# Testing Lepton Flavor Universality and CKM Unitarity with Rare Pion Decays
in the PIONEER experiment

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. Di Canto  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

###### Abstract

ABSTRACT: The physics motivation and the conceptual design of the PIONEER
experiment, a next-generation rare pion decay experiment testing lepton flavor
universality and CKM unitarity, are described. Phase I of the PIONEER
experiment, which was proposed and approved at Paul Scherrer Institut, aims at
measuring the charged-pion branching ratio to electrons vs. muons,
$R_{e/\mu}$, 15 times more precisely than the current experimental result,
reaching the precision of the Standard Model (SM) prediction at 1 part in
$10^{4}$. Considering several inconsistencies between the SM predictions and
data pointing towards the potential violation of lepton flavor universality,
the PIONEER experiment will probe non-SM explanations of these anomalies
through sensitivity to quantum effects of new particles up to the PeV mass
scale. The later phases of the PIONEER experiment aim at improving the
experimental precision of the branching ratio of pion beta decay (BRPB),
$\pi^{+}\to\pi^{0}e^{+}\nu(\gamma)$, currently at $1.036(6)\times 10^{-8}$, by
a factor of three (Phase II) and an order of magnitude (Phase III). Such
precise measurements of BRPB will allow for tests of CKM unitarity in light of
the Cabibbo Angle Anomaly and the theoretically cleanest extraction of
$|V_{ud}|$ at the 0.02% level, comparable to the deduction from superallowed
beta decays.

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2021)

###### Contents

  1. I Executive Summary
  2. II Introduction
  3. III Motivation
  4. IV PIONEER Experiment
    1. IV.1 Experiment Overview and Strategy
    2. IV.2 Conceptual Design
      1. IV.2.1 Beam
      2. IV.2.2 Active Target
      3. IV.2.3 Cylindrical Tracker
      4. IV.2.4 Liquid Xenon Calorimeter
      5. IV.2.5 Considerations on the Alternative LYSO Calorimeter
      6. IV.2.6 Trigger and Data Acquisition System
    3. IV.3 Simulations
      1. IV.3.1 ATAR Simulation
      2. IV.3.2 CALO Simulation
  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
  7. VII Summary

##  I Executive Summary

In recent years, there have been an increasing number of intriguing hints for
lepton flavor universality violation (LFUV). Motivated by these indications of
physics beyond the Standard Model, Phase I of the PIONEER experiment, approved
at the Paul Scherrer Institute (PSI), aims to measure the charged-pion
branching ratio to electrons vs. muons $R_{e/\mu}$ to 1 part in $10^{4}$,
improving the current experimental result $R_{e/\mu}\hskip
2.84544pt\text{(exp)}=1.2327(23)\times 10^{-4}$ Zyla  _et al._ (2020);
Aguilar-Arevalo  _et al._ (2015a); Bryman  _et al._ (1986); Britton  _et al._
(1994); Czapek  _et al._ (1993) by a factor of 15. This precision on
$R_{e/\mu}$ will match the theoretical accuracy of the SM prediction allowing
for a test of LFU at an unprecedented level, probing non-SM explanations of
existing LFUV anomalies through sensitivity to quantum effects of new
particles up to the PeV mass scale.

Phase II and III of PIONEER experiment aim to improve the experimental
precision of the branching ratio of pion beta decay,
$\pi^{+}\to\pi^{0}e^{+}\nu(\gamma)$, currently at $1.036(6)\times 10^{-8}$, by
a factor of three and an order of magnitude, respectively. The improved
measurements of pion beta decay would allow one to extract
$\left|V_{ud}\right|$ in a theoretically pristine manner. The ultimate
precision of $\left|V_{ud}\right|$ is expected to reach the 0.02% level, which
is comparable to the currently most precise deduction from superallowed beta
decays, allowing for a stringent test of CKM unitarity. Furthermore, the
PIONEER experiment will also improve the experimental limits Bryman and Shrock
(2019a, b); Aguilar-Arevalo  _et al._ (2021) by an order of magnitude or more
to a host of exotic decays probing for effects of heavy neutrinos and dark
sector physics.

The conceptual design of the Phase-I PIONEER experiment includes a 3$\pi$-sr
25 radiation length liquid xenon calorimeter, a segmented low gain avalanche
detector (LGAD) stopping target, a positron tracker, and other detectors.
Compared to the previous generation of rare pion decay experiments, the 4-D
(position and time) tracking capability of the LGAD-based active target allows
for excellent separation of $\pi\rightarrow e\nu$ signal from vast amount of
$\pi\to\mu\to e$ background ($\pi\to\mu\nu$ followed by $\mu\rightarrow
e\nu\overline{\nu}$).

The PIONEER collaboration consists of participants from both the nuclear and
particle physics communities including PIENU, PEN/PiBeta, and MEG/MEGII
collaborations, as well as 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 plans R&D in
several critical areas including i) beam studies, ii) LGAD-based active target
(sensor and readout electronics), iii) LXe calorimeter (optical sensor and
optical segmentation), iv) DAQ, and v) trigger, in preparation for a technical
design report. The collaboration is still developing and welcomes new members.

This Snowmass white paper describes the physics motivation and the conceptual
design of the PIONEER experiment, and is prepared based on the PIONEER
proposal Altmannshofer  _et al._ (2022) submitted to and approved with high
priority by the PSI (CHRISP - Swiss Research InfraStructure for Particle
physics) program advisory committee. Using intense pion beams, and state-of-
the-art instrumentation and computational resources, the PIONEER experiment is
aiming to take data at PSI by the end of this decade.

##  II 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 the Paul Scherrer Institute (PSI),
where the highest intensity low energy pion beams are delivered. The Phase I
of PIONEER Altmannshofer  _et al._ (2022), which has been approved by PSI
(CHRISP - Swiss Research InfraStructure for Particle physics) program advisory
committee with high priority, 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 $\approx 3\sigma$ tension Zyla
_et al._ (2020). PIONEER is an ambitious program that will span more than a
decade of research activity at PSI. While we focus on the measurement of the
$\pi\to e\nu$ branching ratio $R_{e/\mu}$ in this paper, 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.

##  III Motivation

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.

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 $1+\epsilon_{\ell\ell}$ where
$\ell=e,\mu$.

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.,
$R_{e/\mu}\hskip 2.84544pt\text{(SM)}=1.23524(19)\times 10^{-4}$. In
comparison, 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)

is more than a factor of 15 worse. 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. Comparison between
$R_{e/\mu}$ in theory and experiment provides a stringent test of the
$e$–$\mu$ universality of the weak interaction; a disagreement with the
theoretical expectation would unambiguously imply the existence of NP. With
the PIONEER Phase I physics goal of improving $R_{e/\mu}$ experimental
precision by a factor of 15 to 0.01% level, NP at the PeV scale can be probed
Bryman  _et al._ (2011), even up to several PeV in specific models such as
leptoquarks. 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.

The significance of the CAA, a $3\sigma$ tension with the CKM unitarity
illustrated in Fig. 1 (left) Bryman  _et al._ (2021); Cirigliano  _et al._
(2021), depends crucially on experimental input quantities used for the
extraction of CKM matrix elements as well as a number of theory corrections.
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, which
allows one to extract $\left|V_{ud}\right|$ in a theoretically pristine
manner. 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

$\frac{\Gamma(\pi^{+}\to\pi^{0}e^{+}\nu)}{\Gamma(\text{Total})}=1.036\pm
0.004~{}(\text{stat})\pm 0.004~{}(\text{syst})\pm 0.003~{}(\pi\to e\nu)\times
10^{-8},$ (3)

where the first uncertainty is statistical, the second systematic, and the
third is the $\pi\to e\nu$ branching ratio uncertainty. While the pion beta
decay provides the theoretically cleanest determination of the magnitude of
the CKM matrix element $\left|V_{ud}\right|$, the current extraction of
$\left|V_{ud}\right|=0.9739(28)_{\textrm{exp}}(1)_{\textrm{th}}$ at 0.3% is
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,
a two-step improvement in experimantal precision is identified. As advocated
in Ref. Czarnecki  _et al._ (2020), the first step is a three-fold improvement
in BRPB precision compared to Ref. Počanić  _et al._ (2014) as proposed in
PIONEER Phase II would allow for a 0.2% determination of
$\left|V_{us}/V_{ud}\right|$ via improving the measurement of the ratio

$R_{V}=\frac{\Gamma\left(K\rightarrow\pi
l\nu(\gamma)\right)}{\Gamma\left(\pi^{+}\rightarrow\pi^{0}e^{+}\nu(\gamma)\right)}=1.9884(115)_{\pi}(93)_{K}\times
10^{7},$ (4)

when combined with $K_{\ell 3}$ decays. As shown in Fig. 1, this would match
the precision of the current extraction of $\left|V_{us}/V_{ud}\right|$ from
the axial channels Marciano (2004) via

$R_{A}=\frac{\Gamma\left(K\rightarrow\mu\nu(\gamma)\right)}{\Gamma\left(\pi\rightarrow\mu\nu(\gamma)\right)}=1.3367(25),$
(5)

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. In the second step,
an order of magnitude improvement in the BRPB precision will be sought in
PIONEER Phase III program. 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).

Finally, PIONEER will improve sensitivity to a host of exotic decays,
including probes for the effects of heavy neutrinos Shrock (1980, 1981); Abela
_et al._ (1981); Minehart  _et al._ (1984); Bryman  _et al._ (1983); Azuelos
_et al._ (1986); Britton  _et al._ (1992); Aguilar-Arevalo  _et al._ (2015a,
2018, 2019); Bryman and Shrock (2019a, b); Aguilar-Arevalo  _et al._ (2021) ,
unique capabilities to search for pion decays to various light dark sector
particles Altmannshofer  _et al._ (2020); Dror (2020); Batell  _et al._
(2018); Aguilar-Arevalo  _et al._ (2021), and lepton-flavor-violating decays
of the muon into light NP particles $\mu\to eX$.

##  IV PIONEER Experiment

###  IV.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 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. Generically, the detector
will have the features sketched out in Fig. 2.

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.

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.

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. 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, the core calorimeter, mechanics, tracker, and
DAQ systems will be designed to meet the needs of both experiments with
limited modifications.

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.

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 CollaborationMihara (2011).

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.
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. New low gain avalanche detector (LGAD)
sensors have been identified as meeting these requirements. Simulation studies
show that, by combining information from the active target and the
calorimeter, $\mu-e$ backgrounds in the tail region can be suppressed to a
level such that uncertainty in the tail fraction contributes $<0.01\%$ to the
error in $R_{e/\mu}$.

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, it is also possible 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.

###  IV.2 Conceptual Design

The previous section described a generic PIONEER design in Fig. 2 and
described the motivation for certain design choices. Figure 4 shows a more
specific conceptual design, which includes the beamline and beamline
instrumentation, the ATAR, a cylindrial tracker surrounding the ATAR, and a
liquid xenon (LXe) calorimeter. An alternative calorimeter based on LYSO
cystals, which provides natural segmentation, is also being investigated as an
alternative to LXe. In this section, each component of this conceptual design
is briefly described and opportunities for detector innovation and R&D are
identifed. More detail is available in Altmannshofer  _et al._ (2022).

Figure 4: PIONEER conceptual design. The sphere is a LXe calorimeter, with the
beam entering from the left, and the ATAR at the center. For scale, the lid is
3.05 m diameter. The yellow circles are merely representative of the LXe
photosensors; they are not placed accurately.

####  IV.2.1 Beam

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 required
beam properties are summarized in Table 1 and can be provided by the $\pi$E5
beam at PSI, which is a high-intensity low-energy muon and pion beamline, with
a maximum momentum of 120 MeV/$c$, that is used for particle physics
experiments, and is currently home to the MEG II and Mu3e experiments.
Simulations for both pion production and transport of particles down the
$\pi$E5 channel were performed using the G4Beamline toolkit Roberts  _et al._
(2008). 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 due to
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.

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.

####  IV.2.2 Active Target

A highly segmented active target (ATAR) Mazza (2021) is a key new feature of
the proposed PIONEER experiment. Relative to previous experiments, the use of
ATAR allows for discrimination against backgrounds by looking for deposition
patterns internal to the target that are associated with the various signals’
decay topologies. The ATAR will define the fiducial pion stop region, provide
high resolution timing information, and will furnish selective event triggers.
Examples of simulated ATAR event displays for $\pi\to e\nu$ and $\pi\to\mu\to
e$ events are shown in Fig. 5.

Figure 5: 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.

To adequately supress background from $\pi\rightarrow\mu\rightarrow e$ decay
at rest ($\pi$DAR), pion and muon decay-in-flight (DIF), and accidental muon
stops that precede the trigger signal, 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 chosen technology for the ATAR is Low Gain Avalanche Detector (LGAD)
Pellegrini  _et al._ (2014), thin silicon detectors with moderate internal
gain; the LGAD technology was chosen over standard silicon technology because
of the intrinsic gain and thin bulk. 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. There are two specific LGAD technology
options under consideration. The first option, AC-LGADs, overcome the
granularity limitation of traditional LGADs and have been shown to provide
spatial resolution of the order of tens of $\mu$m Tornago  _et al._ (2021).
AC-LGAD design also allows to have a completely active sensor with no dead
regions. The second option is Trench Isolated (TI) LGADs, which are a novel
silicon sensor technology that utilizes a deep narrow trench to electrically
isolate neighboring pixels to prevent breakdown, as opposed to standard LGADs
which use a junction termination extension to prevent breakdown at the pixel
edges Paternoster  _et al._ (2020). By utilizing the deep trench isolation
technology, the no-gain region is reduced to a few micrometers, thus achieving
a higher fill factor than regular LGADs.

A preliminary design for the ATAR is shown in Fig. 6. In this design, the ATAR
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 $\sim 6\text{\,}\mathrm{mm}$. The detector is arranged in a strip
geometry, with the strips oriented at $None$ to each other in subsequent
staggered planes to provide measurement of both coordinates of interest, and
with the electronic readout connected on the side of the active region via
wire bonding. The 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. Sensor thickness is around
$120\text{\,}\mathrm{\SIUnitSymbolMicro m}$, such that $\thicksim$50 planes
are needed to reach a total thickness of about $6\text{\,}\mathrm{mm}$. The
detectors are paired with the high-voltage facing each other in a pair to
avoid ground and high voltage in proximity and 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.
Readout from both ends is being investigated to reduce the average material
traversed by exiting positrons; in the single-sided readout design, the
maximum material in the path of the positrons occurs when 12 flexes are
traversed.

Figure 6: 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.

R&D and optimization of the ATAR design is ongoing. Preliminary LGAD studies
done 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 $10\text{\,}\mathrm{\char 37\relax}$. The effect of gain
saturation that was reported in the community in the past year E. Rivera
(2021) also needs to be studied. Strip AC-LGAD prototypes from Brookhaven
National Lab (BNL) have been tested with a laboratory IR laser TCT station Par
and at a Fermilab (FNAL) test beam H. Sadrozinski (2021); the position
resolution of this prototype sensor varies between 5-15 $\mu m$ in the
direction perpendicular to the strip. Prototypes TI-LGADs sensors from
Fondazione Bruno Kessler (FBK) Paternoster  _et al._ (2020) were studied at
UCSC and found to have the standard response of a conventional LGAD with a
small amount of “cross-talk” constant response of the sensor along the strip.
In the next few years, several prototypes will be tested in laboratories and
test beams to identify an optimized LGAD configuration for PIONEER.

The amplifier ASIC to read out the ATAR needs to be fast enough for the sensor
in use; for the signal rise time in the 120 $\mu$m-thick prototype sensors, a
bandwidth of 1 GHz should be sufficient. However, the high dynamic range
(2000) requirement for the ATAR brings major complications to the readout.
Current fast readout chips usually have a dynamic range of $<$ 1000, since
they are targeted at MIPs-only detection in tracker sub-systems. One
possibility is to develop an amplifier chip with logarithmic response or
dynamic gain switching as well as a high enough bandwidth, currently no such
chip exists with the necessary characteristics. Already available integrated
chips, such as FAST Olave  _et al._ (2021) and FAST2, are being evaluated.
Some new ASIC technologies that are being developed at UCSC in collaboration
with external companies can run with 2.5V maximum signal, this allows for an
increased dynamic range.

To successfully reconstruct the decay chains, the ATAR is expected to be fully
digitized at each event. To achieve this goal, a high bandwidth digitizer with
sufficient bandwidth and sampling rate have to be identified. The same issue
afflicting the amplifier, the high dynamic range, is also problematic for the
digitization stage. A digitizer that would suit PIONEER’s requirements needs
to be identified; a ready commercial solution would be the best option but the
cost per channel might be prohibitive. For this reason the collaboration is
exploring the possibility to develop a new kind of digitizer specific to this
application.

####  IV.2.3 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. The detector
has an inner diameter of $5\text{\,}\mathrm{cm}$ and a length of
$25\text{\,}\mathrm{cm}$. 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.

####  IV.2.4 Liquid Xenon Calorimeter

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 vacuum ultraviolet (VUV) silicon
photomultiplier (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 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. PIONEER, like MEG,
detects only scintillation light (other experiments rely on both scintillation
and charge collection) and is a high rate experiment. The PIONEER LXe detector
is foreseen to be a 25 radiation length, 3$\pi$-sr sphere surrounding the
ATAR.

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 7, 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 7, 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. This
choice, along with the spherical shape and optimization of the calorimeter
geometrical parameters and assessment of the expected detector sensitivity is
ongoing.

Figure 7: 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.

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) achieved a quantum efficiency
of $15\text{\,}\mathrm{\char 37\relax}$. The gain of the PMTs was found to
decrease due to damage to the dynode induced by photoelectrons; however the
PMT lifetime is sufficiently long to not be of concern for PIONEER. In order
to improve the granularity for the inner surface in the MEG-II experiment, a
silicon photomultiplier, with an active area of 12$\times$12 mm2, was
developed. There are several advantages, in additional to higher granularity,
to using SiPMs 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, while the MEG-II collaboration reported a
photon detection efficiency (PDE) of $\sim 20\%$ Baldini  _et al._ (2018),
they observed later degradation of the PDE in LXe Onda (2020) which is under
investigation. For this reason, 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 photosensor
technology may evolve depending on the developments regarding SiPM performance
degradation.

The digitization and readout electronics proposed for the calorimeter are
shown in Fig. 8. The 12 channel digitization boards will utilize the Analog
Devices AD 9234 dual channel, 12 bit 1 giga-samples per second (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. 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. 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
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.

Figure 8: 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.

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. Details of the cryogenics,
purification, and mechanical engineering have been considered and are
described in more detail in Altmannshofer  _et al._ (2022).

Figure 9: Possible use of an inner array of tapered LYSO crystals within the
open volume of the existing PEN CsI calorimeter. a) Opened view showing in
blue the array of LYSO crystals that matches one-to-one to the existing
geometry of the PEN crystals shaded in gray. b) An example array ideal for
testing the concept. c) An individual pentagonal crystal, 16$X_{0}$ in depth.
Each such crystal would be read out by a thin array of SiPMs.

####  IV.2.5 Considerations on the Alternative LYSO Calorimeter

A naturally segmented array of tapered LYSO crystals provides an attractive
alternative to our proposed LXe-based calorimeter. As shown in Fig. 9a, we are
exploring a geometry that matches that of the PEN pure CsI detector Počanić
_et al._ (2006); Frlež  _et al._ (2004a); Počanić  _et al._ (2004); Frlež  _et
al._ (2004b); Bychkov  _et al._ (2009). An inner array of LYSO crystals, a
Cerium doped Lutetium based scintillator, can be inserted between the ATAR and
the existing PEN CsI array. Figures 9b and c indicated prototype geometries
that are designed to fit inside the PEN calorimeter. On this option, we have
collected pros and cons as well as experiences of other groups from experts in
the field Zhu (2021). LYSO is radiation hard, non-hygroscopic, and has high
density ($X_{0}$= 1.14 cm, $R_{M}$=2.07 cm) and a light yield comparable to
the highly luminous NaI (Tl), but with much faster light signals. Its 420 nm
typical scintillation light has a 40 ns single exponential decay time and the
spectrum is well matched to conventional SiPM photosensors. On the other hand,
the growth of relatively long LYSO crystals is a fairly new and expensive R&D
effort, and the energy resolution may be a limitation based on existing tests
Atanov  _et al._ (2016). In order to advance this alternative design, it is
imperative to improve on the uniformity of light production and transmission
along the length of the crystal Mao  _et al._ (2012). We plan to perform R&D
regarding the possibilities of using LYSO for PIONEER.

####  IV.2.6 Trigger and Data Acquisition System

All triggers will start with a PI signal, which is a loose condition for an
incident beam particle defined as a coincidence of the beam detectors upstream
of the ATAR. The key point is that this trigger must not introduce any bias
between $\pi\to e\nu$ and $\pi\to\mu\to e$ events. The main time distributions
in the vicinity of the PI signal are sketched in Fig. 10. 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 10: 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, several main triggers are formed, including a
minimum bias trigger, with the PI signal prescaled by about k=1000, a trigger
to select high energy (E${}_{tot}\gtrsim$ 58 MeV) events detected by the CALO
within a time range TR=[-300,700] ns relative to PI, a trigger for all events
with a TRACKER hit within time range TR relative to PI, prescaled by about
k=50, and a trigger to select prompt events with a TRACKER hit in time range
[2,32] ns relative to PI, potentially prescaled. For all triggers, a full
event readout, including the CALO waveforms, the ATAR and the BEAM and TRACKER
detectors, will be initiated.

Figure 11: Proposed topology of the trigger and subdetector readout systems.

Figure 11 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
platform supports flexible high speed synchronous command and triggering, as
well as options for direct IO for receiving timing signals or generating
trigger signals for devices expecting analog triggers. 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.

The PIONEER data acquisition system must handle the readout, 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 an operating system. The overall layout is depicted
schematically in Fig. 12. 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, and an analysis
responsible for monitoring of data integrity.

Figure 12: 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.

The DAQ 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. Other possibilities are zero suppression of
CALO islands and realtime fitting of CALO pulses. These algorithms are well
suited to parallel processing using GPUs.

R&D is planned 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 conceptual design and R&D plan draw on experience
with similar architectures of distributed data acquisition systems for the
MuLan, MuCap and MuSun experiments at the PSI and the g-2 experiment at FNAL.

###  IV.3 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). 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.

Figure 13: 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.

####  IV.3.1 ATAR Simulation

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 13 (left) shows
the ATAR concept and (right) a simulation of energy deposit by exiting
positrons as a function of polar angle of emission.

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. Experience from other experiments and PIONEER
simulations indicate that $\pi\to\mu\to e$ background in the tail region from
the dominant pion decay at rest will be suppressed to a negligible level,
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, and $\mu$DIF can be
suppressed to about $10\%$ of the tail fraction $f$.

Another potentially significant low energy background in the tail region comes
from $\pi$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 $\pi$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, the estimated
$\pi$DIF contribution to the uncertainty in the tail correction $f$ is
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 background. It has already been demonstrated with the in-ATAR
$\pi$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, there are further potential gains from
deep neural networks, especially Convolutional Neural Networks (CNN), which
have shown extraordinary performance in image processing and classification
applications.

####  IV.3.2 CALO Simulation

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. 14a) 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. 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. 14b) 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.

(a)

(b)

Figure 14: (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.

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

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). Modeling and prototype studies will
be pursued for evaluating these effects in LXe.

##  V Sensitivity

The sensitivity of PIONEER has been evaluated using performance assumptions
that are chosen to be compatible with the experimental conceptual design
described above.

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

The first phase of PIONEER ($R_{e/\mu}$) will employ a beam with a 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. To estimate the running time required
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 2: $Br(\pi\to e\nu)$ 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
2. 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 15 shows the result of a toy MC
study for the expected sensitivity (90% confidence level (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, improved
energy resolution for decay positrons with respect to the PIENU calorimeter
Aguilar-Arevalo  _et al._ (2015b), and negligible acceptance corrections due
to the larger detector acceptance. Compared with PIENU (red curves in the
right panel in Fig. 15), the expected sensitivity in PIONEER would be improved
by one order of magnitude.

Figure 15: 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 sensitivity 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 16 shows the results of the simulation and the
PIENU experiment Aguilar-Arevalo  _et al._ (2019).

Figure 16: 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 $|U_{\mu i}|^{2}$ (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 17 shows the 90% C.L. upper limits of the branching ratio
from different experiments and the expected sensitivity for PIONEER.

Figure 17: 90% C.L. limit of the branching ratio 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. 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.222In 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

The PIONEER collaboration consists of participants from PIENU, PEN/PiBeta, and
MEG/MEGII as well as 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.

The collaboration anticipates performing detector R&D in several areas,
including the following:

  * •

Beam studies will be preformed in $\pi E5$ (and possibly $\pi E1$) to
establish the required beam conditions. Two weeks of beam time has been
approved for 2022.

  * •

After initial sensor characterization and design optimization a PIONEER
specific ATAR sensor prototype will be produced. The characterization includes
studies on LGAD energy resolution and gain suppression mechanism.

  * •

A first ATAR demonstrator with a few planes of available sensor prototypes
will be produced. An electronics board with suitable characteristics needs to
be designed and produced. The prototype would be then tested in a pion/muon
beamline.

  * •

Identification of suitable chips for the ATAR analog amplification and
digitization.

  * •

ATAR mock-ups: the support mechanics and thermal load will be studied with
mock-up prototypes and silicon heaters.

  * •

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.

  * •

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: A prototype APOLLO Command Module will be used. A
4-channel prototype of the digitizer board for evaluation and communications
development will be built.

An optimistic schedule for PIONEER assuming that funding decisions are
positive and proceed expeditiously, would allow an increasing amounts of
prototype instrumentation on various sub systems (e.g. ATAR, DAQ) to be tested
in the following years leading to the full-scale measurement program of Phase
I to begin in 2029.

##  VII Summary

In this SNOWMASS white paper, the physics motivation and the conceptual design
of a next-generation rare pion decay experiment, PIONEER, are described. Built
upon the excellent 4D tracking capability of the LGAD-based active target and
a large-acceptance, deep, fast, and uniform liquid Xenon calorimeter with
excellent energy resolution, the Phase I PIONEER experiment, approved at PSI,
aims at measuring the charged-pion branching ratio to electrons vs. muons
$R_{e/\mu}$ at a precision of 1 part in $10^{4}$. This precise measurement of
$R_{e/\mu}$ can be compared with the Standard Model (SM) prediction at similar
precision to probe non-SM explanations of several experimental anomalies
pointing towards the potential violation of lepton flavor universality through
sensitivity to quantum effects of new particles up to the PeV mass scale. The
later phases of the PIONEER experiment aim at improving the experimental
precision of the branching ratio of pion beta decay,
$\pi^{+}\to\pi^{0}e^{+}\nu(\gamma)$, to test CKM unitarity and to extract
$|V_{ud}|$ at the 0.02% level.

###### Acknowledgements.

This document was prepared by the PIONEER collaboration in coordination with
scientific staff members at PSI. The members of the collaboration are
supported by the U.S. Department of Energy, Office of Science, Offices of High
Energy Physics and Nuclear Physics; the U.S. National Science Foundation;
Natural Sciences and Engineering Research Council (Canada); TRIUMF; the Swiss
National Science Foundation; and JSPS KAKENHI (Japan).

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