# PSI Ring Cyclotron Proposal R-22-01.1
PIONEER: Studies of Rare Pion Decays

W. Altmannshofer  Santa Cruz Institute for Particle Physics (SCIPP),
University of California Santa Cruz, 1156 High street, Santa Cruz (CA) 95064
USA  H. Binney  Department of Physics, University of Washington, Box 351560,
Seattle, Washington 98195 USA  E. Blucher  Enrico Fermi Institute and
Department of Physics, University of Chicago, 5720 South Ellis Avenue,
Chicago, IL 60637 USA  D. Bryman  Department of Physics & Astronomy,
University of British Columbia 6224 Agricultural Road, Vancouver V6T 1Z1
Canada  TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3 Canada  L. Caminada
Paul Scherrer Institute, 5232 Villigen PSI Switzerland  S. Chen  Department of
Engineering Physics, Tsinghua University, 30 Shuangqing Road, Haidian
District, Beijing, 100084 P. R. China  V. Cirigliano  Institute for Nuclear
Theory, University of Washington, Seattle WA 98195-1550 USA  S. Corrodi
Argonne National Laboratory, High Energy Physics Division, 9700 S Cass Ave,
Lemont, IL 60439 USA  A. Crivellin  Paul Scherrer Institute, 5232 Villigen PSI
Switzerland  Physik-Institut University of Zurich Winterthurerstrasse 190
CH-8057 Zurich Switzerland  Division of Theoretical Physics, CERN,Espl. des
Particules 1, 1211 Meyrin Switzerland  S. Cuen-Rochin  Tecnológico de
Monterrey, School of Engineering and Sciences, Blvd. Pedro Infante 3773 Pte,
Culiacan 80100 Mexico  A. DiCanto  Physics Department, Brookhaven National
Laboratory, Upton, NY, 11973 USA  L. Doria  PRISMA+ Cluster of Excellence and
Johannes Gutenberg Universität Mainz, Institut für Kernphysik, J.-J.-Becher-
Weg 45, 55128 Mainz Germany  A. Gaponenko  Fermi National Accelerator
Laboratory (FNAL), P.O. Box 500, Batavia IL 60510-5011 USA  A. Garcia
Department of Physics, University of Washington, Box 351560, Seattle,
Washington 98195 USA  L. Gibbons  Department of Physics, Cornell University,
109 Clark Hall, Ithaca, New York 14853 USA  C. Glaser  Department of Physics,
University of Virginia, P.O. Box 400714, 382 McCormick Road, Charlottesville,
VA 22904-4714 USA  M. Escobar Godoy  Santa Cruz Institute for Particle Physics
(SCIPP), University of California Santa Cruz, 1156 High street, Santa Cruz
(CA) 95064 USA  D. Göldi  ETH Zurich, Main building, Rämistrasse 101, 8092
Zurich Switzerland  S. Gori  Santa Cruz Institute for Particle Physics
(SCIPP), University of California Santa Cruz, 1156 High street, Santa Cruz
(CA) 95064 USA  T. Gorringe  Department of Physics and Astronomy, University
of Kentucky, 505 Rose Street Lexington, Kentucky 40506-0055 USA  D. Hertzog
Department of Physics, University of Washington, Box 351560, Seattle,
Washington 98195 USA  Z. Hodge  Department of Physics, University of
Washington, Box 351560, Seattle, Washington 98195 USA  M. Hoferichter  Albert
Einstein Center for Fundamental Physics, Institute for Theoretical Physics,
University of Bern, Sidlerstrasse 5, 3012 Bern Switzerland  S. Ito  KEK, High
Energy Accelerator Research Organization, 1-1, Oho, Tsukuba-city, Ibaraki
305-0801 Japan  T. Iwamoto  International Center for Elementary Particle
Physics (ICEPP), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
113-0033 Japan  P. Kammel  Department of Physics, University of Washington,
Box 351560, Seattle, Washington 98195 USA  B. Kiburg  Fermi National
Accelerator Laboratory (FNAL), P.O. Box 500, Batavia IL 60510-5011 USA  K.
Labe  Department of Physics, Cornell University, 109 Clark Hall, Ithaca, New
York 14853 USA  J. LaBounty  Department of Physics, University of Washington,
Box 351560, Seattle, Washington 98195 USA  U. Langenegger  Paul Scherrer
Institute, 5232 Villigen PSI Switzerland  C. Malbrunot  TRIUMF, 4004 Wesbrook
Mall, Vancouver V6T 2A3 Canada  S.M. Mazza  Santa Cruz Institute for Particle
Physics (SCIPP), University of California Santa Cruz, 1156 High street, Santa
Cruz (CA) 95064 USA  S. Mihara  KEK, High Energy Accelerator Research
Organization, 1-1, Oho, Tsukuba-city, Ibaraki 305-0801 Japan  R. Mischke
TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3 Canada  T. Mori  International
Center for Elementary Particle Physics (ICEPP), The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-0033 Japan  J. Mott  Fermi National Accelerator
Laboratory (FNAL), P.O. Box 500, Batavia IL 60510-5011 USA  T. Numao  TRIUMF,
4004 Wesbrook Mall, Vancouver V6T 2A3 Canada  W. Ootani  International Center
for Elementary Particle Physics (ICEPP), The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033 Japan  J. Ott  Santa Cruz Institute for Particle
Physics (SCIPP), University of California Santa Cruz, 1156 High street, Santa
Cruz (CA) 95064 USA  K. Pachal  TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3
Canada  C. Polly  Fermi National Accelerator Laboratory (FNAL), P.O. Box 500,
Batavia IL 60510-5011 USA  D. Počanić  Department of Physics, University of
Virginia, P.O. Box 400714, 382 McCormick Road, Charlottesville, VA 22904-4714
USA  X. Qian  Physics Department, Brookhaven National Laboratory, Upton, NY,
11973 USA  D. Ries  Department of Chemistry – TRIGA site, Johannes Gutenberg
University Mainz, Fritz-Strassmann-Weg 2, 55128 Mainz Germany  R. Roehnelt
Department of Physics, University of Washington, Box 351560, Seattle,
Washington 98195 USA  B. Schumm  Santa Cruz Institute for Particle Physics
(SCIPP), University of California Santa Cruz, 1156 High street, Santa Cruz
(CA) 95064 USA  P. Schwendimann  Department of Physics, University of
Washington, Box 351560, Seattle, Washington 98195 USA  A. Seiden  Santa Cruz
Institute for Particle Physics (SCIPP), University of California Santa Cruz,
1156 High street, Santa Cruz (CA) 95064 USA  A. Sher  TRIUMF, 4004 Wesbrook
Mall, Vancouver V6T 2A3 Canada  R. Shrock  C. N. Yang Institute for
Theoretical Physics and Department of Physics and Astronomy, Stony Brook
University, Stony Brook, NY 11794 USA  A. Soter  ETH Zurich, Main building,
Rämistrasse 101, 8092 Zurich Switzerland  T. Sullivan  Department of Physics
and Astronomy, Elliott Building, University of Victoria, Victoria, BC V8P 5C2
Canada  M. Tarka  Santa Cruz Institute for Particle Physics (SCIPP),
University of California Santa Cruz, 1156 High street, Santa Cruz (CA) 95064
USA  V. Tischenko  Physics Department, Brookhaven National Laboratory, Upton,
NY, 11973 USA  A. Tricoli  Physics Department, Brookhaven National Laboratory,
Upton, NY, 11973 USA  B. Velghe  TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3
Canada  V. Wong  TRIUMF, 4004 Wesbrook Mall, Vancouver V6T 2A3 Canada  E.
Worcester  Physics Department, Brookhaven National Laboratory, Upton, NY,
11973 USA  M. Worcester  Instrumentation Division, Brookhaven National
Laboratory, Upton, NY, 11973 USA  C. Zhang  Physics Department, Brookhaven
National Laboratory, Upton, NY, 11973 USA

(January 10, 2022)

###### Abstract

ABSTRACT: A next-generation rare pion decay experiment, PIONEER, is strongly
motivated by several inconsistencies between Standard Model (SM) predictions
and data pointing towards the potential violation of lepton flavor
universality. It will probe non-SM explanations of these anomalies through
sensitivity to quantum effects of new particles even if their masses are at
very high scales. Measurement of the charged-pion branching ratio to electrons
vs. muons $R_{e/\mu}$ is extremely sensitive to a wide variety of new physics
effects. At present, the SM prediction for $R_{e/\mu}$ is known to 1 part in
$10^{4}$, which is 15 times more precise than the current experimental result.
An experiment reaching the theoretical accuracy will test lepton flavor
universality at an unprecedented level, probing mass scales up to the PeV
range. Measurement of the rare process of pion beta decay,
$\pi^{+}\to\pi^{0}e^{+}\nu(\gamma)$, with 3 to 10-fold improvement in
sensitivity, will determine $\left|V_{ud}\right|$ in a theoretically pristine
manner and test CKM unitarity, which is very important in light of the
recently emerged tensions. In addition, various exotic rare decays involving
sterile neutrinos and axions will be searched for with unprecedented
sensitivity. The experiment design benefits from experience with the recent
PIENU and PEN experiments at TRIUMF and the Paul Scherrer Institut (PSI).
Excellent energy and time resolutions, greatly increased calorimeter depth,
high-speed detector and electronics response, large solid angle coverage, and
complete event reconstruction are all critical aspects of the approach. The
PIONEER experiment design includes a 3$\pi$ sr 25 radiation length
calorimeter, a segmented low gain avalanche detector stopping target, a
positron tracker, and other detectors. Using intense pion beams, and state-of-
the-art instrumentation and computational resources, the experiments can be
performed at the PSI ring cyclotron.

###### Contents

  1. I Introduction
  2. II Theory
    1. II.1 Lepton flavor universality tests and $R_{e/\mu}$
    2. II.2 CKM unitarity and pion beta decay
    3. II.3 Constraints on New Physics
    4. II.4 Heavy Neutrinos and other Dark Sector Physics
  3. III PIONEER Experiment
    1. III.1 Experiment Overview and Strategy
      1. III.1.1 Requirements for measuring $R_{e/\mu}$
      2. III.1.2 Requirements for measuring pion beta decay
      3. III.1.3 Simulations Guiding the Design
    2. III.2 Beam
      1. III.2.1 Beam requirements and target setup
      2. III.2.2 Beam line at $\pi$E5
      3. III.2.3 Beam optimization and studies
    3. III.3 Active target (ATAR)
    4. III.4 Cylindrical Tracker
    5. III.5 LXe Calorimeter
      1. III.5.1 Overview
      2. III.5.2 Photosensors
      3. III.5.3 Cryogenics and Purification
      4. III.5.4 Calorimeter Mechanical Engineering
      5. III.5.5 Other Calorimeter Options
    6. III.6 Trigger and Backend electronics
      1. III.6.1 Trigger design
      2. III.6.2 Calorimeter backend electronics
    7. III.7 DAQ
      1. III.7.1 Data acquisition system
      2. III.7.2 Data Policy
  4. IV Simulations
    1. IV.1 ATAR Simulations
      1. IV.1.1  Background Suppression for the Measurement of the $\pi\to e\nu$ tail fraction
    2. IV.2 Calorimeter Simulations
      1. IV.2.1 Pileup
      2. IV.2.2 Additional Calorimeter Studies
  5. V Sensitivity
    1. V.1 $\pi\to e\nu$
    2. V.2 Exotics
      1. V.2.1 Massive neutrino searches $\pi^{+}\to\ell^{+}\nu_{H}$
      2. V.2.2 Two body muon decay $\mu^{+}\to e^{+}X_{H}$
      3. V.2.3 Other decays
    3. V.3 Pion Beta Decay
  6. VI  Planning for Realization of PIONEER
    1. VI.1 Collaboration
    2. VI.2 R&D
    3. VI.3 ATAR R&D
  7. A  PIENU and PEN
  8. B PiBeta
  9. C Alternative LYSO Calorimeter Considerations
  10. D ATAR technical details
    1. D.1 ATAR R&D plan
    2. D.2 Sensor technology
    3. D.3 High granularity LGAD ongoing R&D
      1. D.3.1 AC-LGADs
      2. D.3.2 TI-LGADs
    4. D.4 Electronics and readout chain
    5. D.5 ATAR0 prototype

##  I Introduction

Precise low-energy measurements of observables that can be very accurately
calculated in the Standard Model (SM) offer highly sensitive tests of new
physics (NP). In light of the existing intriguing hints for lepton flavor
universality (LFU) violating NP Crivellin and Hoferichter (2021); Fischer  _et
al._ (2021); Bryman  _et al._ (2021), the ratio
$R_{e/\mu}=\Gamma(\pi^{+}\rightarrow
e^{+}\nu(\gamma))/\Gamma(\pi^{+}\rightarrow\mu^{+}\nu(\gamma))$ for pion
decays to positrons relative to muons is especially promising: it is one of
the most precisely known observables involving quarks within the SM and NP can
even have (chirally) enhanced effects, making it an extremely sensitive probe
of NP. However, while the uncertainty of the SM calculation for $R_{e/\mu}$ is
very small (with relative precision $1.2\times 10^{-4}$ Cirigliano and Rosell
(2007a)), the current experimental world average is about a factor 15 less
precise, limiting the NP reach.

A new experiment, PIONEER, is proposed at Paul Scherrer Institute (PSI), where
high-intensity pion beams can be delivered. In Phase I, it will bridge the gap
of a factor 15 between theoretical and experimental precision for $R_{e/\mu}$.
With measurements at the $0.01\%$ level in precision, NP up to the PeV scale
Bryman  _et al._ (2011) may be revealed. Such precision would contribute to
stringent tests of LFU in a context where several intriguing hints of LFU
violation (LFUV) have emerged. In addition, it will allow extended searches
for exotics such as heavy neutral leptons and dark sector processes. In later
Phases (II,III), PIONEER will also study pion beta decay
$\pi^{+}\to\pi^{0}e^{+}\nu(\gamma)$ ultimately aiming at an order of magnitude
improvement in precision to determine $\left|V_{ud}\right|$ in a theoretically
pristine manner and test CKM unitarity, for which there is presently a
$3\sigma$ tension Zyla  _et al._ (2020). PIONEER is an ambitious program that
will span more than a decade of research activity.

While we focus on the measurement of the $\pi\to e\nu$ branching ratio
$R_{e/\mu}$, the following sections discuss the theoretical motivation for
pursuing the full rare pion decay program. Discussions of the PIONEER detector
concepts, simulations, estimated sensitivities, and planning for realization
follow. In the final section, we discuss aspects related to training, equity,
diversity and inclusion. Appendices contain greater detail on some of the
topics.

##  II Theory

While no particles or interactions beyond those of the SM have been observed
so far, intriguing hints for LFUV have been accumulated in recent years
Crivellin and Hoferichter (2021); Fischer  _et al._ (2021); Bryman  _et al._
(2021). In particular, the measurements of the ratios of branching ratios (Br)
$R(D^{(*)})=Br[B\to D^{(*)}\tau\nu_{\tau}$]/Br[$B\to D^{(*)}\ell\nu_{\ell}$]
Lees  _et al._ (2012); Aaij  _et al._ (2018); Abdesselam  _et al._ (2019) ,
where $\ell=\mu,e$, and $R(K^{(*)})=Br[B\to K^{(*)}\mu^{+}\mu^{-}$]$/$Br[$B\to
K^{(*)}e^{+}e^{-}$] Aaij  _et al._ (2017, 2019, 2021) deviate from the SM
expectation by more than $3\sigma$ Amhis  _et al._ (2021); Murgui  _et al._
(2019); Shi  _et al._ (2019); Blanke  _et al._ (2019); Kumbhakar  _et al._
(2020) and $4\sigma$ Algueró  _et al._ (2019); Aebischer  _et al._ (2020);
Ciuchini  _et al._ (2019); Arbey  _et al._ (2019), respectively. In addition,
anomalous magnetic moments $(g-2)_{\ell}$ ($\ell=e,\mu,\tau$) of charged
leptons are intrinsically related to LFUV, as they are chirality flipping
quantities. Here, the longstanding discrepancy in $(g-2)_{\mu}$, just
reaffirmed at the level of $4.2\sigma$ Bennett  _et al._ (2006); Abi  _et al._
(2021); Aoyama  _et al._ (2020), can be considered as another hint of LFUV,
since, if compared to $(g-2)_{e}$, the NP contribution scales with a power of
the lepton mass Davoudiasl and Marciano (2018); Crivellin  _et al._ (2018). In
addition, there is a hint for LFUV in the difference of the forward-backward
asymmetries ($\Delta A_{\rm FB}$) in $B\to D^{*}\mu\nu$ vs $B\to D^{*}e\nu$
Bobeth  _et al._ (2021); Carvunis  _et al._ (2021). As another possible
indication of LFUV, CMS observed an excess in non-resonant di-electron pairs
with respect to di-muons Sirunyan  _et al._ (2021). Furthermore, the possible
deficit in first-row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix,
known as the Cabibbo angle anomaly (CAA) (see Fig. 1 (left)), can also be
viewed as a sign of LFUV Coutinho  _et al._ (2020); Crivellin and Hoferichter
(2020). For these reasons, there is very strong motivation for an upgraded
$R_{e/\mu}$ experiment whose precision matches that of the SM prediction (see
Sec. II.1). Moreover, the significance of the CAA depends crucially on
experimental input quantities used for the extraction of CKM matrix elements
as well as a number of theory corrections. Here, an improved measurement of
pion beta decay would allow one to extract $\left|V_{ud}\right|$ in a
theoretically pristine manner, requiring a gain of a factor $3$ in
experimental precision when combined with $K_{\ell 3}$ decays Czarnecki  _et
al._ (2020) and an order of magnitude for a stand-alone extraction (see Sec.
II.2). Finally, an experiment capable of addressing these physics goals would
at the same time be able to improve sensitivity to a host of exotic decays, as
described in Sec. II.4.

###  II.1 Lepton flavor universality tests and $R_{e/\mu}$

The branching ratio $R_{e/\mu}=\frac{\Gamma\left(\pi^{+}\rightarrow
e^{+}\nu(\gamma)\right)}{\Gamma\left(\pi^{+}\rightarrow\mu^{+}\nu(\gamma)\right)}$
for pion decays to electrons over muons provides the best test of
electron–muon universality in charged-current weak interactions. In the SM,
$R_{e/\mu}$ has been calculated with extraordinary precision at the $10^{-4}$
level as Cirigliano and Rosell (2007a, b); Marciano and Sirlin (1993)

$R_{e/\mu}\hskip 2.84544pt\text{(SM)}=1.23524(15)\times 10^{-4},$ (1)

perhaps the most precisely calculated weak interaction observable involving
quarks.111Reference Bryman  _et al._ (2011) estimates the uncertainty due to
the unknown non-leading-logarithmic contributions of
$O(\alpha^{2}\log(m_{\mu}/m_{e})$ in a different way compared to Ref.
Cirigliano and Rosell (2007a). This leads to a larger total uncertainty, i.e.,
$R_{e/\mu}\hskip 2.84544pt\text{(SM)}=1.23524(19)\times 10^{-4}$. Because the
uncertainty of the SM calculation for $R_{e/\mu}$ is very small and the decay
$\pi^{+}\rightarrow e^{+}\nu$ is helicity-suppressed by the $V-A$ structure of
charged currents, a measurement of $R_{e/\mu}$ is extremely sensitive to the
presence of pseudoscalar (and scalar) couplings absent from the SM; a
disagreement with the theoretical expectation would unambiguously imply the
existence of NP. With measurements of 0.01% experimental precision, NP at the
PeV scale can be probed Bryman  _et al._ (2011), even up to several PeV in
specific models such as leptoquarks.

The uncertainty of the SM prediction (1) for $R_{e/\mu}$ arises from low-
energy constants in chiral perturbation theory, which absorb the divergences
in the two-loop calculation of Refs. Cirigliano and Rosell (2007a, b), but
whose finite parts need to be determined by other means. Fortunately, in the
case of $R_{e/\mu}$ these non-perturbative uncertainties only affect the SM
prediction at the relative precision of $10^{-4}$, more than an order of
magnitude beyond the current experimental precision Zyla  _et al._ (2020);
Aguilar-Arevalo  _et al._ (2015a); Bryman  _et al._ (1986); Britton  _et al._
(1994); Czapek  _et al._ (1993)

$R_{e/\mu}\hskip 2.84544pt\text{(exp)}=1.2327(23)\times 10^{-4}.$ (2)

$R_{e/\mu}$ thus provides a unique opportunity for a pristine test of LFU in
the quark sector.

The comparison between theory and experiment provides a stringent test of the
$e$–$\mu$ universality of the weak interaction. We express the results in
terms of the effective couplings $A_{\ell}$ multiplying the low-energy charged
current contact interaction

${\cal
L}_{CC}=A_{\ell}[\bar{u}\gamma^{\mu}P_{L}d][\bar{\nu}_{\ell}\gamma_{\mu}P_{L}\ell],$
(3)

where $P_{L}\equiv(1-\gamma_{5})/2$. In the SM at tree level the couplings are
given by $A_{\ell}=-2\sqrt{2}G_{F}V_{ud}$ and thus satisfy LFU, i.e.,
$A_{\ell}/A_{\ell^{\prime}}=1$. The measurement of $R_{e/\mu}$ results in

$\left(\frac{A_{\mu}}{A_{e}}\right)_{R_{e/\mu}}=1.0010(9)\,,$ (4)

which is in agreement with the SM expectation and provides the best available
test of LFU. A deviation from $A_{\ell}/A_{\ell^{\prime}}=1$ can originate
from various mechanisms. In the literature it is common to interpret
deviations from $A_{\ell}/A_{\ell^{\prime}}=1$ in terms of flavor-dependent
couplings $g_{\ell}$ of the $W$-boson to the leptonic current, in which case
$A_{\ell}\propto g_{\ell}$. We note that in the context of modified $W$-boson
couplings LFU tested with $R_{e/\mu}$ probes the couplings of a longitudinally
polarized $W$-boson, whereas tests using purely leptonic reactions such as
$\tau\to\ell\nu_{\tau}\nu_{\ell}$ ($\ell=e,\mu$) test the couplings of
transversely polarized $W$-boson and are thus complementary.

Figure 1: Left: Tensions in the first-row CKM unitarity test (see text) Bryman
_et al._ (2021). Right: Constraints (1$\,\sigma$) on modified $W\ell\nu$
couplings from CKM unitarity (green) and LFUV (red) (adapted from Ref.
Crivellin and Hoferichter (2020)). The light bands show the current status and
the dark bands include the expected PIONEER sensitivity. The SM values of
$A_{\ell}$ are assumed to be modified by $1+\varepsilon_{\ell\ell}$ where
$\ell=e,\mu$.

Assuming that LFUV originates from modified $W\ell\nu$ couplings, the
determination of CKM elements will also be affected. Importantly, beta decays
have an enhanced sensitivity to a modified $W\mu\nu$ coupling, due to a CKM
enhancement by $\left|V_{ud}/V_{us}\right|^{2}\sim 20$. Such a modification of
the $W\ell\nu$ couplings would also affect $R_{e/\mu}$, albeit for a different
flavor combination (see Fig. 1 (right)). This connection provides further
motivation for an improved $R_{e/\mu}$ measurement, especially because the
sensitivity to LFUV would be comparable to future improved constraints from
beta decays. Moreover, recent global fits to electroweak observables and tests
of LFU show a preference for $R_{e/\mu}$ larger than its SM expectation
Coutinho  _et al._ (2020); Crivellin  _et al._ (2020). Furthermore, $R(K^{*})$
can be correlated to $R_{e/\mu}$ Capdevila  _et al._ (2021) and a combined
explanation of the deficit in the first-row CKM unitarity and the CMS excess
in di-electrons even predicts that $R_{e/\mu}$ should be larger than its SM
value Crivellin  _et al._ (2021a).

###  II.2 CKM unitarity and pion beta decay

The detector optimized for a next-generation $R_{e/\mu}$ experiment will also
be ideally suited for a high-precision measurement of pion beta decay.
Precision measurements of beta decays of neutrons, nuclei, and mesons provide
very accurate determinations of the elements $\left|V_{ud}\right|$ and
$\left|V_{us}\right|$ of the CKM quark-mixing matrix Cabibbo (1963); Kobayashi
and Maskawa (1973). Recent theoretical developments on radiative corrections
and form factors have led to a $3\sigma$ tension with CKM unitarity
illustrated in Fig. 1 (left) Bryman  _et al._ (2021); Cirigliano  _et al._
(2021), and with specific assumptions on theory corrections and processes
considered, higher significances have been obtained Seng  _et al._ (2021a);
Aoki  _et al._ (2021). However, in these determinations hadronic Marciano and
Sirlin (2006); Seng  _et al._ (2018, 2019); Czarnecki  _et al._ (2019); Seng
_et al._ (2020); Hayen (2021); Shiells  _et al._ (2021) and nuclear Miller and
Schwenk (2008, 2009); Gorchtein (2019); Hardy and Towner (2020) corrections
play an important role, to the extent that they dominate the systematic
uncertainty of the $\left|V_{ud}\right|$ extraction from superallowed beta
decays Hardy and Towner (2020). A determination from pion beta decay would be
much cleaner, provided it could be measured to sufficient precision.

The branching ratio for pion beta decay was most accurately measured by the
PiBeta experiment at PSI Počanić  _et al._ (2009); Frlež  _et al._ (2004a);
Počanić  _et al._ (2004); Frlež  _et al._ (2004b); Bychkov  _et al._ (2009) to
be

$\frac{\Gamma(\pi^{+}\to\pi^{0}e^{+}\nu)}{\Gamma(\text{Total})}=1.036\pm
0.004(\text{stat})\pm 0.004(\text{syst})\pm 0.003(\pi\to e\nu)\times 10^{-8},$
(5)

where the first uncertainty is statistical, the second systematic, and the
third is the $\pi\to e\nu$ branching ratio uncertainty. Pion beta decay,
$\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$, provides the theoretically
cleanest determination of the magnitude of the CKM matrix element
$\left|V_{ud}\right|$. With current input one obtains
$\left|V_{ud}\right|=0.9739(28)_{\textrm{exp}}(1)_{\textrm{th}}$, where the
experimental uncertainty comes almost entirely from the
$\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ branching ratio (BRPB) Počanić
_et al._ (2004) (the pion lifetime contributes ${\delta}V_{ud}=0.0001$), and
the theory uncertainty has been reduced from
$({\delta}V_{ud})_{\textrm{th}}=0.0005$ Sirlin (1978); Cirigliano  _et al._
(2003); Passera  _et al._ (2011) to $({\delta}V_{ud})_{\textrm{th}}=0.0001$
via a lattice QCD calculation of the radiative corrections Feng  _et al._
(2020). The current precision of 0.3% on $\left|V_{ud}\right|$ makes
$\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ not presently relevant for the CKM
unitarity tests because superallowed nuclear beta decays provide a nominal
precision of 0.03%.

In order to make $\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)$ important for CKM
unitarity tests, two precision experimental stages can be identified: (1) As
advocated in Ref. Czarnecki  _et al._ (2020), a three-fold improvement in BRPB
precision compared to Ref. Počanić  _et al._ (2014) would allow for a 0.2%
determination of $\left|V_{us}/V_{ud}\right|$, via improving the measurement
of the ratio

$R_{V}=\frac{\Gamma\left(K\rightarrow\pi
l\nu(\gamma)\right)}{\Gamma\left(\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)\right)}=1.9884(115)_{\pi}(93)_{K}\times
10^{7},$ (6)

where the uncertainties are due to the pion partial width and the $K_{L}$
lifetime and branching ratio. Equation (6) is independent of the Fermi
constant and SM short-distance corrections, but subject to structure-dependent
long-distance radiative corrections. This would match the precision of the
current extraction of $\left|V_{us}/V_{ud}\right|$ from the axial channels
Marciano (2004), which proceeds via

$R_{A}=\frac{\Gamma\left(K\rightarrow\mu\nu(\gamma)\right)}{\Gamma\left(\pi\rightarrow\mu\nu(\gamma)\right)}=1.3367(25),$
(7)

(see Fig. 1), thus providing a new competitive constraint on the
$\left|V_{us}\right|$–$\left|V_{ud}\right|$ plane and probing NP that might
affect vector and axial-vector channels in different ways. The theoretical
case for this approach was recently strengthened by improved analysis of
radiative corrections in $K\to\pi e\nu$ decays Seng  _et al._ (2021b). (2) In
the second phase, an order of magnitude improvement in the BRPB precision will
be sought. This would provide the theoretically cleanest extraction of
$\left|V_{ud}\right|$ at the 0.02% level, comparable to the current value from
superallowed beta decays Hardy and Towner (2020).

###  II.3 Constraints on New Physics

There are several ways that (heavy) NP can affect $R_{e/\mu}$ and the
extraction of $\left|V_{ud}\right|$ from beta decays, relevant for this
proposal. Concerning the former, there are several possibilities: a modified
$W\ell\nu$ coupling and a contribution to an $\ell\nu ud$ operator
($\ell=\mu,e$), while only modified $W\mu\nu$ couplings and an $e\nu ud$
operator affect the latter. However, $\left|V_{ud}\right|$ is also sensitive
to a direct NP contribution to muon decays via an $e\mu\nu\nu$ operator
entering through the Fermi constant, necessary to extract
$\left|V_{ud}\right|$ from beta decays Crivellin  _et al._ (2021b).

The following NP models (see Ref. de Blas  _et al._ (2018) for a complete
categorization) give potential observable tree-level effects in $R_{e/\mu}$
and/or in the determination of $\left|V_{ud}\right|$ from beta decays (direct,
or indirect via muon decay):

  * •

A $W^{\prime}$ bosons can generate tree-level effects in beta decays and in
$R_{e/\mu}$ as well as modified $W\ell\nu$ couplings via mixing with the SM
$W$.

  * •

Vector-like leptons (VLL) affect $W\ell\nu$ couplings via their mixing with SM
leptons after EW symmetry breaking (see Ref. Crivellin  _et al._ (2020) for a
recent analysis).

  * •

A singly charged $SU(2)_{L}$ singlet scalar can give a necessarily
constructive tree-level effect in muon decay such that the CAA can be solved
Crivellin  _et al._ (2021c); Marzocca and Trifinopoulos (2021).

  * •

An $SU(2)_{L}$ triplet scalar can give a necessarily destructive effect in
muon decay.

  * •

A neutral vector boson ($Z^{\prime}$) can give a constructive effect in muon
decay if it has flavor-violating couplings.

  * •

A leptoquark can generate a left-handed vector current and/or a scalar current
affecting beta decays and $R_{e/\mu}$.

  * •

A charged Higgs gives rise to pseudoscalar operators such that chirally
enhanced effects in $R_{e/\mu}$ can be generated.

Therefore, the PIONEER results will be important for a very wide range of SM
extensions containing one or more of these particles.

###  II.4 Heavy Neutrinos and other Dark Sector Physics

The PIONEER experiment will also achieve improved sensitivity in probing for
effects of heavy neutrinos. If a heavy neutrino has a sufficiently low mass
that it can be emitted, the signature will be a monochromatic peak in the
energy of the outgoing charged lepton at an anomalously low value. Even if the
heavy neutrino has a mass greater than the kinematic limit for emission, there
will, in general, still be an apparent violation of $e$–$\mu$ universality,
i.e., a deviation in the measured ratio $R_{e/\mu}\equiv BR(\pi^{+}\to
e^{+}\nu_{e})/BR(\pi^{+}\to\mu^{+}\nu_{\mu})$ from its SM value Shrock (1980,
1981a, 1981b). Constraints from early experiments on $\pi^{+}_{\ell 2}$ decays
were reported in Refs. Abela  _et al._ (1981); Minehart  _et al._ (1984);
Bryman  _et al._ (1983); Azuelos  _et al._ (1986); Britton  _et al._ (1992).
Recent results on $\pi^{+}_{\ell 2}$ decays include Aguilar-Arevalo  _et al._
(2015a, 2018, 2019). Constraints from the non-observation of neutrinoless
double beta decays imply that the heavy neutrinos of relevance here are Dirac
fermions. This can be arranged in various NP scenarios. There are also
constraints from primordial nucleosynthesis. Heavy neutrinos with masses of
relevance here are consistent with these primordial nucleosynthesis
constraints in several NP theories Argüelles  _et al._ (2021). Recent limits
include Bryman and Shrock (2019a, b).

Looking beyond sterile neutrinos, dark sectors that consist of particles that
interact very feebly with the SM are highly motivated extensions of the SM.
There is an ever-growing interest in exploring the parameter space of such
scenarios. The PIONEER experiment has unique capabilities to search for pion
decays to various light NP states. One example is the three-body decay
$\pi^{+}\to\ell^{+}\nu_{\ell}X$, where $X$ could, for example, be an axion-
like-particle (ALP) that mixes with the neutral pion Altmannshofer  _et al._
(2020), or a light gauge boson coupling to differences of lepton numbers Dror
(2020). Another interesting process is the three-body decay
$\pi^{+}\to\ell^{+}XY$, where both $X$ and $Y$ are light dark sector particles
Batell  _et al._ (2018). Existing limits from PIENU Aguilar-Arevalo  _et al._
(2021) already probe some of these models. Moreover, PIONEER can also look for
lepton-flavor-violating decays of the muon into light NP particles $\mu\to
eX$.

##  III PIONEER Experiment

###  III.1 Experiment Overview and Strategy

The main challenge in developing a next generation experiment for a high
precision measurement of rare pion decays is accurately assessing the
performance of the chosen detector technology in suppressing sources of
systematic uncertainties and handling increased rates. The PIONEER detector
design concept, described in the next sections, is based on the experience
gathered with the PIENU Aguilar-Arevalo  _et al._ (2015a) and PEN/PiBeta
Počanić  _et al._ (2006); Glaser  _et al._ (2018); Počanić  _et al._ (2014)
experiments, which are reviewed in the Appendix. Generically, the detector
will have the features sketched out in Fig. 2. An intense pion beam is brought
to rest in an instrumented (active) target (ATAR) and an electromagnetic
calorimeter (CALO) surrounds the stopping target. A cylindrical tracker
surrounding the ATAR is used to link the locations of pions stopping in the
target to showers in the calorimeter. Features of the PIONEER approach will
include improved time and energy resolutions, greatly increased calorimeter
depth, high-speed detector and electronic response, large solid angle
coverage, and complete event reconstruction. The proposed detector will
include a 3$\pi$ sr, 25 radiation length ($X_{0}$) electromagnetic
calorimeter, an advanced design segmented stopping target, and beam and
positron trackers.

Figure 2: Layout of the PIONEER rare pion decay experiment. The intense
positive pion beam enters from the left and is brought to rest in a highly
segmented active target (ATAR). Decay positron trajectories are measured from
the ATAR to an outer electromagnetic calorimeter (CALO) through a tracker. The
CALO records the positron energy, time and location.

Phase I of PIONEER aims to measure $R_{e/\mu}$ with precision of 0.01%, where
the uncertainty budget is equally allocated to statistics and systematics;
$2\times 10^{8}$ $\pi^{+}\to e^{+}\nu$ events are required. This Proposal is
specifically focused on the $R_{e/\mu}$ measurement. However, we envision
extension of PIONEER in Phase II (III), the details of which will be proposed
in future. These future phases will focus on a 3-fold (10-fold) improvement in
the measurement of the ultra-rare pion beta decay process,
$\pi^{+}\to\pi^{0}e^{+}\nu$. The $\pi^{+}\to\pi^{0}e^{+}\nu$ branching ratio
is $10^{4}$ times smaller than the $\pi\to e\nu$ channel and will require
running with a 100x more intense pion flux. The event identification is more
straightforward owing to the characteristic signature of the
$\pi^{0}\rightarrow\gamma\gamma$ decay in the calorimeter. While the
optimization of the beam properties, instrumentation, and stopping target
details for the pion beta decay experiment may require replacements of some
systems, our aim is that the core calorimeter, mechanics, tracker, and DAQ
systems will be designed to meet the needs of both experiments with limited
modifications. We emphasize that the requirements for measuring $R_{e/\mu}$
drive the PIONEER design. In subsequent sections we describe the beam, target,
positron detectors, calorimeter, DAQ, and electronics aspects of the
experiment. The Appendices include additional technical information and
priority R&D plans.

####  III.1.1 Requirements for measuring $R_{e/\mu}$

At rest, the pion lifetime is 26 ns and the muon lifetime is 2197 ns. The
monoenergetic positron from $\pi\rightarrow e\nu$ has an energy of 69.3 MeV.
Positrons from ordinary muon decay form the Michel spectrum from 0 to an
endpoint of 52.3 MeV. In principle, the monoenergetic $e^{+}$ from $\pi\to
e\nu$ is well isolated above the Michel endpoint and can be easily identified
using a high-resolution, hermetic calorimeter. To determine $R_{e/\mu}$ we
measure the ratio of positrons emitted from $\pi\to e\nu$ and $\pi\to\mu\to e$
decays for which many systematic effects such as solid angle acceptance cancel
to first order. However, counting all $\pi\rightarrow e$ events with a
precision of one part in $10^{4}$ requires determining the low-energy tail of
the electromagnetic shower and radiative decays that hide under the Michel
spectrum from the $\pi\rightarrow\mu\rightarrow e$ chain, which has four
orders of magnitude higher rate.

Figure 3 illustrates the relationship between the two channels and their
respective positron energy spectra. Here, we have modeled the spectrum from
both channels assuming a high resolution, $25\,X_{0}$ calorimeter. There
remains an unavoidable tail fraction below 53 MeV that must be determined
accurately in order to obtain the branching ratio. That challenge was critical
to previous generations of experiments and was responsible for the leading
systematic uncertainty in the PIENU experiment at TRIUMF. PIONEER will
minimize the intrinsic tail fraction through the use of a $25\,X_{0}$ LXe
calorimeter, the design of which is based on the considerable experience of
the MEG Collaboration.

Figure 3: The positron energy spectra from muon decays (blue) and from $\pi\to
e\nu$ decays (orange) for a calorimeter resolution of 1.5% and a depth of
$25\,X_{0}$. The simulation includes energy losses owing to photonuclear
interactions.

The $\pi\to e\nu$ branching ratio $R_{e/\mu}$ will be obtained by first
separating events into high- and low-energy regions at an energy cut value
($E_{cut}$) as discussed in the Appendices for the PIENU experiment. The time
spectra will be fit in each region with the $\pi^{+}\rightarrow e^{+}\nu$ and
$\pi^{+}\rightarrow\mu^{+}\rightarrow e^{+}$ timing distribution shapes, along
with backgrounds originating from different sources including event pile-up
effects, pion decays in flight, and effects from old muon decays.

PIONEER will incorporate improvements to the previous techniques including a
deeper calorimeter. However, it is also important to be able to create
triggers that can isolate $\pi\rightarrow e$ from
$\pi\rightarrow\mu\rightarrow e$ chains within the stopping target, identify
pion and muon decays in flight, as well as identify pileup from long-lived
muons remaining in the target from earlier pion stops. Figure 4 illustrates
several key processes that will occur at different rates in the stopping
target. The signal event (1) has a pion decay at rest; its Bragg peak energy
deposition as well as its depth within the target identifies it as a pion
stop. The much higher background (and normalization) channel (2) is
illustrated by that same pion stop followed by a decay to a 4.1 MeV muon,
which travels through a number of planes and then stops, leaving behind an
image of its own short trajectory and Bragg peak. If the muon decays in the
prompt window being observed for the pion decays (typically 3 – 50 ns after
the pion stop), its Michel positron will be recorded in the CALO. More rare
but subtle processes may also occur. A pion can also decay in flight within
the target to a muon before it stops (3). In very rare cases, the emitted 4.1
MeV muon can decay in flight before stopping (4) providing a Lorentz boost to
the emitted Michel positron, which contaminates the signal spectrum above the
ordinary stopped muon endpoint.

To distinguish event types, we will use an active target that can provide 4D
tracking (at the level of 150 $\mu$m in space and $<$1 ns in time) and energy
measurements from the O(30) keV signals for positrons to the 4000 keV Bragg
peaks of stopping pions and muons. As discussed in Sec. III.3, our
collaboration is focusing on the new low gain avalanche detector (LGAD)
sensors as a centerpiece of the experiment. Simulations using optimized LGAD
parameters provide confidence that triggers can be constructed to isolate and
measure all event types.

The calorimeter tail fraction for $\pi\to e\nu$ events will be measured in
situ by suppressing the $\pi\to\mu\to e$ decays using information provided by
the active target. $\pi\to\mu\to e$ events can be identified and suppressed by
the presence of the 4.1 MeV pulse from $\pi\to\mu\nu$ decay, use of a narrow
time window, $\pi-\mu$ particle identification, and tracking information to
identify pion decay-in-flight ($\pi$DIF), and muon decay-in-flight ($\mu$DIF)
following pion decay-at-rest ($\pi$DAR). As discussed in Sec. IV, we
anticipate that $\mu-e$ backgrounds in the tail region can be suppressed to a
level that will allow the uncertainty in the tail fraction to contribute
$<0.01\%$ to the error in $R_{e/\mu}$.

The experiment will require a continuous wave low-momentum pion beam that can
be focused to a small spot size and stop within the ATAR dimensions. Ideal
characteristics include a relatively low momentum of $55\,$ MeV/$c$ ($\pm
2\%$) and a flux of 300 kHz. At this low momentum, a separator is very
effective to reduce background from beamline muons and positrons. The $\pi$E5
beam can provide the needed flux. We are also investigating use of the $\pi$E1
line. Because of the high data rate, state-of-the-art triggering, fast
digitizing electronics, and high bandwidth data acquisition systems are
required.

Figure 4: Illustration of event types in the $\pi\rightarrow e$ and
$\pi\rightarrow\mu\rightarrow e$ chains. The stars are indicative of the
energy deposited at the Bragg peak for pions (red) or muons (purple) that stop
in the segmented ATAR. The main channels of interest include 1) the
$\pi\rightarrow e$ “signal channel” decay that emits a monoenergetic 69.3 MeV
positron; 2) the dominant $\pi\rightarrow\mu$ decay, where the 4.1 MeV muon
travels up to 0.8 mm and also stops in the ATAR before emitting a positron.
Events 3) and 4) represent situations that can confuse the classification of
events into categories 1) or 2). In 3) the pion decays within the ATAR prior
to stopping; the muon stop can then appear as a pion stop. In 4), the pion
stops, and the decay muon (very rarely, but importantly) decays in the short
time prior to stopping. Because it is a decay in flight, the Lorentz boost can
push the positron energy beyond the 52.3 MeV endpoint. The ATAR is being
designed to distinguish these event patterns.

####  III.1.2 Requirements for measuring pion beta decay

In Phase II (III), pion beta decay $\pi^{+}\to\pi^{0}e^{+}\nu$ will be
measured by observing the characteristic (nearly) back-to-back gammas from
$\pi^{0}$ decay normalized to $\pi\to e\nu$ decay as in Počanić  _et al._
(2009); Frlež  _et al._ (2004a); Počanić  _et al._ (2004); Frlež  _et al._
(2004b); Bychkov  _et al._ (2009). In PIONEER we also expect to observe the
low-energy positron absorbed in the ATAR in coincidence with the gammas in the
calorimeter. The Phase II (III) pion beta decay experiment will require
$7\times 10^{5}$ ($7\times 10^{6}$) events at an intrinsic branching ratio of
$10^{-8}$. This will require running at a significantly higher pion flux of
$\geq 10$ MHz. The beam momentum and emittance may be higher than for the
$\pi\to e\nu$ measurement to achieve the higher flux. The higher rate can be
handled because of the gamma ray coincidence identification and nearly fixed
energy sum. The $\pi$E5 beamline appears to have the necessary properties for
this measurement.

####  III.1.3 Simulations Guiding the Design

The discussion of the beamline and detector that follows is based on
simulations reported in Section IV. Briefly, there are three distinct efforts:
beamline and upstream detectors, simulation of the ATAR and event topologies,
and simulation of the calorimeter response. A G4beamline Roberts  _et al._
(2008) model of $\pi$E5 is being used to extrapolate from the existing surface
muon tunes used in the MEG program to the $55-70$ MeV/$c$ range of interest
for positive pions required for PIONEER. Descriptions of the ATAR and CALO are
included in the GEANT-4 Agostinelli  _et al._ (2003) models. The models
include inactive materials such as walls, cables, and windows and a Tracker
detector that surrounds the ATAR.

###  III.2 Beam

####  III.2.1 Beam requirements and target setup

The basic beam requirements for PIONEER are summarized in Table 1. The values
given are initial estimates, and some of the requirements, e.g. in the
longitudinal and transverse beam extent, might be relaxed pending further
studies. In the following we will only discuss PIONEER Phase I beam
requirements, but the parameters for the full experimental program are also
considered.

Phase | p |  $\Delta$p/p |  $\Delta$Z |  $\Delta$X x $\Delta$Y |  $\Delta$X’,$\Delta$Y’ | Rπ
---|---|---|---|---|---|---
| (MeV/c) | (%) | (mm) | (mm${}^{2})$ |  | (106/s)
I | 55-70 | 2 | 1 | 10x10 |  $\pm$10° | 0.3
II,III |  $\approx$ 85 |  $\leq$ 5 | 3 | 15x15 |  $\pm$10° | 20
Table 1: Required beam properties. $\Delta$Z and $\Delta$X $\times$ $\Delta$Y
are longitudinal (FWHM) range width and transverse (FWHM) beam sizes at target
location, respectively.

The 0.01% precision goal of the $R_{e/\mu}$ measurement places stringent
requirements on the beam and target as discussed below. (Margin=1cm,
Hang1=true,Hide2=0,Numbers1=r,Numbers2=r,Progressive*=.5 cm,Start1=1) & Pion
stops: The efficiency for detecting the $\pi-\mu$ sequence should be the same
as for a $\pi$ stop; thus all decay muons must be fully contained in ATAR.
This drives the requirement for the small longitudinal and lateral size of the
stopped $\pi$ distribution. Upstream detectors (if necessary) will be
minimized, as they increase the beam spot by scattering.

Positron detection: The ATAR should be small to reduce the positron energy
deposited in it, though largely this loss can be reconstructed. The constraint
on the beam entrance divergence is necessary to keep the opening angle of the
beam entrance cone to 10° relative to its axis. (A larger cone will decrease
the solid angle for positron detection and, in particular, increase the
surface for shower leakage.) This requirement limits the phase space
acceptance to 175 $\pi\,$cm mrad.

Figure 5: Beam counters and ATAR. An active degrader disk (not shown) is
optional, and only required for p$>$55 MeV/c. The beam detectors systems LGAD1
and LGAD2 provide an event by event trajectory for entering particles. It is
conceivable that they can be rotated out of the beam for production running at
the lowest operating momenta. Figure 6:  Range-energy (left) and momentum-
energy (right) relations for pions and muons. Muons from $\pi$DAR have 4.12
MeV kinetic energy and travel 0.8 mm in Si.

Figure 5 sketches the baseline set-up for the beam-target section of the
experiment. For a more complete description of the overall ATAR-CALO design we
refer to Sec. III.5.4. Pions selected by an E$\times$B separator pass through
a beam window of $70\,\mu$m Mylar, two LGAD detector planes (two crossed
layers of $50\,\mu$m thick AC LGADS, each, denoted as BEAM in this proposal)
to stop in the ATAR. No degrader or upsteam LGAD detectors may be necessary if
a suitable beam at p=55 MeV/$c$ can be established. As sufficient beam
intensity is expected, the beam spot may be improved by collimation just
upstream of the detector entrance. Collimators would also serve to suppress
muons and electrons displaced by the angular deflection in the separator but
their design has to be carefully optimized between the competing requirements
of collimating close to the target focus while absorbing positrons and gammas
before they reach the CALO. Some important aspects of the stopping beam can be
understood from the pion range-energy relations shown in Fig. 6.222These were
calculated by SRIM (http://www.srim.org/) to describe the slowing down of
particles at low energies..

A momentum of 55 MeV/$c$ has several advantages including that the separator
will work more efficiently and a range width $\Delta Z$ of less than 0.4 mm is
expected for a 2% $\Delta$p/p beam momentum acceptance. (The stopping range
width would increase to 0.8 mm at 70 MeV/$c$.) The range-energy curve also
shows how the separation between pions and muons of the same energy improves
with the energy deposited in ATAR.

####  III.2.2 Beam line at $\pi$E5

The PSI High Intensity Proton Accelerator (HIPA) chain consists of a
Cockcroft-Walton pre-accelerator, delivering 870 keV protons to a set of two
isochronous cyclotrons which further accelerate to the maximum 590 MeV. In the
Ring cyclotron, the protons are accelerated by four copper resonator cavities
operated in continuous wave (CW) mode at a frequency of 50.6 MHz, giving the
periodic 19.75 ns beam microstructure and their final energy of 590 MeV. The
$\pi$E5 channel is a high-intensity low-energy muon and pion beamline, with a
maximum momentum of 120 MeV/$c$, that views the second graphite production
target, Target E, at 165∘ with respect to the proton beam axis. The $\pi$E5
channel is used exclusively for particle physics experiments, and is currently
home to the MEG II and Mu3e experiments. The channel length from Target E to
end of the QSB43 quadrupole magnet and the entrance to the experimental area
is 13 m, giving approximately 7 m of free space between the concrete wall and
current MEG II infrastructure. In this area the SEP41 E$\times$B Wien Filter
for particle separation, QSK quadrupole triplet for focusing the beam on the
ATAR and the PIONEER installation could be placed.

Figure 7: The G4Beamline model of the $\pi$E5 beamline including a stand-in
calorimeter.

####  III.2.3 Beam optimization and studies

Simulations for both pion production at Target E and transport of particles
down the $\pi$E5 channel were performed using the G4Beamline toolkit Roberts
_et al._ (2008). A figure of the $\pi$E5 beamline from the G4Beamline
simulation, beginning at Target E and ending at the PIONEER calorimeter, is
shown in Fig. 7. The pion production simulation utilizes the parameterized
cross sections developed for the High Intensity Muon Beamline (HiMB) project
Berg  _et al._ (2016). All simulation results are scaled to the nominal 2.2 mA
proton beam current at PSI.

The G4Beamline simulation was originally tuned for 28 MeV/$c$ muons and has
been rescaled for the respective pion momenta. Some additional tuning was
performed for the last two dipoles and quadrupole triplets to optimize
transmission through the SEP41 and on to the ATAR. The physical volume of the
SEP41 is included but its electric and magnetic fields are not enabled for
these simulations. Rates for pions and muons reaching the entrance to the
experimental area (QSB43) and 4.8 m downstream at the center of the
calorimeter volume (CALO center) for beamline central momenta ranging from 55
to 75 MeV/$c$ are shown in Fig. 8. The rates for those particles at the lower
and upper end of the possible momentum ranges are listed in Table 2. The pion
rates calculated in the simulation at the center of the calorimeter for a 2%
momentum-bite are sufficient for the $R_{e/\mu}$ measurement planned in Phase
I of PIONEER, even when further losses in the SEP41 or upstream collimation,
necessary for reducing background events in the ATAR and calorimeter, are
included. For PIONEER Phase II, III increasing the momentum and the momentum
bite will be required.

Figure 8: The rates for pions and muons at the entrance to the experimental area (QSB43) and reaching the center of the calorimeter, calculated in the $\pi$E5 G4Beamline simulation. Beamline Position |  $p_{\pi}$ (MeV/$c$) |  $\pi^{+}$ Rate |  $\mu^{+}$ Rate
---|---|---|---
QSB43 |  55 |  6.3 |  12.3
CALO Center |  55 |  1.0 |  6.1
QSB43 |  75 |  61.5 |  30.2
CALO Center |  75 |  11.1 |  15.1
Table 2: Particle Rates ($\times 10^{6}$ $s^{-1}$) in $\pi$E5 for a 2%
momentum-bite calculated in the G4Beamline simulation.

A very preliminary study to focus the beam onto the calorimeter center
positions by simulating 65 MeV/c pions with their decay disabled is displayed
in Fig. 9. The horizontal ($x-x^{\prime}$) phase space indicates a pronounced
non-Gaussian nature, while the vertical ($y-y^{\prime}$) phase space
demonstrates a well defined focus. The complex structure of of the horizontal
phase space emphasizes that full G4Beamline simulations are required to tune
the beam and, in particular, experimental verification is indispensable to
achieve the desired small beam spot on ATAR. At the moment, there is no
readily available experimental data that could verify our preliminary
simulations for $\pi^{+}$ beams. The above used simulation code was verified
so far using surface muon beams of 28 MeV/c momentum only. The last experiment
using pion beams at $\pi$E5 was the PiHe experiment that needed high $\pi^{-}$
rates for pionic helium spectroscopy Hori  _et al._ (2020).

(a)

(b)

Figure 9: Preliminary pion phase space distributions at the CALO center
position for 65 MeV/$c$ pions with decay disabled from the G4Beamline
simulation of $\pi$E5. Left: Horizontal. Right: Vertical. The calculated
emitance $\epsilon$ for each is included in the plot as text. The non-Gaussian
structure of these phase spaces present a challenge in correctly modeling the
beam transport.

Key experimental parameters, including the design of the beam conduit into the
calorimeter and the geometry of the ATAR rely on a detailed understanding of
the $\pi^{+}$ beam properties at $\pi$E5 at the targeted momentum range (55-75
MeV/$c$). The most important parameters to be determined are the
$\pi^{+}/\mu^{+}/e^{+}$ rates as a function of beam momentum, the momentum
bite $\Delta p/p$, the final focus and the capability to select a clean
$\pi^{+}$ beam by applying a Wien (E$\times$B) filter. Measurements of
available $\pi^{+}$ rates and comparison to simulation will be critical in
determining achievable pion rates at the ATAR. For this purpose we propose to
carry out detailed measurement program of the $\pi$E5 pion beam at PSI,
adapting SiPM-based beamline instrumentation that was used to characterize
pion and muon rates in the past. Because of their urgency in informing the
detector design we request a first study in 2022 (beam request submitted
separately).

###  III.3 Active target (ATAR)

A highly segmented active target (ATAR) Mazza (2021) is a key new feature of
the proposed PIONEER experiment; technical details and alternative designs of
the sub-detector can be found in Appendix D with a detailed timeline described
in Appendix D.1. The ATAR will define the fiducial pion stop region, provide
high resolution timing information, and will furnish selective event triggers.
Examples of event displays for $\pi\to e\nu$ and $\pi\to\mu\to e$ events are
shown in Fig. 10.

Figure 10: Simulated example displays of pion decay events in the ATAR. Pions
enter horizontally from the left; the red dotted lines show the positions of
the pion stops. The color of the bars indicates the deposited energy. Left
column: X-Z (top) and Y-Z (bottom) strip views of a $\pi\to e\nu$ event. Right
column: Same views of a $\pi\to\mu\to e$ event. The blue dotted line shows the
position of the decay muon stop.

For the measurement of the calorimeter response to $\pi\to e\nu$ decays, the
ATAR will suppress the $\pi\rightarrow\mu\rightarrow e$ decay at rest
($\pi$DAR), and pion and muon decay-in-flight (DIF) low energy backgrounds.
DAR events are identified by a good pulse pair resolution observing the 4.1
MeV $\pi\to\mu$ decay, and a tight positron observation window of about one
pion lifetime. $\pi$DIF events are identified by kinks in the trajectories,
$\mathrm{d}E/\mathrm{d}x$ measurements along the track, and observed range in
the target. Furthermore, the ATAR will suppress accidental muon stops that
precede the trigger signal; these were a significant source of pile-up
background in the previous experiments. Confirmation that the observed
positron belongs to the pion stopping vertex will also be obtained using
tracking in the ATAR and in additional tracking detectors (discussed in Sec.
III.4).

To fulfill these goals the ATAR must be able to detect both the exiting
$e^{+}$, a minimum ionizing particle (MIP), and larger ($\thicksim$100 MIPs)
energy deposits from $\pi^{+}$ and $\mu^{+}$. The large dynamic range O(2000)
of the signals is a significant challenge for the readout electronics in the
amplification and digitization stages. The position of the energy deposits
needs to be identified with sufficient granularity along the beam direction
and in the transverse plane. Furthermore, to identify single components of the
decay processes a $\sim 1.5\text{\,}\mathrm{ns}$ pulse pair resolution is
needed.

The ATAR tentative design dimensions are 2$\times$2 ${\mathrm{cm}}^{2}$
transverse to the beam. In the beam direction individual silicon sensors are
tightly stacked with a total thickness of $\sim 6\text{\,}\mathrm{mm}$. A
strip geometry with the electronic readout connected on the side of the active
region via wire bonding is foreseen. The strips are oriented at $None$ to each
other in subsequent staggered planes to provide measurement of both
coordinates of interest and to allow space for the readout and wire bonds. The
preliminary sensor geometry has strips with a pitch of
$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$, so that a sensor would have 100
strips mated to a chip with 100 channels and $2\text{\,}\mathrm{cm}$ width, a
standard dimension for microchips. A best estimate at present for the sensor
thickness is around $120\text{\,}\mathrm{\SIUnitSymbolMicro m}$ to avoid
support structures for the sensor, which would introduce dead area. To reach a
total thickness of about $6\text{\,}\mathrm{mm}$, $\thicksim$50 planes are
needed, so in total the ATAR would comprise $\thicksim$5000 channels. The
detectors are paired with the high-voltage facing each other in a pair to
avoid ground and high voltage in proximity. In the preliminary design, shown
in Fig. 11, the strips are wire bonded, with a connection alternating on the
four sides, to a flex that brings the signal to a readout chip positioned a
few cm away from the active volume. This removes the chip from the path of the
exiting positrons, reducing its degradation of their energy resolution. The
flex will be produced with aluminium traces so that the cable material per
flex would be $\sim
0.025\text{\,}\mathrm{g}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}$. In the
figures in this proposal, all cables are shown exiting downstream. A readout
from both ends is being investigated to reduce the average material traversed
by exiting positrons. At present, the maximum material in the path of the
positrons occurs when 12 flexes are traversed. The readout ASIC sits on the
first flex that tapers out to accommodate the additional traces. Then the flex
is connected, via connector, to a PCB connected to a second flex that brings
the amplified signal to the digitizers in the back end.

Figure 11: Left: ATAR position in the beam line. Right: Concept schematic
design of the ATAR. The flex from the first, third and fifth sensors is
directed in and out of the page. The modules are attached on the HV side and
with a few $\mathrm{\SIUnitSymbolMicro m}$ of separation on the strip side. 48
sensors are coupled in 24 pairs.

The chosen technology for the ATAR is Low Gain Avalanche Detector (LGAD)
Pellegrini  _et al._ (2014) (detailed description in Appendix D.2), thin
silicon detectors with moderate internal gain. A
$120\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick LGAD sensor, coupled to fast
electronics, has a time resolution of less than $100\text{\,}\mathrm{ps}$ on
the rising edge and can separate a single hit from two overlapping hits if
they arrive more than $1.5\text{\,}\mathrm{ns}$ apart. Preliminary studies
made with X-rays coming from the Stanford light source (SSRL) Galloway  _et
al._ (2019) and PSI Andrä  _et al._ (2019) show that LGADs have an energy
resolution of around $10\text{\,}\mathrm{\char 37\relax}$; more detailed
results are reported in Appendix D.2. The effect of gain saturation that was
reported in the community in the past year E. Rivera (2021) also needs to be
studied. The LGAD technology was chosen over standard silicon technology
because of the intrinsic gain and thin bulk. Normal silicon detectors without
gain need 300–500 $\mathrm{\SIUnitSymbolMicro m}$ of active silicon to have
enough collected charge for high MIP detection efficiency. This would degrade
granularity in the beam direction, time resolution and pulse separation
discrimination. A brief discussion on alternative technologies is presented in
Appendix D.2.

Current standard LGADs have a limitation in terms of granularity and active
area. To achieve a $\sim 100\text{\,}\mathrm{\char 37\relax}$ active area
several technologies still at prototype level are being evaluated for PIONEER,
such as AC-LGADs Apresyan  _et al._ (2020). Studies were made on strip AC-LGAD
prototypes from BNL as shown in Appendix D.3.1. Results on sensor simulation
are also reported in Appendix D.3.1 and additional LGAD technologies are being
evaluated as reported in Appendix D.3.2.

To read out the ATAR sensors two crucial electronic components need to be
identified: an amplifier chip and a digitization board. Preliminary tests on
available solutions are reported in Appendix D.4. Since the amplification chip
has to be positioned away from active region, the effect of placing a short
($5\text{\,}\mathrm{cm}$) flex cable between the sensor and the amplification
stage will be studied. To successfully reconstruct the decay chains the ATAR
is expected to be fully digitized at each triggered event. The fast charge
collection time of thin LGADs will allow separation of subsequent charge
depositions as mentioned before. To achieve this goal a high bandwidth
digitizer with sufficient sampling rate has to be used. A discussion on
available amplifier chips and digitizers is reported in Appendix D.4.

Relative to previous experiments, the use of a highly segmented active target
allows for discrimination against backgrounds by looking for deposition
patterns internal to the target that are associated with the various signals’
decay topologies.

###  III.4 Cylindrical Tracker

A dual layer cylindrical silicon strip tracker is situated between the ATAR
and the calorimeter to measure the positron position in two dimensions (along
the beam direction, $z$, and azimuthal angle, $\phi$), and time, as indicated
in Fig. 5. The detector has an inner diameter of $5\text{\,}\mathrm{cm}$ and a
length of $25\text{\,}\mathrm{cm}$. The readout ASIC will be wire bonded at a
location outside the calorimeter active solid angle. Overlapping lengths of
long strips (about $10\text{\,}\mathrm{cm}$) are needed to cover the entire
region.

Two layers of strips with a small stereo angle between them will provide O(mm)
$z$ resolution and $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ resolution in
the direction perpendicular to the strips. An alternative under consideration
is to connect two or three strip sensors in a line reading out both ends to
obtain O(mm) position information along the strip position using charge
attenuation information.

The silicon strip sensors may be constructed with either regular silicon or
LGADs. Regular silicon would have $\sim 300\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ of thickness for positron detection with a time resolution
$<1\text{\,}\mathrm{ns}$, while LGADs can be
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ or less with a time resolution of
$<50\text{\,}\mathrm{ps}$. However, LGAD silicon strips with length of 10 cm
present an additional challenge while for the ATLAS detector standard silicon
strips with $\sim 10\text{\,}\mathrm{cm}$ of length have been successfully
fabricated on 8-inch wafers CER (2017).

###  III.5 LXe Calorimeter

####  III.5.1 Overview

Due to its fast timing properties, high light yield with excellent energy
resolution and highly uniform response, liquid xenon (LXe) read out by UV
sensitive phototubes and state-of-the-art VUV SiPMs is considered for the
calorimeter. Here, experience is drawn from the MEG Baldini  _et al._ (2016)
and MEG-II Baldini  _et al._ (2018) experiments which use a large scale, high
rate LXe detector to search for the lepton flavor violating muon decay,
$\mu^{+}\rightarrow e^{+}\gamma$. Experiments searching for the elusive dark
matter (e.g. XENON, LUX-ZEPLIN) and (neutrinoless) double beta decay events
(KamLAND-Zen, (n)EXO) also use detectors with similar scale liquid xenon
cryostats. Unlike those latter experiments, MEG, like PIONEER, only detects
scintillation light (other experiments rely on both scintillation and charge
collection) and is a high rate experiment. In MEG, the rate of muon stops in
the target was $3\times 10^{7}\,\mathrm{\mu^{+}/s}$ and the LXe calorimeter
rate due to photons was $\mathcal{O}$(0.3 MHz). The anticipated PIONEER
calorimeter rate (due to pion stop rate of 300 kHz in the ATAR for the
$R_{e/\mu}$ measurement) is of the order handled by the MEG LXe calorimeter.
The main difference comes from the nature of the particles entering the
calorimeter (gammas in the case of MEG and positrons for PIONEER) and the
geometry of the calorimeter leading to different event “signatures”. The
PIONEER LXe detector is foreseen to be a 25 radiation length, 3$\pi$ sr sphere
surrounding the ATAR. A discussion on the capability of a large single volume
to handle pileup events is given in Sec. IV.2.

The homogeneity of the LXe detector is an advantage in achieving the high
energy resolution which is important for determining accurately the low energy
“tail” fraction of $\pi\rightarrow e\nu$ events. MEG currently reports an
energy resolution of $\sigma=1.8\%$ for 50 MeV gammas and they continue to
study possible improvements. The baseline energy resolution goal for PIONEER
at 70 MeV is 1.5%.

The energy resolution is impacted by the efficiency of collection of
scintillation light which is itself influenced by design parameters (like
photo-sensor coverage) and physical or technical parameters (like the light
attenuation due to impurities in LXe, reflection of VUV light on surfaces,
photo sensor refraction index, the level of dark current which impact the
photo-electron threshold for summing the energies of the different photo-
sensors, etc). In addition to the finite energy resolution of the calorimeter,
photo-nuclear interactions, shower leakage and geometrical acceptance
contribute to the low energy tail. The impact of photo-nuclear effects in LXe,
for which little literature exists, will be determined by simulation and
bench-marked against available data and new measurements.

A GEANT-4 simulation of a bare LXe calorimeter geometry was used to determine
the residual tail fraction below the Michel end point versus calorimeter depth
for $\pi\to e\nu$ events. Figure 12, Left, shows the energy deposited in the
spherical calorimeter vs. the angle Theta with respect to the beam axis for a
25 $X_{0}$ calorimeter depth. Figure 12, Right, shows the fraction of the
energy deposited that is below 58 MeV vs. depth. The volume of LXe required
scales as the radius cubed and the required photo-sensor coverage scales as
the radius squared. These practical factors are optimized for smaller depth.
The containment of the shower slowly improves with increased depth.The depth
was chosen to be 25 $X_{0}$, which we use throughout this proposal. This
choice, along with the spherical shape and $>3\pi\,\mathrm{sr}$ coverage,
limits the effect of secondaries being missed by the calorimeter (e.g. Bhabha
scattered events) and will significantly reduce the contribution of shower
leakage. We will continue to carefully model the calorimeter geometrical
parameters and assess the expected detector sensitivity; see discussion in
Sec. IV.2.

Figure 13 shows the energy spectrum for a 25 $X_{0}$ calorimeter of varying
intrinsic resolution; these results indicate that the tail correction is
relatively insensitive to resolution. We are aiming for resolution
$\sigma=1.5\%$, based on the performance of the MEG calorimeter.

Figure 12: Left: The energy deposited by monoenergetic 69.3 MeV $e^{+}$ from
$\pi\to e\nu$ decays in a 25 $X_{0}$ calorimeter with an energy resolution of
1.5% vs. the angle Theta with respect to the beam axis. The grey bands
indicate the boundaries of the fiducial volume region (here, $30^{\circ}$).
Right: The shower tail fraction below 58 MeV vs. the calorimeter depth in
radiation lengths for the 69.3 MeV $\pi\rightarrow e\nu$ events.  Figure 13:
The effect of energy resolution on a 25 $X_{0}$ calorimeter. The events
indicated with a solid line are monoenergetic 69.3 MeV $e^{+}$ from
$\pi\rightarrow e\nu$ decay. The events indicated with a dashed line are the
Michel spectrum from muon decay. The dashed grey line at 53 MeV represents the
nominal endpoint of the Michel spectrum.

The xenon scintillation light absorption length has been measured for MEG to
be more than 1 m Baldini  _et al._ (2005). However, the light absorption
length can be significantly reduced through absorption by impurities such as
H2O and O2. A large scale detector requires purification at the ppb level
which was achieved by MEG. The purification system and the cryostat design
(needed to maintain the xenon at 165 K Mihara (2011)) of MEG will be
considered for scaling up the design for PIONEER (see Sec. III.5.3).

MEG-II performed extensive R&D in collaboration with Hamamatsu to develop
large MPPC (Multi-Pixel Photon Counter) detectors
($12\times$$12\text{\,}{\mathrm{mm}}^{2}$) while maintaining optimal
performance characteristics of a small decay constant and good gain
uniformity. Efficient detection of VUV light requires careful choice of the
silicon layer assembly and coatings. For their chosen sensor, the MEG-II
collaboration reported a photon detection efficiency (PDE) of $\sim 20\%$
Baldini  _et al._ (2018) but observed later degradation of the PDE in LXe Onda
(2020) which is under investigation. Below we discuss details of photosensor
options considered for PIONEER.

####  III.5.2 Photosensors

In order to readout the liquid xenon scintillation light, special photo
sensors are necessary due to the short scintillation wavelength of 175 nm and
the low operation temperature of 165 K. Two types of photo sensors were
developed for this purpose by Hamamatsu K.K. and the MEG/MEG II collaboration:
2-inch photomultipliers (PMT) and multi-pixel photo sensors (MPPC). A round-
shaped 2-inch PMT sensitive to VUV light (R9869) has been developed using
Bialkali (K-Cs-Sb) photocathode and a synthetic silica window. It achieved a
quantum efficiency of $15\text{\,}\mathrm{\char 37\relax}$. Aluminum strips
were added in the photocathode to prevent an increase of the sheet resistance
at low temperature.

In order to improve the granularity for the inner surface in the MEG-II
experiment, a silicon photomultiplier, called MPPC (S10943-4372) with an
active area of 12$\times$12 mm2, was developed. The main developments
consisted in removing the protective layer, matching the optical properties of
the silicon surface to that of the LXe, and reducing the thickness of the
insensitive layer. Besides achieving higher granularity, there are several
advantages to using SiPM with respect to photomultiplier tubes: they are
insensitive to magnetic fields, the single photoelectron peak can be used for
calibration of the sensor and the required supply voltage is relatively low
(less than $100\text{\,}\mathrm{V}$).

However, as mentioned above, the PDE of the SiPMs were found to drastically
decrease under exposure to the muon beam. Investigations are ongoing to
understand the causes. It was however shown that the PDE could be recovered
through an “annealing” procedure performed during the accelerator shutdown
period. The gain of the PMTs was also found to decrease due to damage to the
dynode induced by photoelectrons. The PMT lifetime is however sufficiently
long and thus should not be of concern for PIONEER.

Considering the above, the baseline design for PIONEER is the use of PMTs on
the outer surface targeting a coverage of $20\text{\,}\mathrm{\char 37\relax}$
(1000 phototubes) of the surface. The choice of the photosensor technology
might evolve depending on the developments regarding SiPM performance
degradation.

Simulations will be performed to study the impact on track identification
capabilities and energy resolution of adding SiPMs on the inner surface
regions of the calorimeter. The ATAR is small ($130\text{\,}\mathrm{mm}$) and
surrounded by a positron tracker which can measure the positron’s incident
position right before it enters the LXe calorimeter. In these conditions the
addition of reflective material coatings on the inner surface may be
sufficient for the PIONEER needs. However, it is notably difficult to
accurately simulate UV optical properties on large scales. Agreement between
data and photon transport simulations are sometimes poor, mainly because of
the large number of optical interfaces, i.e., surfaces with a certain shape,
absorbance and reflectance, that are not well known for the UV light from LXe
(optical properties are indeed most often measured in vacuum). Apart from
differences in refraction indices between vacuum and LXe, LXe may also alter
the optical properties of some materials (e.g. Silva  _et al._ (2010); Akerib
_et al._ (2015); Neves  _et al._ (2017)). It is thus particularly important to
perform in-situ measurements in LXe to evaluate both the performance of SiPM
in the LXe environment and deduce the appropriateness of surfaces for coatings
(as well as possibly segmentation for pile-up rejection, see discussion in
Sec. IV.2). For this purpose we have planned measurements at facilities where
LXe setups are available.

####  III.5.3 Cryogenics and Purification

A system consisting of the following equipment is required in order to
stabilize a large volume of liquid xenon in the detector:

  1. 1.

High-pressure gas tanks for xenon storage,

  2. 2.

Gas xenon purification system,

  3. 3.

Liquid xenon purification system,

  4. 4.

Refrigeration,

  5. 5.

Temperature and pressure control system.

Piping for transporting xenon either in the gas or liquid phase is required as
appropriate. In addition to these, a cryostat that can temporarily hold xenon
in a liquid state during emergencies or maintenance ensures efficient
operation of the detector.

(Start1=1) 1\. High-pressure gas tanks for xenon storage: Xenon is stored in
high-pressure gas tanks at room temperature during detector maintenance
periods. A storage tank that can withstand a pressure of 5.8 MPa at 17oC
(1.1g/cm3, the critical point of xenon) is required. After detector operation,
the xenon is recovered in the storage tank by cooling the tank with liquid
nitrogen. This requires a liquid nitrogen bath to cool the high-pressure gas
tank.

2\. Gas xenon purification system: When operating the LXe detector, it is
necessary to reduce the xenon gas pressure provided from the high-pressure
tanks and then to remove impurities in the gas before filling in the detector
cryostat. Metal-heated getter purifier technology has been used in previous
experiments and will be employed also in the PIONEER experiment.

3\. Liquid Xenon Purification System: Based on the experience of the MEG
experiment Baldini  _et al._ (2016), it is known that even if the xenon gas is
liquefied in the detector after impurity removal by the gaseous-phase
purification system, impurities remaining on the detector surface may dissolve
into the liquid, causing absorption of scintillation light and degradation of
detector performance. Among these impurities, water is the one most likely to
affect the propagation of liquid xenon scintillation as its absorption cross
section overlaps with the xenon scintillation light spectrum. In order to
efficiently remove the water dissolved into the liquid, the xenon is
circulated in the liquid phase by a low-temperature liquid pump through a
filter containing molecular sieves with a pore size 13A, which is suitable to
remove water molecules. In the MEG experiment, 70L/hour circulation is
achieved with this system, resulting in preparing sufficiently pure liquid in
a reasonable time.

4\. Small refrigerator: As used in the MEG experiment, a small refrigerator
installed on the top the detector is used to liquefy xenon and re-liquefy the
constantly evaporating xenon gas. The use of a pulse-tube refrigerator is
suitable from the viewpoint of low vibration noise, but to obtain a high
refrigeration power, a GM-type refrigerator can be installed at a distance
from the detector with a vacuum insulated pipe to transfer the liquid to the
detector. Both types of refrigerators have been used in MEG, and there are no
technical difficulties.

5\. Temperature and pressure control system: The cryostat is always subject to
heat by conduction through the support structure and cables as well as heat
generation from electronics circuits and photo sensors placed in the cryostat.
After liquefaction completes, the liquid xenon evaporates continuously due to
the heat generated by these, and the pressure rises. In order to control the
temperature and pressure of the liquid xenon, xenon is re-liquefied by the
refrigerator. In order to maintain the liquid state at a temperature and
pressure suitable for operation, the refrigerator cooling power is controlled
by changing the heater output on the cold head while the refrigerator
continues to operate at maximum capacity. This method has already been used in
MEG and many other experiments using liquid xenon, and there is no problem in
maintaining the stability of the liquid.

####  III.5.4 Calorimeter Mechanical Engineering

#### Requirements

Mechanical engineering considerations for the LXe calorimeter are discussed
below.

[itemize] (Start1=1) & The CALO mechanical design has to support a load of
about 9 tons of LXe as well as the required cryogenic envelope, consisting of
a cold vessel and an insulation vacuum. Ideally, the heat load of the new
system should be compatible with existing MEG cooling and purification
infrastructure. The beam region consist of an entrance cone to focus a beam
with 10° divergence onto a beam spot of about 1 cm2. The entrance side will
support the BEAM detectors. The exit side should be in air, allow the
insertion of ATAR and TRACKER and their associated electronics, and provide
sufficient heat removal. The ATAR target region should be surrounded by thin
beam pipes. The goal is to minimize material in the CALO acceptance of close
to degree=140° in polar angle, while covering the full azimuth. The ATAR and
TRACKER region is very space limited, while increasing the inner pipe radii is
problematic, both in terms of solid angle and window strengths. A compromise
between these conflicting requirements needs to be optimized. The PIONEER
detector is designed for a measurement program extending over a decade. Both
routine services as well as major repairs and upgrades must be supported by
the design.

#### Conceptual design

The calorimeter is built of interactive functional blocks incorporating a top
load concept with the intent to be modular and to allow for ease of
maintenance. The functional blocks are described below and a drawing is shown
in Figure 14.

Figure 14: Concept design of the liquid xenon calorimeter. For scale, the lid
is 3.05 m diameter. The yellow circles are merely representative of the
photosensors; they are not placed accurately.

(Start1=1) 1\. Liquid xenon vessel: This vessel has a spherical bottom to
follow the contour of the detector mounting surface. This both reduces bending
stress in the walls and reduces the volume of xenon required to cover the
detectors. Running through this vessel horizontally is a cone-tube pathway.
The tube portion, which surrounds the target, is envisioned as beryllium. The
cone may be of a variety of metals. The connection between the two components
is designed to be a braze or weld.

2\. Detector mounting surface: Beyond the basic requirement of being spherical
and holding detectors, the inner radius is set at 0.9 m to achieve the
required number of radiation lengths of xenon.

3\. Thermal insulation: To achieve the best insulation, the calorimeter has
been designed to be a vacuum dewar. The support of the liquid xenon vessel is
achieved by hanging it on turnbuckles made of material which does not conduct
heat well. Stainless steel is seen as the most likely option. If additional
reduction in heat load is needed the link could be changed to titanium,
allowing for a reduced cross section. The more complicated portion of the
thermal insulation is maintaining vacuum around the incoming beam and the
target space. This is made easier by having a break in this tube. The beam
tube loads from one side, the target tube from the other. Both terminate in
thin vacuum barrier windows which allow beam passage. To accommodate both
temperature induced dimensional changes and deflection from weight loading,
there are two bellows present. The tube running through the xenon vessel has
bellows on the target loading side. There is a large bellows on the top of the
xenon vessel to allow cabling and piping to pass through the vacuum space.

4\. Target air space: The tube the target resides in is envisioned as
beryllium. This tube is mounted on a flange on the vacuum vessel and protrudes
past the centerline by approximately 175 mm. The inside end of the tube is
capped with a window that allows passage of the beam and also acts as a vacuum
barrier. This tube also contains the tracking detector and the necessary
cabling.

5\. Beam path to the target: The beam is shown focusing with a center line to
the beam edge angle of 10 degrees. The inner cone is between the beam (at
atmospheric pressure) and the vacuum (insulation). The outer cone is the
barrier between the vacuum and the xenon. Further studies might lead to a
modification of the downstream exit pipe to mirror the entrance side, and the
optimization of the ATAR holder, to allow pass through of $\pi$DIF muons.

####  III.5.5 Other Calorimeter Options

A LYSO crystal calorimeter is also being investigated as an alternative to
LXe; it would provide natural segmentation as in the PEN/PiBETA experiments.
We discuss this further in the Appendix.

###  III.6 Trigger and Backend electronics

All triggers will start with a PI signal, which is a loose condition for an
incident beam particle. PI can be defined as a coincidence of the BEAM
detectors (LGAD telescope layers). The key point is that this trigger must not
introduce any bias between $\pi\to e\nu$ and $\pi\to\mu\to e$ events. For the
estimates we assume that a separator is installed, so that the rate RPI=300
kHz corresponds to the design beam rate and is dominated by pions.

The main time distributions in the vicinity of the PI signal are sketched in
Fig. 15. After an initial build-up with the pion lifetime, positron rates from
$\pi\to\mu\to e$ reach their maximum before decreasing with the muon lifetime.
The constant accidental rate from muon decays of other pions stopped in ATAR
is high.

Figure 15: Positron rates after PI per second in 1 ns time bins. $\pi\to e\nu$
positron rates are multiplied by a factor 100. $\pi\to\mu\to e$ rates
generated by PI shown in red and positron rates from old muons, i.e. from
accidental pions, shown in blue.

After requiring the PI signal, the following main triggers are formed:
[enumerate] (Start1=1) & PI: This is a minimum bias trigger, with the PI
signal prescaled by about k=1000. CaloH: Selection of high energy
(E${}_{tot}\gtrsim$ 58 MeV) events detected by the CALO within a time range
TR=[-300,700] ns relative to PI. TRACK: All events with TRACKER hit within
time range TR relative to PI, prescaled by about k=50. We note that the
probability to observe a $\pi\to\mu\to e$ positron in TR is 0.19, while the
probably for detecting an old muon positron is 0.3, thus accidentals are a
significant part of this trigger. PROMPT: Selected prompt events with a
TRACKER hit in time range [2,32] ns relative to PI, potentially prescaling
required.

For all triggers a full event readout will be initiated. The properties and
required bandwidth for these trigger classes are summarized in Table 3.
Additional data flow from the TRACKER and BEAM counters is small, and not
included.

triggers | prescale | range | rate | CALO |  ATAR digitizer |  ATAR high thres
---|---|---|---|---|---|---
|  | TR(ns) | (kHz) |  $\Delta$T(ns) | chan | MB/s |  $\Delta$T(ns) | chan | MB/s | chan | MB/s
PI | 1000 | -300,700 | 0.3 | 200 | 1000 | 120 | 30 | 66 | 2.4 | 20 | 0.012
CaloH | 1 | -300,700 | 0.1 | 200 | 1000 | 40 | 30 | 66 | 0.8 | 20 | 0.004
TRACK | 50 | -300,700 | 3.4 | 200 | 1000 | 1360 | 30 | 66 | 27 | 20 | 0.014
PROMPT | 1 | 2,32 | 5 | 200 | 1000 | 2000 | 30 | 66 | 40 | 20 | 0.2
Table 3: Main triggers: time range TR and trigger rates. For detector systems
readout island length $\Delta$T, average number of channels and required
readout bandwidth are given.

The main purpose of CaloH and TRACK is the selection of true $\pi\to e\nu$ and
$\pi\to\mu\to e$ events, respectively. The $E_{tot}$ CALO energy sum will be
calculated in the trigger processor with a latency of 200 ns. Events above the
Michel continuum with $E_{tot}>E_{H}\approx$ 58 MeV will be assigned to CaloH.

The full event readout includes the CALO waveforms, the ATAR and the BEAM and
TRACKER detectors.

The CALO data will comprise islands of contiguously digitized ADC samples from
the SiPMs / PMTs readout of the calorimeter. We assume 2-bytes per sample, 200
samples per island, and 1000 islands channels per trigger. Thus a trigger rate
of 5 kHz generates 2 GB/s.

The zero suppressed ATAR waveforms of typical length of $\Delta$T=30 ns will
be stored, with the readout window extended if the signal remains above
threshold at the end of the island. The dominant $\pi\to\mu\to e$ event will
fire about 66 strips. Depending on strip cross talk, which differs for LGAD
technology choices, i.e. AC-LGAD vs. TI-LGADS, this strip count could be
3-times higher. With a 1 GSa/s digitization and 4 Bytes required per hit, 66
channels of 30 ns islands correspond to 30*66*4=8 kB. Thus a trigger rate of 5
kHz generates 40 MB/s.

In addition (see ATAR high thres in Table 3) the trigger processor will also
receive high threshold logic signals from the ATAR low and high threshold
discriminators located at the frontend of the ATAR digitizers and will time
stamp those with coarse resolution (few ns). Those hits will always be read
out for a time period of 10 $\mu$s preceding PI. This data can determine
whether a previous pion stopped at the stop location of PI, to potentially
apply a local pile-up for those events.

By far the most challenging is the PROMPT trigger which is of critical
importance for the experiment. (Margin=2cm,
Hang1=true,Hide2=0,Numbers1=r,Numbers2=r,Progressive*=.5 cm,Start1=1) & It
will trigger on all prompt TRACK events, where the $\pi\to\mu\to e$ events are
suppressed by a factor 6.4$\times 10^{-3}$ in [2,32] ns. This should verify
that the CaloH trigger does not miss events by its more complicated Etot
trigger configuration. If required this part of the trigger can be prescaled.
PROMPT is critical to measure $\pi\to e\nu$ events which are lost because the
CALO response falls below $E_{H}$. The uncertainty in those losses were the
limiting systematics in the last generation of experiments. We consider
additional ATAR requirements at trigger level, like hits in the most upstream
layers and no hit in the most down stream layers within the ATAR time
resolution of 100 ps. We will design the trigger processor and DAQ bandwidth
such that all PROMPT events can be transferred in streaming mode to a front
end computer farm. Thus the stored data volume will be reduced in a
combination of trigger processor and software decisions, by applying ATAR cuts
on track topology and energies to suppress $\pi\to\mu\to e$ events. Ideally,
this should be done in an unbiased way. However, as the main purpose is a
measurement of the loss term of $\pi\to e\nu$ events, small biases can be
tolerated and even prescaling can be considered if unavoidable.

In addition, the PROMPT trigger will select a sample of $\pi$DAR-$\mu$DIF
events. Positrons from immediate $\mu$DIF decay are indistinguishable from the
$\pi\to e\nu$ radiative tail events. Measurements of the spectrum of positrons
after PI, where the muon deposits only a fraction of its 4 MeV energy, will
constrain this background class.

####  III.6.1 Trigger design

Figure 16 shows the planned topology for readout and triggering of PIONEER.
The design takes advantage of the APOLLO Zou (2021) platform designed for the
trigger track finder and pixel readout in the CMS experiment at the LHC. The
Command Module (CM) component of the APOLLO board provides a highly
configurable environment supporting a dense high speed IO environment via 25
Gbps Samtec Firefly fir (2021) optical inputs. The platform already supports
the flexible high speed synchronous command and triggering TCDS2 (Trigger and
Timing Control and Distribution System) CMS (2021) for the CMS phase II
upgrade, as well as options for direct IO for receiving timing signals or
generating trigger signals for devices expecting analog triggers. We
anticipate using a single FPGA version of the board (utilizing the Xilinx
VU13P) with an interposer in the second FPGA slot to bring all the serial
links to the VU13P. While by some measures this board likely provides more
power than needed for PIONEER, it has already undergone significant
prototyping with full production anticipated in 2024, and can satisfy several
of the needs of the system with a single platform. The engineering group that
designed the CM will also contribute to calorimetry readout, providing
additional coherence.

Figure 16: Proposed topology of the trigger and subdetector readout systems.

PIONEER anticipates use of the 16.1 Gbps Firefly implementation. This protocol
serializes 64 bit words with a 64b/66b encoding, resulting in an effective
transmission of 64 bit words at rates up to 244 MHz. Each channel supports
both transmit and receive functions, which will allow for significant
flexibility in the command and control system.

The Samtec Firefly system already supports PCI Express (PCIe) Gen 3 and Gen 4
integration, with commercial PCIe over firefly adapter cards already available
for Gen 3. As discussed further in Sec. III.7, PIONEER proposes use of PCIe as
the protocol underlying the DAQ system.

The main trigger APOLLO processor will receive trigger inputs, either via
inputs connected to the FPGA standard IO pins, or from the firefly inputs and
apply the appropriate logic algorithms to generate triggers and guide
sparsification. The processors encode the resulting trigger and configuration
information into the TCDS (or equivalent) datastream, which gets transmitted
to all subdetectors. The processor will also receive status and health
information from the subdectector, communicating any alarm conditions to the
DAQ system for appropriate action.

The trigger processor will receive trigger inputs from the BEAM counters and
from the tracker to form the PI, Track and PROMPT triggers, with configurable
prescale factors applied as noted earlier. The processor will also receive
energy sums from subsections of the calorimeter (see Sec. III.6.2) and
complete the total energy sum used to form the CaloH trigger in coincidence
with the (unprescaled) PI trigger. The processor can flexibly accommodate the
needs of the beta decay (Phase II) of the experiment, completing, for example,
opening angle or mass estimates based on energy-weighted position sums from
the calorimeter electronics.

The processor will also interact with the ATAR, level 3 trigger system and DAQ
system to coordinate additional trigger information from the patterns in the
ATAR as described above.

####  III.6.2 Calorimeter backend electronics

Figure 17 illustrates the digitization and readout electronics proposed for
the calorimeter. The 12 channel digitization boards will utilize the Analog
Devices AD 9234 dual channel, 12 bit 1 GSPS ADC chip, chosen for its low
latency of 59 ns from presentation of the signal at the front end to output of
the digitized signal. These chips communicate the digitized output via the
JESD204 protocol, which will present the data for each ADC channel as 64 bit
words containing four samples at 250 MHz. At these rates, the calorimeter
information can be summed with a pipelined adder and potentially corrected
with a running pedestal measurement as the first stage in a total energy
measurement. By clocking the ADC at the slightly lower rate of 976 MHz, the
ADC information can be synchronized to the firefly data transfer rate of 244
MHz, simplifying synchronization of the system.

The ADCs will sample continuously with samples stored initially in a ring
buffer on the FPGA. Upon receipt of a trigger, a configurable time window will
be stored in DIMM memory. By deploying a DIMM with a 128 bit data path,
simultaneous reading and writing can be accomplished via two 64 bit pathways.

Figure 17: Proposed calorimeter digitization and readout. The 12 channel
digitizer boards utlize the dual channel AD9234 12 bit, 1 GSPS ADCs, Xilinx
Ultrascale FPGAs for contro, and Samtec FireflyTM high speed communications to
a CMS APOLLO board. The APOLLO board can receive up to 22 boards in this
configuration – instrumenting quadrant of an order 1000 channel calorimeter.

A single FPGA will control one pair of ADCs (four calorimeter channels). It
can compare the energy sum from each channel against a channel activity
threshold (or thresholds), as well as combine the four running energy sums as
the first stage of a total energy sum for the high energy trigger. That FPGA
will also drive a single firefly channel. The 64 bit word for the firefly
communication provides much flexibility. After reserving 48 bits for readout
of the four channels upon receipt of a trigger, 16 bits can provide triggering
information at the full 244 MHz rate. Possible configurations include a 12 bit
sum of the four calorimeter channels along with a bit for each channel
flagging a sum over threshold. With a coarse 8 bit sum, 2 bits could be
devoted to each individual channel. For the beta decay phase, the trigger
could pass energy-weighted position information for a mass calculation. Xilinx
kintex ultrascale FPGAs provide sufficient numbers of high speed serial lines
at a reasonable cost.

The digitizer boards will communicate with intermediate Apollo boards via the
16.1 GHz firefly links, which come packaged with a minimum of four individual
links. Three of these links will provide the TCDS (or equivalent) clock and
control signals and send the trigger and channel readout information to each
of three sets of 4 ADC channels. The fourth firefly line will provide PCIe or
ethernet communication to allow board configuration and other slow control
functions.

After taking into account communication links to the trigger processor and
between the intermediate Apollo boards, each intermediate Apollo can
accommodate 22 12-channel digitizer boards for a total of 264 channels. Four
such boards would instrument a calorimeter with up to 1056 channels. With a
more complex, run-state dependent scheme for communications, 16 channels per
board could be accommodated.

The intermediate APOLLO boards will collate the waveforms read from all
channels for each trigger, and send that information directly to the DAQ
system. Each APOLLO can sustain a full readout rate of about 18.5 kHz for the
264 channels, allowing for significant headroom given the anticipated trigger
rates (see Tab. 3) and use of sparsification for an order 1000 channel
calorimeter.

The total calorimeter energy sum proceeds in several stages. Each quad-channel
FPGA adds those four signals as noted above. Each intermediate Apollo will
combine the those sums from the $22\times 3=66$ quad channels. The trigger
process will provide the final combination of the four intermediate sums
needed for the complete calorimeter sum.

The latency in the energy sum has three main contributions: the ADC latency,
the FPGA summation time, and the serialization/deserialization overhead for
the high speed links. The Xilinx GTY transceivers have a high degree of
configurability, resulting in a total serialize/deserialize latency for the
readout chain above that ranges from 65 ns to 175 ns at the 16.1 GHz serial
rate. Recent studies Oliveira (2020) show that even the simpler, lower latency
settings, can achieve reliable links. With 100 ns as a reasonable estimate, 50
ns as a limit for the energy summation at 244 MHz, and the 50 ns ADC latency,
we estimate a total latency of 200 ns.

###  III.7 DAQ

####  III.7.1 Data acquisition system

The PIONEER data acquisition system must handle the read out, event assembly
and data storage for the active target, positron tracker, electromagnetic
calorimeter and other detector sub-systems of the experimental setup. It must
provide a deadtime-free, distortion-free record of the datasets identified by
the various physics and calibration triggers. It must facilitate the
monitoring needed to guarantee the overall integrity of data taking and
provide the metadata needed to document the experimental configuration during
data taking. Finally, it must enable the configuration of the readout
electronics and the associated trigger, clock and control system.

The acquisition will be implemented as a modular, distributed system on a
parallel, layered processor array consisting of networked, multi-core,
commodity PC’s running a scientific Linux operating system. The overall layout
is depicted schematically in Fig. 18. It will comprise a frontend processor
layer responsible for readout and processing of event fragments from the FPGA-
based fast electronics instrumenting the various detector sub-systems, a
backend layer responsible for event building and data storage, a slow control
layer responsible for configuration and readback, and a data quality layer
responsible for monitoring of data integrity.

To maximize the bandwidth the frontends will utilize memory-mapped, Gen3 PCI
Express communication with the Apollo readout boards and the downstream DAQ
layers will utilize memory-mapped, Gen3 PCI Express host / target adaptors for
data transfer and sharing system resources (disks, GPUs, etc). PCI-Express 3.0
delivers an effective data transfer rate of nearly 1 GB/s per serial lane.
Commercial host-to-target optical interfaces are now available for the Apollo
FPGA to frontend computer communication (e.g.,
www.dolphinics.com/products/PXH842.html). Commercial peer-to-peer
communication is also now available for direct PCI-Express data transfer
between devices (e.g., www.dolphinics.com/products/PXH810.html). The setup
will offer the capability of direct transfer of data to / from FPGA and CPU /
GPU memory for rapid realtime processing.

Figure 18: Schematic of the data acquisition system showing the frontend layer
for data readout and experiment configuration, the backend layer for event
assembly and data storage, and the analysis layer for data quality monitoring.
The number of frontends and the topology of the FPGA-to-frontend and frontend-
to-backend networks will be based on the calorimeter, ATAR and FPGA technology
choices.

The DAQ software will be based on the MIDAS data acquisition package mid
(2018), CUDA GPU toolkit cud (2021), ROOT data analysis package roo (2021),
and Linux PCI Express system and utility libraries. The MIDAS software
consists of library functions for data flow between different processes on
local / remote devices as well as infrastructure for data logging,
experimental configuration and local /remote run control. It also incorporates
an integrated alarm system and slow control system. The devices drivers for
the configuration and the readout of the Apollo board FPGAs will be based on
the PCI Express communication protocols / libraries.

As discussed in Sec. III.6.1 and Table 3, we anticipate the various physics
triggers to include a prescaled beam trigger PI, a beam particle - high energy
CALO trigger CaloH, a prescaled beam particle - low threshold CALO trigger
PROMPT, and a beam particle - outgoing positron trigger TRACK (as identified
by either the ATAR or the tracker). The cumulative trigger rate in Table 3 is
estimated at approximately 8.8 kHz.

The ATAR data will comprise above-threshold islands of contiguously digitized
ADC samples from the fired detector strips of the active stopping target.
Based on a 1 GSPS sampling rate, 4 Bytes per sample, and 66 above-threshold
strips per trigger, we anticipate an ATAR data rate of about 70 MB/s for the
aforementioned trigger types.

The CALO data will comprise islands of contiguously digitized ADC samples from
the SiPM / PMT readout of the calorimeter. Based on a 1 GSPS sampling rate, 2
Bytes per sample, 200 samples per island and 1000 islands / channels per
trigger, we anticipate a CALO data rate of about 3.5 GB/s for the
aforementioned trigger types.

Other detector systems will include the various beam detectors upstream of the
ATAR and the positron tracking detector surrounding the ATAR. The data rates
from beam detectors and tracking detector are expected to be a small fraction
of the ATAR / CALO data rate.

Separate frontend processors running MIDAS frontends will readout the ATAR,
calorimeter, tracker and beam sub-systems via the PCI-express bus using
commericial transparent host / target PCI Express adapters to the Virtex FPGAs
on the Apollo readout boards. The memory-mapped readout from the Virtex FPGAs
chip will permit both high data transfer rates and direct data transition to
system CPU and GPU memories. We plan to utilize IPBus over PCI Express for the
configuration of the readout electronics and the trigger, clock and control
system.

The data acquisition system will process in real-time the data from a roughly
3.5 GB/sec raw data rate to a roughly $\sim$300 MB/sec processed data rate for
data storage on PSI’s Petabyte archive. One option for the data processing is
the lossless compression of the slow decay-time calorimeter signals via a
combination of delta encoding and Golomb coding. The delta encoding will
exploit the correlations between sequential ADC samples to shrink the word
usage distribution while Golomb coding is suited to situations in which the
occurrences of small values are significantly more likely than the occurrences
of large values. Other possibilities are zero suppression of CALO islands and
realtime fitting of CALO pulses. These algorithms are well suited to parallel
processing using GPUs.

We are initiating an R&D effort to demonstrate both the technology for the
FPGA-to-CPU / GPU communication via optical PCI-express links and the
performance of the data compression schemes. The R&D setup will allow for code
development, testing and debugging as well as the evaulation of the rate
capabilities and the compression capabilities of the system. We plan to use
commercial PCI-Express FPGA development boards as data simulators for the
detector sub-systems in order to prototype and benchmark the DAQ.

The PIONEER DAQ group has developed and operated similar architectures of
distributed data acquisition systems for the MuLan, MuCap and MuSun
experiments at the Paul Scherrer Institute and the g-2 experiment at Fermi
National Accelerator Lab.

####  III.7.2 Data Policy

The PIONEER collaboration will comply with the _data policy for PSI research
data_ PSI  and will publish the experiment’s data under PSI’s custody after a
suitable embargo period. We are also committed to publish our software under
an open source license at a suitable time.

##  IV Simulations

Each of the design elements discussed above is being actively studied using
GEANT4-based Agostinelli  _et al._ (2003) simulations. The simulation efforts
include beamline and upstream detector simulations, simulation of the active
target, and simulation of the calorimeter.

The $\pi$E5 beamline at PSI is simulated using G4Beamline Roberts  _et al._
(2008) discussed in Section III.2.3. The remainder of the simulation is done
primarily using GEARS, an extension of GEANT4, which streamlines readout for
rapidly iterating systems. The geometries for each of the experimental
components are generated using a stand-alone Python script and geometry
library, which takes as its input a json file of various parameters (e.g.
diameters, number of elements, which detectors to implement, etc.) and exports
a GDML file which is then read in by the Geant4 simulation. This file contains
a full description of the physical geometry of the detectors, as well as their
material properties (density, reflectivity, scintillation yield, etc.).
Because of this workflow, it becomes trivial to implement scans over various
parameters to perform systematic studies.

In the following sections, we discuss the initial ATAR and calorimeter
simulations.

###  IV.1 ATAR Simulations

Simulations of the active target are done with both GEANT4, which allows us to
model pions and their decay products through the full chain of detectors, and
TRIMZiegler  _et al._ (1985), which allows us to track particle energy
deposition precisely in a simulated detector readout. Figure 19 (left) shows
the ATAR concept and (right) a simulation of energy deposit by exiting
positrons as a function of polar angle of emission.

Figure 19: Left: An image of the simulated ATAR, showing the active planes
(white) and readout strips (orange). Right: Total energy deposited in the ATAR
by the decay positron as a function of the angle $\theta$ at which it enters
the calorimeter.

The active target is implemented in the simulation as alternating layers of
cross-hatched silicon strips. The number of strips per layer, their
thicknesses, and the number of layers is fully configurable. The nominal
configuration consists of 48 120 $\mu$m thick planes of 100 strips each for a
total size of $20\times 20\times 5.76\,\mathrm{mm^{3}}$. Optional ‘dead’ zones
can be implemented in each pixel, to simulate the effect of trenches between
pixels within a plane or a dead backing layer. Each plane of the ATAR has a
fully simulated readout cable, consisting of Kapton and Silicon, simulating
the ultimate flex cable readout. These readouts introduce an asymmetry in the
energy reconstructed by the calorimeter, and as such have the potential to
introduce a systematic bias to our analysis. The design of the readouts will
be informed by this simulation in order to minimize such an effect.

####  IV.1.1  Background Suppression for the Measurement of the $\pi\to e\nu$
tail fraction

With an anticipated tail fraction $f=0.5\%$ of $\pi\to e\nu$ events, $\mu-e$
decays must be suppressed to a level that allows measurement of $\Delta f/f$
with accuracy 1–2%. This can be accomplished by using ATAR information to
identify stopped pions (and reject incoming muons) by energy loss, and range-
energy relations, using a narrow time window (e.g. 3–35 ns) following the pion
stop, rejecting events with observation of the 4.1 MeV decay muon, and
suppressing events with pion decay-in-flight ($\pi$DIF), and muon decay-in-
flight ($\mu$DIF) following pion decay-at-rest ($\pi$DAR) by tracking and
energy loss measurements.

Assuming a 10% energy resolution (comparable to that of the PIENU target)
$\pi\to\mu\to e$ background in the tail region from the dominant pion decay at
rest will be suppressed to a negligible level as found in PIENU. Radiative
decays $\pi\to\mu\nu\gamma$ followed by $\mu\to e$ decays which may leave
$<4.1$ MeV in the target will be suppressed by observation of the gamma and
detection of the muon pulse and residual energy. In addition, muons that
originate from $\pi$DAR in the ATAR can decay in flight in the 12 ps it takes
before stopping ($\mu\,\mathrm{DIF}$), leaving a positron with the same time
distribution as $\pi^{+}\rightarrow e^{+}\nu$ events. $\mu\,\mathrm{DIF}$
events, although the probability of occurrence is small ($6\times 10^{-6}$),
would represent a significant background comparable to the low energy tail
fraction since it has the same time distribution as $\pi\to e\nu$ events.
Thanks to the high granularity of the ATAR, it is possible to observe the
energy deposition at the pion decay origin and to measure the local energy
loss along the positron track. Typically, a 4.1 MeV muon travels 0.8 mm in the
ATAR and leaves high dE/dx hits in 4 strips on average. An initial simulation
of $\mu\,\mathrm{DIF}$ events, indicated a suppression factor of 20 from local
dE/dx measurements and we expect another order of magnitude suppression from
positron tracking, pulse detection, and total energy measurements. This would
put the $\mu\,\mathrm{DIF}$ at about $10\%$ of the tail fraction $f$. (We are
also studying the possibility of reducing the LGAD strip thicknesses in the
stopping region to enhance rejection of this background and/or using a
separate thin layer ATAR setup for studying this effect.) Furthermore, we
expect that experimental studies of observable $\mu\,\mathrm{DIF}$ will enable
us to know the background component accurately so it can be subtracted.

As illustrated in Fig. 4, another potentially significant low energy
background in the tail region comes from $\pi\,\mathrm{DIF}$ in the ATAR
followed by muon decay at rest. This component dominated the background
suppressed spectrum in PIENU. Simulations indicate that 0.1% of pions decay in
flight in the ATAR before stopping and initial studies indicate that the
$\pi\,\mathrm{DIF}$ events can be suppressed by a factor of 5000 using ATAR
tracking information which recognizes kinks in the topology and measures dE/dx
along the track. Along with suppression of muon decays by selecting a narrow
time window e.g. 3–35 ns after the pion stop, we estimate that the $\pi$DIF
contribution to the uncertainty in the tail correction $f$ will be negligible.

There is an ongoing effort to apply machine learning tools to boost the
sensitivity to $\pi^{+}\rightarrow e^{+}\nu$ events in the tail region and
suppress the backgrounds. It has already been demonstrated with the in-ATAR
$\pi\,\mathrm{DIF}$ events that gradient boosting decision trees (BDT) are
able to outperform the manual cut-based methods. Although the BDT model shows
excellent classification performance, only manually-constructed physics-
inspired high-level information has been used as input features for the model
training. As deep neural networks, especially Convolutional Neural Networks
(CNN), have shown extraordinary performance in various image processing and
classification applications, it could be advantageous to make use of deep
neural networks’ ability to automatically learn high-level features directly
from the complete pixel-level energy deposit information.

###  IV.2 Calorimeter Simulations

####  IV.2.1 Pileup

Simulation studies of the LXe calorimeter response have been performed using
the GEANT4 package Agostinelli  _et al._ (2003) with optical photon tracking.
A simple geometry (see Fig. 20a) that is representative of the current design
was implemented. $\pi\rightarrow\mu\rightarrow e$ events were generated in the
target at the center of the LXe sphere and optical photons originating from
LXe scintillation induced by the showers generated by the positrons were
tracked until the outside sensitive surface of the LXe sphere. The simulated
pulses obtained are similar to the ones reported by MEG. A pulse fitting
algorithm was employed to evaluate the possibility of separating events that
overlap in time i.e. pulse pileup. Pulse separation down to 5 ns was achieved
(see illustration in Fig. 20b) across a wide range of amplitudes. This gives a
first indication (without digitization) of the performance of the detector and
subsequent data analysis with respect to dealing with pileup.

Further studies are anticipated to introduce and optimize optical qualities of
the surfaces, optimize photo-sensing detectors’ coverage, and improve the
simulation of the originating scintillation photons. Much of the input for
these simulations will be provided by test measurements.

(a)

(b)

Figure 20: (a) Rendering of the simplified geometry used in the first Monte-
Carlo simulation of the PIONEER LXe calorimeter (b) Example of simulated pulse
shapes of a single $\pi\rightarrow\mu\rightarrow e$ event (top) and 3 events
happening closely in time (bottom) and recorded in the LXe calorimeter. Pulse
shape fitting based on a template allows accurate identification and energy
reconstruction of multiple pulses down to $\pm$5 ns separation.

Position resolution will also augment pile-up handling capabilities. The
position resolution capabilities of the detector and its importance for
achieving the targeted rate will be modeled and studies are envisaged in the
apparatus which will also be used to test the photo-sensors in LXe. Depending
on the outcome of the pileup studies, segmentation of the LXe volume may be
considered.

####  IV.2.2 Additional Calorimeter Studies

At the current design stage and given the targeted level of precision, further
simulations assessing the performance of the calorimeter will be carried out
in conjunction with development of design parameters for the beam, ATAR, and
tracking detectors. One important aspect of the calorimeter design that is
being informed by the simulations is understanding how energy from a decay
positron is ‘lost’ before it reaches the calorimeter. While energy lost in the
ATAR is measured, losses occurring in inactive material e.g. the ATAR cabling,
and calorimeter entrance windows, depend on the angle of emission. Simulations
are being used to study these effects on the positron energy resolution.

Another important study involves modeling of photonuclear interactions. As
decay positrons interact with atomic nuclei in the simulation, they will
occasionally cause a nucleus to enter into an excited state with single or
multiple neutron emission. When these neutrons escape the calorimeter without
depositing their energy the observed energy is shifted down by multiples of
the neutron binding energy (see Fig. 3). Photonuclear processes were studied
in the PIENU experiment to determine the impact on the NaI(Tl) calorimeter
lineshape. The results were used as input to the calorimeter simulations.
Modeling and prototype studies will be pursued for evaluating these effects in
LXe.

In summary, the robustness of the calorimeter performance for the
determination of the low energy tail, the resolution, and the pileup rejection
will be evaluated by studying the following aspects:

  * •

impact on resolution and reconstruction of energy loss in inactive materials,

  * •

optical properties of the inner surfaces of the LXe detector (reflectivity,
light absorption, etc),

  * •

granularity, layout (inner and outer surfaces) and specification of photo-
sensors (dark current, PDE, etc.), and

  * •

characterizations of scintillation light in LXe; e.g., variations in the
absorption length.

Understanding how these conditions affect the performance of the calorimeter
will determine the critical parameters required for the next phase of the
experimental design.

##  V Sensitivity

###  V.1 $\pi\to e\nu$

The first phase of PIONEER ($R_{e/\mu}$) will employ a beam with pion stopping
rate in the ATAR of approximately $3\times 10^{5}$/s at momentum of $55-70$
MeV/$c$ with $\frac{\Delta p}{p}\leq 2\%$ in a spot size $\leq 2$ cm diameter.
Muon and positron contaminations will be reduced to $<10\%$ with the use of a
separator as discussed above. These requirements are compatible with the beams
available at the $\pi$E5 (and $\pi$E1) beamline.

For the basis of estimating the running time to reach the proposed
sensitivity, we assume that the beam will be available during 5 months per
year. We also assume an overall event acceptance efficiency of 30%, which is
based on the fiducial volume, the timing window cuts, and reconstruction
factors. We assume a data-taking (operations) efficiency of 50% based on the
product of PSI beam delivery and experimental data-collection uptime, along
with an allocation for non-production systematic uncertainty tests. These
factors result in $2\times 10^{8}$ $\pi^{+}\to e^{+}\nu$ events for a 3-year
run satisfying the statistics goal.

| PIENU 2015 | PIONEER Estimate
---|---|---
Error Source | % | %
Statistics | 0.19 | 0.007
Tail Correction | 0.12 | <0.01
$t_{0}$ Correction | 0.05 | <0.01
Muon DIF | 0.05 | 0.005
Parameter Fitting | 0.05 | <0.01
Selection Cuts | 0.04 | <0.01
Acceptance Correction | 0.03 | 0.003
Total Uncertainty | 0.24 |  $\leq$ 0.01
Table 4: $Br(\pi\to e\nu)$ precision for PIENU 2015Aguilar-Arevalo  _et al._
(2015a) (left) and estimated precision for PIONEER (right).

Systematic uncertainties for PIONEER have been estimated based on the
experience of PIENU Aguilar-Arevalo  _et al._ (2015a) and are shown in Table
4. The main systematic uncertainty for PIENU was the uncertainty in the tail
correction for $\pi\to e\nu$ events below 52 MeV. In PIONEER the tail will be
reduced from 3% to $0.5\%$ due to the increased thickness of the calorimeter
(25$X_{0}$ compared to $\leq$19$X_{0}$) and the more uniform acceptance due to
the larger solid angle. The ATAR will allow suppression of $\pi DIF$ and $\mu
DIF$ backgrounds enabling more precise measurement of the tail. Uncertainties
in the other small corrections, e.g. the pion stop time ($t_{0}$) Correction,
Selection Cuts, and Acceptance Correction, are estimated to be reduced due to
the improvements such as in the calorimeter and ATAR timing resolutions. An
additional uncertainty arises from the pion lifetime, presently known to 0.02%
precision Zyla  _et al._ (2020); the PIONEER group intends to make additional
measurements to reduce this uncertainty to $<0.01\%$.

###  V.2 Exotics

####  V.2.1 Massive neutrino searches $\pi^{+}\to\ell^{+}\nu_{H}$

Searches for peaks in the positron energy spectum due to
$\pi^{+}\to\ell^{+}\nu_{H}$ decays were performed in the PIENU experiment
Aguilar-Arevalo  _et al._ (2018, 2019) sensitive to masses $65<m_{H}<135$ MeV
but no significant signal above statistical uncertainty was found. The
measurement of $R_{e/\mu}$Aguilar-Arevalo  _et al._ (2015a) provides limits
for $m_{H}<65$ MeV. To estimate the expected sensitivities for PIONEER with
$100\times$ the statistics (Phase I), reduced backgrounds, and improved
detectors, toy MC simulations were performed.

For $\pi^{+}\to e^{+}\nu_{H}$ decays, the peak search sensitivity was limited
by residual $\pi^{+}\to\mu^{+}\to e^{+}$ background from pion and muon decay-
in-flight ($\pi$DIF and $\mu$DIF). The low energy calorimeter response tail
and statistics of the $\pi^{+}\to e^{+}\nu_{e}$ decay also limits the
sensitivity. Using an active target and a larger electromagnetic calorimeter,
the background $\pi^{+}\to\mu^{+}\to e^{+}$ will be significantly suppressed
compared to PIENU, and a significantly smaller low energy $\pi^{+}\to
e^{+}\nu_{e}$ tail is anticipated. Figure 21 shows the result of a toy MC
study for the expected sensitivity (90% C.L. upper limits) in PIONEER,
assuming $1\times 10^{8}$ $\pi^{+}\to e^{+}\nu_{e}$ events, 1% tail fraction
below 52 MeV, no $\pi^{+}\to\mu^{+}\to e^{+}$ events, and negligible
acceptance corrections due to the larger detector acceptance. Compared with
PIENU (red in Fig. 21), the expected sensitivity in PIONEER (black) would be
improved by one order of magnitude.

Figure 21: Left: simulated $\pi^{+}\to e^{+}\nu_{e}$ energy spectrum.
Right:Limits on $|U_{ei}|^{2}$ (90% C.L.) from PIENU (red)Aguilar-Arevalo  _et
al._ (2015a, 2018)) and expected from PIONEER (black). The lower region limits
($m_{H}$<65 MeV) come from the branching ratio measurement and the higher
($m_{H}$>65 MeV) region from the peak search.

The sensitivity for $\pi^{+}\to\mu^{+}\nu_{H}$ decay will also be improved by
the larger PIONEER statistics . The dominant background is mainly due to the
radiative pion decay $\pi^{+}\to\mu^{+}\nu_{\mu}\gamma$ with branching
fraction $2\times 10^{-4}$ Bressi  _et al._ (1998) (for $E_{\gamma}<1$ MeV). A
toy MC simulation was performed with $1\times
10^{9}~{}{\pi}^{+}\to\mu^{+}\nu_{\mu}$ decays ($\times 100$ larger statistics
than PIENU) including $\pi^{+}\to\mu^{+}\nu_{\mu}\gamma$ background
considering the proper branching fraction, and assuming the same detector
resolution as in PIENU. Figure 22 shows the results of the simulation and the
PIENU experiment Aguilar-Arevalo  _et al._ (2019).

Figure 22: Left: simulated $\pi^{+}\to\mu^{+}\nu_{\mu}$ kinetic energy
spectrum. Right: The PIENU result (red triangles Aguilar-Arevalo  _et al._
(2019)) and expected sensitivity with PIONEER (black circles) for the mixing
matrix element $|U_{\mu i}|^{2}$ (90% C.L. limit).

####  V.2.2 Two body muon decay $\mu^{+}\to e^{+}X_{H}$

Massive or massless weakly interacting neutral bosons $X$ such as axions
Jaeckel and Ringwald (2010); Jeong  _et al._ (2020); Agrawal and Howe (2018);
Alves and Weiner (2018) and Majorons Gelmini and Roncadelli (1981); Chikashige
_et al._ (1981); Aulakh and Mohapatra (1982) have been suggested to extend the
SM including models with dark matter candidates, baryogenesis, and solutions
to the strong $CP$ problem. Wilczek suggested a model Wilczek (1982) which may
lead to charged lepton flavor violation (CLFV) where the boson X can be
emitted in flavor changing interactions.

When decay products from a massive boson $X_{H}$ are not detected due to a
long lifetime, flavor violating two-body muon decays involving a massive boson
$\mu^{+}\to e^{+}X_{H}$ can be sought by searching for extra peaks in the
Michel spectrum. This search was performed with PIENU, resulting in the limit
to the branching ratio $\Gamma(\mu^{+}\to e^{+}X_{H})/\Gamma(\mu^{+}\to
e^{+}\nu\bar{\nu})$ at the level of $10^{-5}$ in mass range $47.8-95.1$
MeV/$c^{2}$ Aguilar-Arevalo  _et al._ (2020a). The statistics will improve by
two orders of magnitude with respect to PIENU.

To estimate the expected sensitivity, $2\times 10^{10}$ muon decays were
simulated. Figure 23 shows the 90% C.L. upper limits of the branching ratio
from different experiments and the expected sensitivity for PIONEER.

Figure 23: 90% C.L. limit on the $\mu^{+}\to e^{+}X_{H}$ branching ratio
anticipated for PIONEER (black circles) and other past experiments (see Refs.
Derenzo (1969); Bryman and Clifford (1986); Bilger  _et al._ (1999); Bayes
_et al._ (2015) for more details).

####  V.2.3 Other decays

Three and four body pion decay modes can be analyzed with the same method as
for the $\pi^{+}\to\ell^{+}\nu_{H}$ searches. However, the signal shapes are
in these cases are represented by continuous lepton energy spectra. The
expected sensitivities will also be improved by one order of magnitude. The
current limits set by the PIENU experiment are described below.

Three body pion decays $\pi^{+}\to\ell^{+}\nu X$, where $X$ is a massive or
massless weakly interacting particle, were searched for in the PIENU
experiment Aguilar-Arevalo  _et al._ (2021). The decay $\pi^{+}\to e^{+}\nu X$
was sought; no signal beyond the statistical uncertainty was observed, and 90%
C.L. upper limits were set on the branching ratio $\Gamma(\pi^{+}\to e^{+}\nu
X)/\Gamma(\pi^{+}\to\mu^{+}\nu)$ with $10^{-7}-10^{-8}$ level in the mass
range of $0<m_{X}<120$ MeV/$c^{2}$.

The $\pi^{+}\to\mu^{+}\nu X$ decay was also searched for. A 90% C.L. upper
limit was derived on the branching ratio $\Gamma(\pi^{+}\to\mu^{+}\nu
X)/\Gamma(\pi^{+}\to\mu^{+}\nu)$ at the $10^{-5}-10^{-6}$ level in the mass
region from 0 to 33.9 MeV/$c^{2}$.

The rare pion decays $\pi^{+}\to\ell^{+}\nu_{\ell}\nu\bar{\nu}$ are highly
suppressed. Thus, the experimental search for these processes could reveal
small non-SM effects such as neutrino-neutrino interactions Bardin  _et al._
(1970) and six-fermion interactions Ericson and Glashow (1964); Vanzha  _et
al._ (1971), which might compete with the SM processes at first order. The
rare pion decays, considering three models (SM, neutrino-neutrino interaction,
and six-fermion) were also searched for in PIENU Aguilar-Arevalo  _et al._
(2020b), and a first result for
$\Gamma(\pi^{+}\to\mu^{+}\nu_{\mu}\nu\bar{\nu})/\Gamma(\pi^{+}\to\mu^{+}\nu_{\mu})<8.6\times
10^{-6}$ and an improved measurement $\Gamma(\pi^{+}\to
e^{+}\nu_{e}\nu\bar{\nu})/\Gamma(\pi^{+}\to\mu^{+}\nu_{\mu})<1.6\times
10^{-7}$ were obtained.

###  V.3 Pion Beta Decay

For the $\pi^{+}\to\pi^{0}e^{+}\nu$ experiment the positive pion stop rate
would have to be higher, $\geq 10^{7}$/s, possibly with a larger momentum bite
$\frac{\Delta p}{p}\approx 3\%$ and likely using higher pion momentum. These
beam conditions are compatible with the $\pi$E5 beam line. This would result
in $7\times 10^{5}$ $\pi^{+}\to\pi^{0}e^{+}\nu$ events collected for 4 years
of (5 months/yr) operation assuming similar efficiency factors as discussed
for the $\pi\to e\nu$ measurement.333In the Phase I measurement of $\pi\to
e\nu$ PIONEER will collect a sizeable sample of pion beta decay events, which
will be helpful to inform the Phase II(III) design. This would be sufficient
to achieve the required statistical precision to improve the pion beta decay
branching ratio measurement precision by a factor of 3 (Phase II). Systematic
effects are expected to be reduced to the 0.06% level ($10\times$ lower than
for the previous PiBeta experiment) due to the combined improvements to the
calorimetry (principally, the time and energy resolutions) and the ATAR which
may facilitate the observation of the positron in $\pi^{+}\to\pi^{0}e^{+}\nu$
decay in coincidence with the $\pi^{0}$ detection.

Running at higher rates may be possible leading to a further precision
improvement of 3 (Phase III) and will depend on the ability of the
spectrometer to deal with higher rates of pile-up of accidental events. In
this regard, we are studying the possibility to optically segmenting the LXe
volume.

##  VI  Planning for Realization of PIONEER

###  VI.1 Collaboration

The PIONEER collaboration consists of participants from PIENU, PEN/PiBeta, and
MEG/MEGII as well as international experts in rare kaon decays, low-energy
stopped muon experiments, the Muon $g-2$ experimental campaign, high energy
collider physics, neutrino physics, and other areas. The collaboration is
still developing and welcomes new members.

We intend to draft a collaboration constitution and institute an appropriate
organizational structure. We have good models, for example, from Muon g-2,
that can be tailored to our smaller, but equally diverse and international,
team. We expect that there will be an elected Executive Board with a Chair
that guides the key technical decisions as an advisory body to the elected
Spokesperson(s) and leaders of the various important technical areas (Beam,
ATAR, Calo, DAQ, etc.).

###  VI.2 R&D

In 2022-23, we anticipate performing detector R&D in several areas including
the following:

  * •

Beam studies. We will carry out beam studies in $\pi E5$ (and possibly $\pi
E1$) to establish the required beam conditions. A beam request for 2022 tests
will be submitted.

  * •

ATAR (see next section).

  * •

Cylindrical positron tracker. Designs with standard 300$\mu m$ thick Si strips
and with LGADs are being considered. We expect to construct and test
prototypes of various geometries.

  * •

LXe prototype. The objectives of this R&D work include determination of the
properties of photo-sensors and optical properties of materials for use in the
LXe calorimeter. We also want to benchmark the photon transport simulations.
We are considering the development of a medium scale calorimeter prototype
that would enable measurements of properties like energy resolution and
photonuclear effects for validation of simulations.

  * •

LXe calorimeter optical segmentation. Small prototypes will be used initially
and UV compatible materials will be evaluated. Some of these studies may be
done using a LXe cryostat at McGill university containing $\sim$2 l of LXe
developed for SiPM tests for nEXO. An assembly hosting SiPMs, reflective
material and a retractable radioactive source will be prepared at TRIUMF and
brought to McGill for measurements.

  * •

SiPMs. SiPM degradation at high rates will be studied. We will test available
photosensors using small LXe prototypes in association with the McGill setup
mentioned above.

  * •

Crystal alternatives to LXe. Arrays of LYSO crystals with varying levels of
doping will be evaluated from various manufacturers. See the Appendix for more
details.

  * •

DAQ. Rate testing of FPGA-to-CPU/GPU and CPU-to-CPU communication via optical
PCI-express links will be done along with performance testing of data
compression algorithms for CALO data.

  * •

Trigger prototyping. We will use a prototype APOLLO Command Module that the
Cornell CMS group will share with PIONEER, and build a 4-channel prototype of
the digitizer board for evaluation and communications development.

###  VI.3 ATAR R&D