Model of particle
physics is incomplete has becoming more stringent and the experimental
community is pressed to engaging in new experiments that would help to uncover
the New Physics. The LHC complex was designed to search for physics Beyond the
Standard Model (BSM) at energies of the order of few TeV. The failure, at
least up to this writing, in discovering any hint of it is an indication of at
least two facts: a) the New Physics most immediately accessible to the
experimenter probably lies at low energies, rather than at high energies, and
b) such New Physics is elusive, and it the couple to the Standard Model
physics too faintly to be detected by experiments at colliders. While the
latter, in fact, have several nice features from the experimental point of
view, the cannot compete in terms of luminosity with fixed target experiments.

The latest theoretical models prefer gauge bosons in the MeV-GeV mass range[1,
2, 3]. In such mass regime, strong astrophysical and cosmological constraints
are weakened or eliminated, while constraints from high energy colliders are,
in most cases, inapplicable. On the other side, in order to successfully
explore those models, beam luminosities considerably higher than those
available at colliders are required , as the former usually, do not exceed the
1034-1035 cm-2sec-1 range. Fixed target experiments in most cases exceed that
range, as they can be carried at high intensity facilities and under
reasonably controlled conditions (as compared, for example, to beam dump
experiments).

The design of the REDTOP experiment is based on the above observations. It is
a high intensity $\eta$/$\eta$’-factory in a fixed target configuration with
beam luminosity of at least 1034 cm-2sec-1. The mass range for potential
discoveries is roughly [15 MeV-950 MeV], limited on the lower side by the
resolution of the detector and on the upper side by the mass of the decaying
mesons.

##  2 Rationale for an $\eta/\eta^{\prime}$-factory

The $\eta$ and $\eta$ ’ meson have been widely studied in the past, as their
special nature has attracted the curiosity of the scientists[4]. The $\eta$ is
a Goldstone boson, therefore its QCD dynamics is strongly constrained by that
property. In nature there are only few Goldstone bosons. Furthermore, the
$\eta$ is, at the same time, an eigenstate of the C, P, CP, I and G operators
with all zero eigenvalues (namely: $I^{G}J^{PC}=0^{+}0^{-+}$) which makes it
identical (except for parity) to the vacuum or the Higgs boson. In that
respect, it is a very pure state, carrying no Standard Model charges and its
decays do not involve charge-changing currents. Any coupling to BSM states,
therefore, does not interfere with Standard Model charge changing operators.
Another consequence of the above properties is that the $\eta$ and $\eta$ ’
have an unusually small decay width, electromagnetic and strong decays are
suppressed up to the order O(10-6 ) favoring the study of more rare decays,
especially those related to BSM particles and to violation of discrete
symmetries.

Figure 1: Physics landscape for an $\eta/\eta^{\prime}$ factory.

Considering the present limits on the parameters associated to BSM physics and
the practical limitations of current detector technologies, the next
generation of experiments should be designed with the goal of producing no
less than$10^{11}-10^{12}$ $\eta$ mesons. The physics reach of an experiment
with such statistics is quite broad, spanning several aspects of physics BSM.
A summary of the physics landscape spanned by REDTOP is presented in Fig. 1
Along with BSM Physics, the availability of such a large sample of flavor-
conserving mesons will also allow to probe the isospin violating sector of low
energy QCD to an unprecedented degree of precision. The large number of
processes that could be studied at the proposed $\eta/\eta^{\prime}$-factory
will provide not only a nice scientific laboratory but also the source of many
topics for Ph.D. thesis.

The REDTOP experiment is currently being proposed for running either at CERN
or Fermilab. BNL is also a suitable laboratory. The design luminosity in the
former case, corresponds to the production of $\sim 10^{12}$ $\eta$
mesons/year, being limited by the availability of an adequately intense beam.
The design luminosity if running at Fermilab, corresponds to the production of
$\sim 10^{13}$ $\eta$ mesons/year, in this case the limitation deriving from
the detector and DAQ technologies available in the foreseeable future. The
production cross section for the $\eta^{\prime}$ meson, in a similar
kinematics regime, is about two order of magnitude smaller, pointing to an
expected meson yield of $10^{10}-10^{11}$ $\eta$’ mesons/year.

##  3 Golden channels

Among the physics processes listed in Fig. 1, some have a larger
signal/background ratio and have more potential for a discovery or for a
direct measurement. Some of these g _olden channels_ are briefly discussed
below.

###  3.1 CP Violation from Dalitz plot mirror asymmetry in
$\eta/\eta^{\prime}$$\rightarrow\pi^{+}\pi^{-}\pi^{o}$

Considering the $\eta$ meson decay:

$\eta\rightarrow\pi^{+}\pi^{-}\pi^{o}$ (1)

if CP invariance is satisfied, the dynamics of the charged pions should be
totally symmetric. This would imply that, the Dalitz plot of decay (1) should
show no signs of asymmetries. If on the other hand the Dalitz plot shows any
mirror-asymmetry, this would be an indication of CP and C violation. This
asymmetry cannot be generated by SM operators at tree level, nor by higher
level operators that generate also EDMs (at tree level). Therefore, CP-
violation from this process is not bounded by EDM as is the case, for example,
for the process: $\eta\rightarrow 4\pi$. Consequently, this channel is
complementary to EDM searches even in the case of T and P odd observables,
since the flavor structure of the $\eta/\eta^{\prime}$ is different from the
nucleus. In this situation, CP violation could arise from the interference of
the CP-conserving weak interaction with a new interaction that breaks C and CP
generating a charge asymmetry in the momentum distribution of
the$\pi^{+}\pi^{-}$ systems. Recent studies[5] indicate that the C- and CP-
violating amplitude with total isospin I=2 is much more severely suppressed
than that with total isospin I=0. Consequently, the I=0 $\eta/\eta^{\prime}$
systems is privileged, compared to any other mesonic systems, for CP-violation
searches.

Figure 2: 3-D representation of the Dalitz plot for the
$\eta\rightarrow\pi^{+}\pi^{-}\pi^{o}$ process (courtesy of S. Gardner and J.
Shi).

A 3-dimensional representation of the X and Y variables for the process (1) is
shown in Fig. 2. The appearance of terms that are odd in X would indicate both
C and CP violation. The detection of charged pions in REDTOP is based on the
measurement of the Cerenkov angle of the photons radiated in the aerogel (cfr.
Sec. 4). Therefore, the non-uniformity of the magnetic field, which in general
corresponds the largest contribution to the systematic error in the asymmetry
of kinematics variables of positive and negative charged particles, plays no
role at REDTOP. The expected sensitivity for this process is currently under
study with the REDTOP detector, although it is expected to be higher than with
more traditional, magnetic spectrometers.

###  3.2 Dark photon searches

A search for a dark photon can be carried out at an
$\eta/\eta^{\prime}$-factory by looking for final states with a photon and two
leptons. Considering the process:

$\eta\rightarrow\gamma A^{\prime}\rightarrow\gamma+l^{+}l^{-}$ (2)

in the hypothesis that the mass of this dark photon is smaller than the mass
of the $\eta/\eta^{\prime}$ meson, it will be relatively straightforward to
observe it. A detailed simulation of the process and the expected background,
including many instrumental effects, has been performed by the Collaboration
within the “Physics Beyond Collider” program[6].

###  3.3

Figure 3: REDTOP sensitivity to the $\epsilon$ parameter for 1012 POT. Figure
4: REDTOP sensitivity to the $\epsilon$ parameter for 1012 POT.

An integrated beam flux of $10^{12}$ POT (as available at CERN, see Sec. 5
below) has been assumed. A simple “ _bump-hunt_ ” analysis was performed, by
looking at the invariant mass of di-leptons associated to a prompt photon. The
sensitivity to the $\epsilon$ coupling constant for $\eta/\eta^{\prime}$
combined runs is shown in Fig. 2. The largest contributing background was
found to be from mis-measured leptons from the 3-body decay
$\eta\rightarrow\gamma+l^{+}l^{-}$. The sensitivity to this channel would be
greatly enhanced by including in the analysis the reconstruction of secondary
vertexes (associated to long decaying dark photons) and with a larger
integrated beam flux (available, for example,at Fermilab or BNL). These
studies are currently in progress.

###  3.4 Searches for Axion Like Particles (ALP)

This study has been performed as part of the “Physics Beyond Collider”
program[6], where specific assumptions were done regarding the coupling of an
ALP to the Standard Model. Among the three benchmark processes designated by
the PBC for this portal, two of them have been exploited at REDTOP: a search
for ALP with fermion dominant coupling and with gluon dominant coupling.

Assuming a single ALP state which predominant couples to fermions, all
phenomenology (production and decay) can be determined as a function of {mALP,
f${}_{l}^{-1}$, f${}_{q}^{-1}$}. For this study, a further assumption:
f${}_{l}^{-1}$= f${}_{q}^{-1}$was made. The processes considered are:

$\eta\rightarrow\pi^{+}\pi^{-}ALP\rightarrow\pi^{+}\pi^{-}+l^{+}l^{-}$ (3)
$\eta\rightarrow\pi^{+}\pi^{-}ALP\rightarrow\pi^{o}\pi^{o}+l^{+}l^{-}$ (4)

An integrated beam flux of $10^{12}$ POT (as available at CERN, see Sec. 5
below) has been assumed. A simple “ _bump-hunt_ ” analysis was performed,
looking at the invariant mass of di-leptons associated to two pions. The
sensitivity to the $g_{Y}=\nicefrac{{2v}}{{f_{l}}}$ coupling constant for
$\eta+\eta^{\prime}$ combined runs is shown in Fig. 3 (left). The largest
contributing background was found to be from mis-measured particles from the
4-body decay $\eta\rightarrow\pi\pi l^{+}l^{-}$.

Figure 5: REDTOP sensitivity for ALP’s with dominant lepton (top) and gluon
(bottom) coupling for$10^{17}$ POT with $E_{kin}$=1.8 GeV on Be targets.

If the ALP has a dominant coupling to gluons, instead, it would mostly be
produced from beamsstrahlung processes associated to the proton beam
interacting with the target matter. Several processes can be responsible for
the emission of an ALP: a) Drell-Yan processes: $q\bar{q}\rightarrow
ALP\rightarrow l^{+}l^{-}$, b) proton beamsstrahlung processes[7]:
$p\,N\rightarrow p\,N\,ALP$ with $ALP\rightarrow l^{+}l^{-}$, c) Primakoff
processes[8]: $p\,Z\rightarrow p\,Z\,ALP$. The sensitivity to the
f${}_{g}^{-1}$ parameter is shown in Fig. 3 (right).

The sensitivity to a ALP decaying into leptons would be greatly enhanced by
including in the analysis the reconstruction of secondary vertexes (observed
in case of long decaying ALPs) and with a larger integrated beam flux
(available, for example,at Fermilab or BNL). These studies are currently in
progress.

###  3.5 New scalar particles

A scalar H could be observed in a $\eta/\eta^{\prime}$ final state in
association with a $\pi^{0}$:

$\eta\rightarrow\pi^{0}H^{\prime}\rightarrow\pi^{0}+l^{+}l^{-}.$ (5)

Within the Standard Model, this process can only occur via a two-photon
exchange diagram with a branching ratio of the order of $10^{-9}$. If such a
light particle exists, even with a mass larger than the $\eta/\eta^{\prime}$
meson, which couples the leptons to the quarks, the probability for this
process could be increased by several orders of magnitude, changing
dramatically the dynamics of the process. Two groups of theoretical models
postulating a BSM light scalar are receiving great attention lately: the
Minimal Extension of the Standard Model Scalar Sector[9, 10] and the models
containing Higgs bosons with large couplings to light quarks[11, 12, 13]. From
the experimental point of view, these models are complementary: the former
predicting large coupling to the b-quark and to gluons but a small one to the
light quarks, while the latter predicts a large coupling to light quarks. An
observation at a $\eta/\eta^{\prime}$ factory of the process (5) would be an
indication that the second set of models would be the most likely extension to
the SM. Vice-versa, an observation of a scalar at a B-factory but not at
REDTOP would favor the first groupp of models.

A detailed simulation of the process (5) and of the foreseen background,
including many instrumental effects, has been performed by the Collaboration
within the “Physics Beyond Collider” program[6] assuming the Minimal Extension
of the Standard Model Scalar model.

###  3.6

Figure 6: REDTOP sensitivity to the $\sin^{2}\theta$ parameter[9, 10] for 1012
POT. Figure 7: REDTOP sensitivity to the $\sin^{2}\theta$ parameter[9, 10] for
1012 POT.

An integrated beam flux of $10^{12}$ POT (as available at CERN, see Sec. 5
below) has been assumed. A simple “ _bump-hunt_ ” analysis was performed,
looking at the invariant mass of di-leptons associated to a prompt photon. The
sensitivity to the $\sin^{2}\theta$ parameter [9, 10] is shown in Fig. 3.6.
The largest contributing background was found to be from the 3-body decay
$\eta\rightarrow\gamma+l^{+}l^{-}$ where an extra $\gamma$ fakes a $\pi^{0}$
in the final state.

A preliminary sensitivity analysis for several experiments (including REDTOP)
based on the second set of models can be found in Ref. [11]

###  3.7 Other Golden channels

Besides the rare processes discussed above, several other processes have a
good potential for discovery. They are briefly listed below.

####  3.7.1 Test of CP invariance via $\gamma$* polarization studies:

CP-violation can also be investigated with a virtual photon decaying into a
lepton-antilepton pair, as in:

$\eta\rightarrow\pi^{+}\pi^{-}\gamma^{*}\text{ with }\gamma^{*}\rightarrow
l^{+}+l^{-}.$ (6)

by considering the asymmetry

$A_{\Phi}=\frac{N(\sin\phi\cos\phi>0)-N(\sin\phi\cos\phi<0)}{N(\sin\phi\cos\phi>0)+N(\sin\phi\cos\phi<0)}$
(7)

where $\phi$ is the angle between the decay planes of the lepton-antilpton
pair and the two charged pions. CP invariance requires $A_{\Phi}$ to vanish.
At the present, the measurement of such asymmetry performed by the WASA
collaboration Adlarson et al. [14] is the best available, and it is consistent
with zero within the measurement errors. Unfortunately, that measurement is
largely dominated by the statistical error, from the production of only $\sim
10^{9}\>\eta$-mesons. The larger statistics of REDTOP will improve the
systematic error by almost two orders of magnitude.

####  3.7.2 The proton radius anomaly

One of the existing and still unexplained anomalies present in the Standard
Model is related to the measurements of the proton radius $R_{p}$ with
electron and muon probes111Although a very recent measurement has reconciled
the anomaly, the difference between the averages is still an open question.
REDTOP will contribute independently to clarify the situation.

The processes involved are:

$\eta\rightarrow\gamma e^{+}e^{-}\text{ and
}\eta\rightarrow\gamma\mu^{+}\mu^{-}$ (8)

Other types of $R_{p}$ measurements, using muonic atoms (see, for example,
CODATA-2012), or using elastic scattering of electrons and muons on hydrogen
atoms, have found a discrepancy corresponding to several sigma in the electron
vs muon case. It is worth noting that such processes occur mainly trough the
exchange of one virtual photon, while processes of the type
$\eta\rightarrow\gamma l^{+}l^{-}$ can occur either via one photon, as shown
in figure 8 diagram a), or two photons, as shown in figure 8 diagram b).

Figure 8:  Diagrams contributing to the proton radius

A light scalar particle S with a different coupling with electrons and muons
would mediate this process, as shown in diagram c) of figure 8, would explain
this anomaly of the Standard Model. Therefore, an experiment able to precisely
measure the branching ratios of this particle might help in explaining the
$R_{p}$ anomaly.

In REDTOP, the processes (8) are detected simultaneously and within the same
experimental apparatus. Consequently, most of the systematic errors are common
to the two processes and they factor out in the ratio of the corresponding
branching ratios, enhancing the precision of the overall measurement.

##  4 The Experimental Technique and Requirements

The most efficient way to produce $\eta/\eta^{\prime}$ mesons is by hadro-
production from nuclear scattering of a proton beam onto a nuclear target.
Above Ekin$\approx 1.4$ GeV several intra-nuclear baryonic resonances are
created, whose decay produce an $\eta$-meson. The $\eta$-meson production
cross section increases almost linearly above such threshold, while the QCD
background remains approximately constant. Although an increase of the beam
energy would impact the $\eta$ yield positively, the larger multiplicity of
the background and the momentum of the final state particles (mostly, baryons,
slow pions and nuclear remnants) would complicate the event selection and
affect adversely the _signal/noise_ ratio.

#### Beam and target requirements

Extensive studies have been conducted with the _GenieHad_[15] event-generator
framework using multiple beam and target parameters. Such studies indicate
that a proton beam with Ekin$\approx 1.8-1.9$ GeV impinging on a thin, low-Z,
high-$\nicefrac{{A}}{{Z}}$ material like a Beryllium or Lithium target has
been found as an optimal configuration. The low-Z requirement helps in
minimizing the multiplicity of the fragmentation products, QCD-generated. For
example, the multiplicity of primary neutrons produced by a Nb target
increases more than 20% wrt a Be target, while the increase of primary protons
is almost 90% (from _GenieHad_ simulations). The high-$\nicefrac{{A}}{{Z}}$
requirement reflects the factor $\sim$7x between the $\eta$ production cross
section for neutrons vs protons. Finally, the thin targets requirement
constrains, on one side, the z-coordinate of the $\eta$ production vertex,
and, on the other side, it minimizes the multiple scattering affecting the
$\eta$ decay products when they escape from the target. By using 10 foils,
spaced 10 _cm_ apart, one would provide the necessary total material budget
for the required luminosity, while the pile-up due to multiple beam
interactions within the same trigger could be easily reduced with vertexing
techniques. A similar study for the $\eta^{\prime}$ case yields an optimal
range for Ekin of about 3.5-4 GeV.

The expected inelastic interaction rate for the combination of energy range
and target systems indicated above as well as the $\eta/\eta^{\prime}$
production has been calculated with several nuclear scattering models
available in _[15]_ (more specifically, _Urqmd, Gibuu, PHSD_ and _Jam_). They
produced comparable results and predict an inelastic interaction probability
of the order of 1% with a probability for an event to contain a $\eta$ meson
of the order of 0.25% - 0.5%. The probability to generate an $\eta^{\prime}$
meson is two orders of magnitude smaller. A CW proton beam delivering $1\times
10{}^{11}$POT/sec would generate a rate of inelastic interaction of about 1
GHz and a $\eta$-meson yield of $2.5-5\times 10{}^{6}$$\eta/sec$,
corresponding to $2.5-5\times 10{}^{13}$$\eta/yr$. The beam power
corresponding to the above parameters is approx. 30 W, of which 1% (or 300 mW)
is absorbed in the target systems. Each of the 10 foils will have to dissipate
about 30 mW, which is easily achievable radiatively. These number roughly
double for the beam required at a $\eta^{\prime}$-factory.

#### Detector requirements

The $\eta$ mesons generated with the above beam parameters are almost at rest
in the lab frame, receiving only a small boost in the direction of the
incoming beam (see Fig. 9). This is a consequence of their production
mechanism as they are the decay products of an intranuclear resonance in the
target material. Studies performed with _GenieHad_ have indicated that the
$\eta-$spectrum is almost independent from the beam energies in the [1.46-2.1]
GeV range. Consequently, an hermetic detector covering the entire solid angle,
is one of the requirements for REDTOP.

Figure 9: Total energy of $\eta$ mesons from a $E_{kin}$=1.8 GeV proton beam
scattered on REDTOP targets (_GenieHad_ simulation).

A correct identification of the final states particles is, also, of paramount
importance for an experiment exploring rare processes. On one side, the vast
majority of the processes listed in Fig. 1 have two leptons at at least one
photon in the final state. On the other side, the QCD background, which has a
production rate two order of magnitudes larger, is populated almost invariably
by protons, neutrons, slow pions and nuclear remnants. These are relatively
slow particles, as shown in Fig. 9 for the case of protons an pions.
Furthermore, neutrons impinging onto the calorimeter would easily be mistaken
as photons if a proper particle identification (PID) is not in place. Finally,
the identification of$e^{+}e^{-}$ pairs from photosn converting in the
material upstream the central tracker will help to reject the large background
originating from QCD production of $\pi{}^{o}$ particles. The detector is
inserted in a solenoidal magnetic field which bends the charged particles for
proper $P_{t}$ and electric charge measurement.

Figure 10: Momentum of protons (left) and charged pions(right) from inelastic
scattering of a $E_{kin}$=1.8 GeV proton on REDTOP targets (_GenieHad_
simulation). Figure 11: Cross section of REDTOP detector

#### The Optical TPC

Protons and slow pions account for the largest charged background at REDTOP.
In average 0.6 charged pions and 1.8 protons are produced every nsec in the
target systems by the $E_{kin}$=1.8 GeV proton beam.

Figure 12: Charged pions (left) and proton (right) multiplicity from inelastic
scattering of a $E_{kin}$=1.8 GeV proton on REDTOP targets (_GenieHad_
simulation).

A charged track detector mostly blind to them is required in order to identify
more rare decays. These particles have a consistently low value of $\beta.$
Consequently, the threshold characteristic of the Cerenkov effect could be
exploited to build a detector insensitive to this hind of background.

The central tracker proposed for REDTOP (the red dodecagon in FIG. 11) is an
Optical TPC[16, 17] (OTPC). It measures the transverse momentum of electrons
or the $\beta$ of heavier particles (muons and fast pions). It is a vessel
filled with gas ($CH_{4}$) with the inner wall covered by an aerogel radiator
with a thickness of 3 cm. The external walls of the chamber are instrumented
with optical photo-sensors (LAPPD or sipm’s) with a pixel size of few
$mm^{2}$. When an electron or a positron with a $\beta$ above the Cerenkov
threshold of $CH_{4}$ traverses the gas, it bends in the solenoidal magnetic
field while also radiating photons. The sweep of the latter, being collected
by the photo-sensors at the external walls of the device, has a specific
pattern corresponding to the $P_{t}$ of the particle. Position and direction
of the particle are obtained by combining the pattern of the ring radiated
when the aerogel is crossed with the information of the impinging point on the
photo-sensors.

Slower particles like muons and pions, typically with $\beta$ below the
Cerenkov threshold in the gas, produce a characteristic photon ring when they
cross the aerogel. This is detected from the OTPC photo-sensors and
reconstructed, providing a measurement of the kinematic parameters of the
particle. Protons and pions from QCD scattering are consistently below
detection sensitivity of the OTPC and do not constitute a sizable background
for the experiment. The magnetic field (0.6 T) also provides the magnetic
bottling preventing these very slow particles particles from reaching the
calorimeter with elevated rates.

#### ADRIANO2 calorimeter

Dual-readout calorimetry[18, 19] is a proposed technique to achieve energy
compensation in hadronic showers produced in high energy experiments

. One particular implementation: ADRIANO, where both readout components are
integrally active, has been developed in recent years by T1015
Collaboration[20, 21]. One of the advantages with ADRIANO is that, with a
proper layout, the dual-readout method can be used also for an electromagnetic
calorimeter in a way that the two read-out components would provides the PID
of the impinging particle. The application of dual-readout for PID purposes is
illustrated in Fig. 13 for particles of different species and same energy (100
MeV). The separation between photons and neutrons, is better than 4$\sigma$,
and it exceeding the requirement of 99% established with software simulations.

Figure 13: Plot of S vs Č signals for several 100 MeV particles in ADRIANO
(ilcroot simulation)

REDTOP also requires a finer granularity than that achievable with the, log
based, ADRIANO technique. A newer implementation of ADRIANO is being proposed:
ADRIANO2, where the lead-glass and the scintillating strips, read by WLS
fibers, are replaced by tiles with direct sipm readout[22, 23, 24].

#### Fiber tracker

A fiber tracker, with an identical technology as implemented for the LHCb
upgrade[25], is located around the beam pipe, at a radius r$\simeq$5 cm around
the z-axis. Three superlayers are stacked together, interspaced with
structural foam of 1 cm providing mechanical stability. Each superlayer is
obtained from a mat of 5 layers of scintillating fibers, with a diameter of
250 $\mu m$. The space resolution of each superlayer is $\sim 70\mu m$, as
measured by LHCb at a test beam. The fiber tracker serves two main purposes:
a) it provides a vertex measurement for the reconstructed event, and b) it
identifies photons converting into $e^{+}e^{-}$ pairs inside the OTPC
(typically, in the inner wall of the chamber or in the aerogel). The
determination of the primary vertex of the event identifies the foil where the
inelastic interaction occurred and it provides the position of the
$\eta$-mesons. If detached vertexes are found not belonging to the very few
produced $K_{short}$, that will be a clear indication that new physics is
being observed.

#### Superconducting solenoid

A 0.6 T solenoidal magnetic field is required to measure the $P_{t}$ of the
particles with $\beta\approx 1$. The field will also magnetically bottle the
very low momentum particles, preventing them from reaching the calorimeter.
The solenoid built for the, now dismantled, Finuda experiments[26] matches all
operational and dimensional parameter required for REDTOP. It fits nicely
trough the hatch that connects the AP50 hall (that would house REDTOP if
running at Fermilab) and it can be transported on rails to its final location.
The Collaboration has made a formal request to Istituto Nazionale di Fisica
Nucleare (owning the magnet) for a loan to the experiment.

##  5 The Acceleration Scheme

Although the beam requirements for REDTOP are modest, none of the existing HEP
laboratories worldwide as a ready-to-go accelerator satisfying all the
conditions. The Collaboration has engaged in a broad exploration and three
possible hosting laboratories have been identified.

##### Fermilab configuration.

The low energy proton beam available at Fermilab has a pulsed structure with
84 bunches and a fixed energy of 8 GeV. The buckets are distributed to the
accelerator complex and either accelerated or dumped in order to create a
secondary beam. On the other hand, REDTOP requires a Continuous Wave (CW)
proton beam with a user selectable energy, with a range considerably lower
than that available (cfr. Sec. 4). The accelerator scheme[27] proposed for
REDTOP foresee the extraction of a single pulse from the booster (consisting
of $\sim$4$\times$1012 protons) which is subsequently injected in the Delivery
Ring (former debuncher in anti-proton production at Tevatron). The energy is,
then removed from the beam by operating the RF cavities in reverse, until it
reaches the required value. The time required for reaching 1.8 Gev is $\sim$5
seconds (about 3.3 for the 3.5 GeV case). Once the desired energy is reached,
the beam is kept circulating inside the ring where the buckets relax
adiabatically. Slow extraction to REDTOP (located in the nearby AP50 hall)
occur over $\sim$40 seconds. The proposed accelerator scheme requires minimal
changes to the existing complex and involves no extra beam elements. In fact,
the extra RF cavity necessary to stabilize the energy removal process is
already available as a spare for the Mu2e experiment. Furthermore, the
extraction point to AP50 corresponds to a betatron phase advance of 270o
compared to the location of the existing Mu2e electrostatic septum.
Consequently, the latter can be used also to shift the protons for the final
extraction via a Lambertson magnet. The total time to decelerate-debunch-
extract the beam is 51 sec, corresponding to a duty cycle $\sim$80%.

With the above scheme, large beam losses in the Delivery Ring will occur if
beam is decelerated from injection at 8 GeV (corresponding to $\gamma$=9.53)
to <2 GeV ($\gamma$ = 3.13) through the natural transition energy of the ring:
$\gamma{}_{t}$ = 7.64. Transition can, however, be avoided by using select
quadrupole triplets to boost $\gamma{}_{t}$ above beam $\gamma$ by 0.5 units
throughout deceleration until $\gamma{}_{t}$ = 7.64 and beam $\gamma$ = 7.14
(corresponding to Ekin=5.76 GeV ). Below 5.76 GeV the Delivery Ring lattice is
reverted to the nominal design configuration. Optical perturbations are
localized within each triplet while the straight sections are unaffected
thereby keeping the nominal M3 injection beamline tune valid[27].

##### CERN configuration.

A preliminary study has been performed at CERN to provide a beam with REDTOP’s
requirements. Several possible schemes have been considered, the most
promising corresponding to the extraction of a 1.8 GeV beam from the
ProtoSynchrotron (PS) which could then be delivered to the East Hall, where
the experiment could be housed. For the moment a 24 GeV/c proton beam is
routinely slow-extracted into the CHARM and IRRAD facilities along the T8 beam
line with a maximum intensity of 6.5$\times$1011 protons per extraction over
0.4 seconds. REDTOP would require a much longer flat top of e.g. 10 seconds at
$\sim$1.8 GeV kinetic energy (as it can be delivered directly from the PS
Booster) in a cycle of 9 basic periods(10.8 s). No show-stoppers have been
identified up to date, although more studies are required. However, the PS the
duty cycle cannot be much higher than 50%, which would already have a
significant impact on the existing CERN physics program. Consequently, the
expected luminosity available to REDTOP at CERN is expected to be
$\sim\nicefrac{{1}}{{10}}$ of that available at Fermilab.

##### BNL configuration.

AT BNL the REDTOP detector could sit comfortably at the end of the existing C4
extraction line. Logistics would be optimal, since the experimental hall is
well accessible and serviced. The beam would be slowly extracted from the AGS
using well known techniques. The instrumentation electronics of the extraction
line is no longer functional and it needs to be refurbished at a very modest
cost ($\mathcal{O}$(100K$)). Altogether, BNL is an excellent candidate for
hosting REDTOP.

##  6 Tagged $\eta$-factory

An upgraded version of the REDTOP, t-REDTOP, could be run in a later stage of
the experiment at the PIP-II facility, currently under construction at
Fermilab. At the 800 MeV, high intensity (100KW-1MW), CW proton beam, the
production mechanism of the $\eta$-meson is substantially different. The
nuclear process providing the $\eta$-meson would be:

$p+De\rightarrow\eta+^{3}He^{+}$ (9)

Therefore, t-REDTOP requires a gaseous Deuterium target and an extra detector
to tag the ${}^{3}He^{+}$ ion. The production cross section for the process
(9) is approximately five orders of magnitude smaller than at 1.8 GeV and the
gaseous target reduces further the luminosity of the beam. However, the large
intensity of PIP-II more than compensate for that and the number of $\eta-
mesons$ produced at t-REDTOP is expected to be in the range
[$10^{13}/year-10^{14}/year$]. The biggest advantages of a tagged
$\eta$-factory are the following:

  * •

By tagging the production of the $\eta$-meson via the detection of the
${}^{3}He^{+}$ ion, the combinatorics background from $non-\eta$ events, is
greatly diminished. Consequently, the sensitivity of the experiment to New
Physics is increased by a factor proportional to the square root of that
reduction;

  * •

By measuring the momentum of the ${}^{3}He^{+}$ ion in process (9), the
kinematics of the reaction is fully closed. That portends to a better
measurements of the kinematics of the particles detected, since a 4-C
kinematic fit could be applied;

  * •

Since the kinematics is closed, any long lived, dark particle escaping
detection could be identified using the _missing 4-momentum_ technique. The
latter is considerably more powerful than the, 1-, missing pt or missing
energy proposed by some recent experiments searching for dark matter.

The disadvantages of a tagged-$\eta$ experiment are due mostly to the larger
complexity of the experiment, requiring an extra detector at very small angles
and to the necessity to control the halo of the beam at a much higher level.
Also, the mass of new physics explored will be lower, since no
$\eta^{\prime}$-meson could be produced at the PIP-II design energy.

##  7 Timeline

The design of REDTOP experiment introduces several innovations from the point
of view of the accelerator as well as the detector. The way the OTPC is
operated at REDTOP, differs substantially from the current applications[16,
17]. Although, in terms of construction, it is nothing more than a vessel
filled with gas and surrounded by photo-sensors, it still requires substantial
R&D before its design is finalized.

A dual-readout has undergone extensive R&D in the past 15 years both in a
sampling and integrally active configuration. The ADRIANO2 layout, has been
proposed recently and a preliminary R&D has is currently on-going within the
Collaboration[24].

Finally, although no stopping issues have been identified for the accelerator
scheme at any of the hosting laboratories being considered, further studies
are necessary, which also include the full design of the extraction line.

In summary, at least 2-3 years of intense R&D are foreseen before the final
design of the experiment could obtained. Mechanical engineering would require
approximately 1-2 years, although it can occur concurrently with the R&D on
the detector. Once the design is finalized, construction and civil engineering
would take between two and three years, although the fabrication of the
individual subdetectors could happen at different times. The in-kind
contribution of the existing Finuda solenoid would help in reducing the
construction schedules. Altogether, once approved, the completion time of the
experiment is of the order of 6-7 years. After an engineering and a
calibration run, the Collaboration intends to take data for about one year at
E=1.8 GeV and another year at E=3.5 GeV.

##  8 Costing

###  8.1 Summary of costs

A preliminary cost estimate[28] for the construction of the detector has been
submitted to CERN in 2018 in partial fulfillment of the requirements for
participating to the European Strategy for Particle Physics. Table 1
summarizes the costs estimate of the individual components. The total expected
cost, including a contingency factor of 50%, is about $ 51M. A cost estimate,
based on more stringent rules adopted in the US, is currently under way.

Solenoid | 0.2
---|---
Refurbishing, shipping | 0.2

Supporting structure | 1.0
---|---

Target+beam pipe | 0.5
---|---

Fiber tracker | 0.93
---|---
Fiber mats | 0.01
Tooling | 0.45
SiPM array | 0.1
Front-end electronics | 0.12
Back-end electronics | 0.05
Mechanics and cooling | 0.2

Optical-TPC | 10.0
---|---
Vessel | 0.5
Aerogel | 1.0
Photo-sensors (LAPPD option) | 6.0
Front-end electronics | 1.8
Back-end electronics | 0.7

ADRIANO2 | 16.0
---|---
Pb-glass | 2.7
Cast scintillator | 0.75
Tile fabrication | 0.6
SiPM | 6.0
Front-end electronics | 4.0
Back-end electronics | 1.5
Mechanics and cooling | 0.5

Trigger | 1.2
---|---
L0 + L1 | 1.0
L2 farm + networking | 0.2

DAQ | 5.0
---|---
Digitizer |
Networking |

Contingency | 17.0
---|---
50% Contingency | 17.0

Total REDTOP | 51.3
---|---

Table 1: Preliminary cost estimate for REDTOP under EU terms.

###  8.2 Cost reduction

Along with the optimization of the detector layout, the Collaboration is
exploring alternative solutions to reduce the overall costs of the experiment.
The largest contributions to the cost of REDTOP (cfr. Table 1) correspond to
the sensors for the Optical TPC and ADRIANO2, the front-end electronics and
the back-end electronics of ADRIANO2. While the number of SiPM’s reading each
10cm x 10cm tile cannot be reduced (or made smaller) without a proportional
reduction in light-yield, we are considering techniques for ganging multiple
tiles, at the cost of a reduced granularity. This technique will reduce the
number of read-out channels and the load on the L0 trigger. Passive and active
ganging is rapidly becoming a cost-cutting resource in the latest large area
detectors. The radial granularity of ADRIANO2 could easily support ganging
multiple tiles of the same kind (i.e., glass or plastics), without loosing
particle identification power. Studies have been planned to explore the
effects that SiPM ganging would have on event pile-up, shower separation and
muon-polarization measurements. A cheaper alternative (SiPM) is being
considered for the sensors of the Optical TPC. Studies are also under way to
verify if the, intrinsically noisier, SiPM’s could be a valid replacement for
the LAPPD.

##  9 Conclusions

The $\eta$ and $\eta$’ mesons are an excellent laboratory for studying rare
processes and physics BSM. The existing world sample is not sufficient for
breaching into decays violating conservation laws or for searching for new
particles with small coupling to the Standard Model. A new
$\eta/\eta$’-factory is being proposed: REDTOP. The goal is to produce
~$10^{12}$ or more$\eta$ mesons/yr in phase I and ~ 1010 η’ /year in phase II.
Running at Fermilab or Brookhaven would provide a factor 10$\times$ more
mesons. More running phases could use different beam species, like, for
example kaons for a _stopped-K_ experiment. When the future PIP-II facility
will become available, REDTOP can be upgraded into a tagged $\eta$-factory
experiment. Several laboratories have the proper infrastructures and
accelerators to host the experiment (FNAL and BNL being the most optimal).
Novel detector techniques need to be developed and/or optimized: they would
set the stage for next generation of High Intensity experiments. The moderate
cost of REDTOP (50-70 M$), along with the many physics measurements
accessible, make this experiment very attractive.

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