EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-032 LHCb-PAPER-2016-059

Observation of the decay ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ and a search
for $C\\!P$ violation

The LHCb collaboration†††Authors are listed at the end of this paper.

A search for $C\\!P$ violation in the decay ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ is presented.
This decay is mediated by flavour-changing neutral-current transitions in the
Standard Model and is potentially sensitive to new sources of $C\\!P$
violation. The study is based on a data sample of proton-proton collisions
recorded with the LHCb experiment, corresponding to an integrated luminosity
of $3\mbox{\,fb}^{-1}$. The ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ decay is
observed for the first time, and two observables that are sensitive to
different manifestations of $C\\!P$ violation are measured,
${\Delta\mathcal{A}_{{C\\!P}}}\equiv\mathcal{A}_{{C\\!P}}({{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}})-\mathcal{A}_{{C\\!P}}({{{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}})$ and $a_{C\\!P}^{\widehat{T}\text{-odd}}$, where the latter is based
on asymmetries in the angle between the ${\mu^{+}}{\mu^{-}}$ and $p{{K}^{-}}$
decay planes. These are measured to be

$\displaystyle{\Delta\mathcal{A}_{{C\\!P}}}$ $\displaystyle=(-3.5\;\pm
5.0\;(\mathrm{stat})\;\pm 0.2\;(\mathrm{syst}))\times 10^{-2},$
$\displaystyle{a_{C\\!P}^{\widehat{T}\text{-odd}}}$
$\displaystyle=(\phantom{+}1.2\;\pm 5.0\;(\mathrm{stat})\;\pm
0.7\;(\mathrm{syst}))\times 10^{-2},$

and no evidence for $C\\!P$ violation is found.

Published in JHEP 06 (2017) 108

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

The phenomenon of $C\\!P$ violation ($\rm CPV$), related to the difference in
behaviour between matter and antimatter, remains an intriguing topic more than
fifty years after its discovery in the neutral kaon system [1]. Within the
Standard Model of particle physics (SM), $\rm CPV$ is incorporated by a
single, irreducible weak phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark
mixing matrix [2, 3]. However, the amount of $\rm CPV$ in the SM is
insufficient to explain the observed level of matter-antimatter asymmetry in
the Universe [4, 5, 6]. Therefore, new sources of $\rm CPV$ beyond the SM are
expected to exist. Experimental observations of $\rm CPV$ remain confined to
the $B$\- and $K$-meson systems. Recently, the first evidence for $\rm CPV$ in
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow p\pi^{-}\pi^{+}\pi^{-}$ was
found at the level of $3.3$ standard deviations [7] and a systematic study of
$\rm CPV$ in beauty baryon decays has now begun.

Among dedicated heavy-flavour physics experiments, the LHCb detector [8] is
unique in having access to a wide range of decay modes of numerous $b$-hadron
species. Beauty baryons are produced copiously at the LHC, and within the LHCb
detector acceptance the production ratio of ${{B}^{0}}:{{\mathchar
28931\relax}^{0}_{b}}:{{B}^{0}_{s}}$ particles is approximately $4:2:1$ [9].
The LHCb collaboration has previously searched for $\rm CPV$ in ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{\pi}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ decays [10], as well as in charmless ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\pi^{-}$, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\mathchar
28931\relax}\phi$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{\mathchar
28931\relax}h^{+}h^{-}$ transitions [11, 12, 13].

Figure 1: Diagrams for the decay ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$, in which
$V_{bq}$ and $V_{qs}$ are CKM matrix elements and $q$ represents one of the
three up-type quarks $u$, $c$ or $t$, the $t$-quark contribution being
dominant. The $u\overline{u}$ pairs originate from the hadronization process.

In this paper, a search for $\rm CPV$ in the hitherto unobserved decay
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$
is reported.111The inclusion of charge-conjugate processes is implied
throughout this paper, unless stated otherwise. It is a flavour-changing
neutral-current process with the underlying quark-level transition
$b\rightarrow s{\mu^{+}}{\mu^{-}}$. The leading-order transition amplitudes in
the SM are described by the loop diagrams shown in Fig. 1. In extensions to
the SM, new heavy particles could contribute to the amplitudes with additional
weak phases, providing new sources of $\rm CPV$ [14, 15]. The limited amount
of $\rm CPV$ predicted for the decay ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ in the SM [16,
15], following from the CKM matrix elements shown in Fig. 1, makes this decay
particularly sensitive to $\rm CPV$ effects from physics beyond the SM.

##  2 $C\\!P$-odd observables

Two types of $C\\!P$-odd observables are studied in this paper. Following
Refs. [17, 7], the differential rate of any pair of $C\\!P$-conjugate
processes can be decomposed into four parts with definite even and odd
transformation properties under the $C\\!P$ and motion-reversal $\widehat{T}$
operators. Here, $\widehat{T}$ is the unitary operator that reverses both
momentum and spin three-vectors, to be distinguished from the antiunitary
time-reversal operator $T$ which reverses initial and final states.

A $\widehat{T}$-even and $C\\!P$-odd asymmetry, $\mathcal{A}_{{C\\!P}}$, is
related to the raw asymmetry $\mathcal{A}_{\text{raw}}$ of the observed decay
candidates

$\mathcal{A}_{\text{raw}}\equiv\frac{N({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}})-N({{\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}\rightarrow{\overline{p}}{{K}^{+}}{\mu^{-}}{\mu^{+}})}{N({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}})+N({{\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}\rightarrow{\overline{p}}{{K}^{+}}{\mu^{-}}{\mu^{+}})},$
(1)

via

$\mathcal{A}_{\text{raw}}\approx\mathcal{A}_{{C\\!P}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}})+\mathcal{A}_{\text{prod}}({{\mathchar
28931\relax}^{0}_{b}})-\mathcal{A}_{\text{reco}}(K^{+})+\mathcal{A}_{\text{reco}}(p),$
(2)

where $\mathcal{A}_{\text{prod}}({{\mathchar 28931\relax}^{0}_{b}})$ is the
${\mathchar 28931\relax}^{0}_{b}$ production asymmetry, due to the $pp$
initial state, and $\mathcal{A}_{\text{reco}}(K^{+})$ and
$\mathcal{A}_{\text{reco}}(p)$ are the reconstruction asymmetries for kaons
and protons, mainly due to the different interaction cross-sections of
particles and antiparticles with the detector material. By measuring the
difference of raw asymmetries between the signal and the Cabibbo-favoured
control mode ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow\mu^{+}\mu^{-})$, the production and reconstruction
asymmetries cancel to a good approximation. No significant $\rm CPV$ is
expected in the latter decay, since its amplitude is dominated by tree-level
$C\\!P$-conserving diagrams, which leads to

$\begin{split}{\Delta\mathcal{A}_{{C\\!P}}}&\equiv\mathcal{A}_{{C\\!P}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}})-\mathcal{A}_{{C\\!P}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}})\\\ &\approx\mathcal{A}_{\text{raw}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}})-\mathcal{A}_{\text{raw}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}).\end{split}$ (3)

Imperfect cancellation in the production and reconstruction asymmetries can
arise from differences in the kinematic distributions of the signal and
control modes. A weighting procedure, discussed in Sec. 5, is applied to
correct for this, with residual effects considered as a source of systematic
uncertainty in Sec. 6.

A pair of $\widehat{T}$-odd and $P$-odd observables, $A_{\widehat{T}}$ and
$\kern 1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$, is obtained by
defining the $\widehat{T}$-odd triple products of the final-state particle
momenta in the ${\mathchar 28931\relax}^{0}_{b}$ rest frame

$\displaystyle{C_{\widehat{T}}}$
$\displaystyle\equiv\vec{p}_{\mu^{+}}\cdot(\vec{p}_{p}\times\vec{p}_{K^{-}}),$
(4) $\displaystyle{\kern 1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}$
$\displaystyle\equiv\vec{p}_{\mu^{-}}\cdot(\vec{p}_{\bar{p}}\times\vec{p}_{K^{+}}),$
(5)

and taking the asymmetries

${A_{\widehat{T}}}\equiv\frac{N({C_{\widehat{T}}}>0)-N({C_{\widehat{T}}}<0)}{N({C_{\widehat{T}}}>0)+N({C_{\widehat{T}}}<0)},\hskip
14.22636pt{\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}\equiv\frac{\overline{N}(-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}>0)-\overline{N}(-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}<0)}{\overline{N}(-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}>0)+\overline{N}(-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}<0)},$ (6)

where $N$($\overline{N}$) is the number of ${\mathchar 28931\relax}^{0}_{b}$
(${\kern 1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}$)
signal candidates. These asymmetries are measured from the angular
distributions of the decay products, with ${C_{\widehat{T}}}$ being
proportional to $\sin\chi$ [18], where $\chi$ is the angle between the decay
planes of the ${\mu^{+}}{\mu^{-}}$ and $p{{K}^{-}}$ systems in the ${\mathchar
28931\relax}^{0}_{b}$ rest frame, as shown in Fig. 2.

Figure 2: Definition of the angle $\chi$ for ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ decays, in the
${\mathchar 28931\relax}^{0}_{b}$ rest frame.

The observables $A_{\widehat{T}}$ and $\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$ are $P$\- and
$\widehat{T}$-odd but are not sensitive to $\rm CPV$ effects [17]. Following
Ref. [18], $C\\!P$-odd and $P$-odd observables are defined as

$a_{C\\!P}^{\widehat{T}\text{-odd}}\equiv\frac{1}{2}\left({A_{\widehat{T}}}-{\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}\right),\hskip
56.9055pt{a_{P}^{\widehat{T}\text{-odd}}}\equiv\frac{1}{2}\left({A_{\widehat{T}}}+{\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}\right),$ (7)

where a non-zero value of $a_{C\\!P}^{\widehat{T}\text{-odd}}$ or
$a_{P}^{\widehat{T}\text{-odd}}$ would signal $C\\!P$ or parity violation,
respectively. These observables are by construction largely insensitive to the
${\mathchar 28931\relax}^{0}_{b}$ production asymmetry and detector-induced
charge asymmetries.

The observables $\Delta\mathcal{A}_{{C\\!P}}$ and
$a_{C\\!P}^{\widehat{T}\text{-odd}}$ are sensitive to different manifestations
of $\rm CPV$ [17]. The $C\\!P$ asymmetry $\mathcal{A}_{{C\\!P}}$ depends on
the interference of $\widehat{T}$-even amplitudes, which can be written as
$\mathcal{M}^{e}_{i}=a^{e}_{i}\exp\left[i(\delta^{e}_{i}+\phi_{i}^{e})\right]$,
where $\delta^{e}_{i}$ are $C\\!P$-even strong phases,
${C\\!P}(\delta^{e}_{i})=\delta^{e}_{i}$, and $\phi_{i}^{e}$ are $C\\!P$-odd
weak phases, ${C\\!P}(\phi_{i}^{e})=-\phi_{i}^{e}$. This convention is such
that all $\rm CPV$ effects are encoded in the $C\\!P$-odd weak phases. The
$\widehat{T}$-even and $C\\!P$-odd part of the differential rate turns out to
be

$\left.\frac{\rm d\Gamma}{\rm d\Phi}\right|^{\widehat{T}-{\rm
even}}_{{C\\!P}-{\rm odd}}\propto
a^{e}_{1}a^{e}_{2}\sin(\delta_{1}^{e}-\delta_{2}^{e})\sin(\phi_{1}^{e}-\phi_{2}^{e}),$
(8)

where only two $\widehat{T}$-even amplitudes are considered for simplicity.
Therefore, $\mathcal{A}_{{C\\!P}}$ is enhanced when the strong phase
difference between the two amplitudes is large.
On the other hand, $a_{C\\!P}^{\widehat{T}\text{-odd}}$ depends on the
interference between $\widehat{T}$-even and $\widehat{T}$-odd amplitudes, the
latter written as
$\mathcal{M}^{o}_{i}=a^{o}_{i}\exp\left[i(\delta^{o}_{i}+\phi_{i}^{o}+\pi/2)\right]$,
following the same convention used for $\widehat{T}$-even amplitudes. The
$\widehat{T}$-odd and $C\\!P$-odd part of the differential rate is therefore

$\left.\frac{\rm d\Gamma}{\rm d\Phi}\right|^{\widehat{T}-{\rm
odd}}_{{C\\!P}-{\rm odd}}\propto
a^{e}_{1}a^{o}_{1}\cos(\delta_{1}^{e}-\delta_{1}^{o})\sin(\phi_{1}^{e}-\phi_{1}^{o}),$
(9)

where one $\widehat{T}$-even and one $\widehat{T}$-odd amplitudes are
considered for simplicity. As a consequence,
$a_{C\\!P}^{\widehat{T}\text{-odd}}$ is enhanced when the strong phase
difference vanishes. Furthermore, the observables
$\Delta\mathcal{A}_{{C\\!P}}$ and $a_{C\\!P}^{\widehat{T}\text{-odd}}$ are
sensitive to different types of $\rm CPV$ effects from physics beyond the SM
[16].

##  3 Detector and simulation

The LHCb detector [8, 19] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex (PV), the impact parameter (IP), is
measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger [20], which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

Simulated signal events are used to determine the effect of the detector
geometry, trigger, reconstruction and selection on the angular distributions
of the signal and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ control sample. Additional simulated samples are used to estimate the
contribution from specific background processes. In the simulation, $pp$
collisions are generated using Pythia [21, 22] with a specific LHCb
configuration [23]. Decays of hadronic particles are described by EvtGen [24],
in which final-state radiation is generated using Photos [25]. The interaction
of the generated particles with the detector, and its response, are
implemented using the Geant4 toolkit [26], as described in Ref. [27].

##  4 Selection of signal candidates

The present analysis is performed using proton-proton collision data
corresponding to $1$ and $2\mbox{\,fb}^{-1}$ of integrated luminosity,
collected with the LHCb detector in 2011 and 2012, at centre-of-mass energies
of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$, respectively. The ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ candidates are
reconstructed from a proton, a kaon and two muon candidates originating from a
common vertex, and are selected using information from the particle
identification system. The ${\mathchar 28931\relax}^{0}_{b}$ flavour is
determined from the charge of the kaon candidate, i.e. ${\mathchar
28931\relax}^{0}_{b}$ for negative and ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}$ for
positive kaons. Only candidates with reconstructed invariant mass,
$m(pK^{-}\mu^{+}\mu^{-})$, in the range
$[5350,6000]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and a $pK^{-}$ invariant
mass, $m(pK^{-})$, below 2350${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are
retained, with the latter requirement being applied to reduce the
combinatorial background contribution. The spectrum in the dimuon mass
squared, $q^{2}$, is considered, excluding the resonance regions
$q^{2}\in[0.98,1.10]$, $[8.0,11.0]$ and
$[12.5,15.0]{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ that correspond to
the masses of the $\phi(1020)$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$, and $\psi{(2S)}$ mesons, respectively.

Several background contributions from exclusive decays are identified and
rejected. These are ${{B}^{0}_{s}}\rightarrow{{K}^{+}}{{K}^{-}}\mu^{-}\mu^{+}$
and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$
decays, in which a kaon or a pion is misidentified as a proton, and
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$
decays, in which proton and kaon assignments are interchanged. Background also
arises from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
p{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow p{{K}^{-}}{\psi{(2S)}}$ decays in which a
muon is misidentified as a kaon and the kaon as a muon. These components are
effectively eliminated by tightened particle identification requirements
combined with selection criteria on invariant masses calculated under the
appropriate mass hypothesis (e.g. assigning the kaon mass to the candidate
proton to identify possible
${{B}^{0}_{s}}\rightarrow{{K}^{+}}{{K}^{-}}\mu^{-}\mu^{+}$ background decays).
After these requirements the background contribution from the above decays is
negligible. No indication of other specific background decays is observed. The
remaining combinatorial background is suppressed by means of a boosted
decision tree (BDT) classifier [28, 29] with an adaptive boosting algorithm
[30]. The BDT is constructed from variables that discriminate between signal
and background, based on their kinematic, topological and particle
identification properties, as well as the isolation of the final-state tracks
[31, 32]. Simulated ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ events in
which the decay products are uniformly distributed in phase space are used as
the signal training sample and a correction for known differences between data
and simulation is applied. Candidates from data in the high mass region,
$m(p{{K}^{-}}{\mu^{+}}{\mu^{-}})>5800{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
are used as the background training sample and then removed from the window of
the mass fit described below. After optimisation of the significance,
$S/\sqrt{S+B}$, where $S$ and $B$ are the number of signal and background
candidates in the region
$m(pK^{-}\mu^{+}\mu^{-})\in[5400,5800]{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
the BDT classifier retains only $0.14\%$ of the combinatorial background
candidates, with a signal efficiency of $51\%$. Events in which more than one
${\mathchar 28931\relax}^{0}_{b}$ candidate survives the selection constitute
less than $1\%$ of the sample and all candidates are retained; the systematic
uncertainty associated with this is negligible. The identical selection is
applied to the control-mode ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$, except that the dimuon squared mass is required to be in the range
$[9.0,10.5]{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$.

##  5 Asymmetry measurements

For the $\Delta\mathcal{A}_{{C\\!P}}$ measurement, the data are divided into
two subsamples according to the ${\mathchar 28931\relax}^{0}_{b}$ flavour. For
the measurements of the triple-product asymmetries, four subsamples are
defined by the combination of the ${\mathchar 28931\relax}^{0}_{b}$ flavour
and the sign of $C_{\widehat{T}}$ (or $\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}$ for ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}$). The
reconstruction efficiencies are studied with simulated events and are found to
be equal for all subsamples.

The observable $\Delta\mathcal{A}_{{C\\!P}}$ can be sensitive to kinematic
differences between the signal and control-mode decays that affect the
cancellation of the detection asymmetries in Eq. 3. This is taken into account
by assigning a weight to each ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ candidate such that the resulting proton and kaon momentum
distributions match those of the signal ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ decays. These
weights are determined from simulation samples for the signal and control
modes. No such weighting is required for $a_{C\\!P}^{\widehat{T}\text{-odd}}$
and $a_{P}^{\widehat{T}\text{-odd}}$, since these observables involve only one
decay mode.

The asymmetry $\mathcal{A}_{\text{raw}}$ is determined from a simultaneous
extended maximum likelihood unbinned fit to the ${\mathchar
28931\relax}^{0}_{b}$ and ${\kern 1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}$ invariant mass distributions. The $A_{\widehat{T}}$
and $\kern 1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$ asymmetries are
determined by means of a simultaneous extended maximum likelihood unbinned fit
to the four subsamples defined above. The signal model for all fits is the sum
of two Crystal Ball functions [33], one with a low-mass power-law tail and one
with a high-mass tail, and a Gaussian function, all sharing the same peak
position. Only the peak position, the total width of the composite function
and the overall normalization are free to vary, with all other shape
parameters fixed from a fit to simulated decays. The background is modelled by
an exponential function. The raw asymmetry $\mathcal{A}_{\text{raw}}$ is
incorporated in the fit model as

$N_{{{\kern 0.70004pt\overline{\kern-0.70004pt\mathchar
28931\relax}}{}^{0}_{b}}}=N_{{{\mathchar
28931\relax}^{0}_{b}}}\frac{1-\mathcal{A}_{\text{raw}}}{1+\mathcal{A}_{\text{raw}}},$
(10)

and $\Delta\mathcal{A}_{{C\\!P}}$ is derived from the raw asymmetries measured
in the signal and control modes according to Eq. 3. The asymmetries
$A_{\widehat{T}}$ and $\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$ are included in the fit as

$\begin{array}[]{cc}N_{{{\mathchar
28931\relax}^{0}_{b}},{C_{\widehat{T}}}>0}=\frac{1}{2}N_{{{\mathchar
28931\relax}^{0}_{b}}}(1+{A_{\widehat{T}}}),&N_{{{\mathchar
28931\relax}^{0}_{b}},{C_{\widehat{T}}}<0}=\frac{1}{2}N_{{{\mathchar
28931\relax}^{0}_{b}}}(1-{A_{\widehat{T}}}),\\\ N_{{{\kern
0.70004pt\overline{\kern-0.70004pt\mathchar 28931\relax}}{}^{0}_{b}},-{\kern
0.70004pt\overline{\kern-0.70004ptC}_{\widehat{T}}}>0}=\frac{1}{2}N_{{{\kern
0.70004pt\overline{\kern-0.70004pt\mathchar 28931\relax}}{}^{0}_{b}}}(1+{\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}),&N_{{{\kern
0.70004pt\overline{\kern-0.70004pt\mathchar 28931\relax}}{}^{0}_{b}},-{\kern
0.70004pt\overline{\kern-0.70004ptC}_{\widehat{T}}}<0}=\frac{1}{2}N_{{{\kern
0.70004pt\overline{\kern-0.70004pt\mathchar 28931\relax}}{}^{0}_{b}}}(1-{\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}),\\\ \end{array}$ (11)

and the observables $a_{C\\!P}^{\widehat{T}\text{-odd}}$ and
$a_{P}^{\widehat{T}\text{-odd}}$ are computed from $A_{\widehat{T}}$ and
$\kern 1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$, which are found to
be uncorrelated. Background yields are fitted independently for each
subsample, while all the signal shape parameters are shared among the
subsamples.

The invariant mass distributions of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ and
${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ candidates, with fit results superimposed, are shown in Fig. 3. The
$\mathcal{A}_{\text{raw}}$ asymmetries are found to be $(-2.8\pm 5.0)\times
10^{-2}$ for signal decays and $(2.0\pm 0.7)\times 10^{-2}$ for the control
mode, which yields efficiency-uncorrected
${\Delta\mathcal{A}_{{C\\!P}}}=(-4.8\pm 5.0)\times 10^{-2}$. The total signal
yields from the fits to the data are $600\pm 44$ candidates for ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$, and
$22\,911\pm 230$ for ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ decays. The uncertainties are statistical only. This represents the
first observation of the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ decay mode.

Figure 3: Invariant mass distributions of (top) ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ and (bottom)
${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ candidates, with fit results superimposed. Plots refer to the (left)
${\mathchar 28931\relax}^{0}_{b}$ and (right) ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}$
subsamples.

Figure 4: Invariant mass distributions of the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ subsamples
used for the $A_{\widehat{T}}$ and $\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$ measurements. Plots refer
to (top) ${\mathchar 28931\relax}^{0}_{b}$ and (bottom) ${\kern
1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}$ decays
divided into the subsamples (left) ${C_{\widehat{T}}}>0,-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}>0$ and (right)
${C_{\widehat{T}}}<0,-{\kern
1.00006pt\overline{\kern-1.00006ptC}_{\widehat{T}}}<0$.

The invariant mass distributions of the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ subsamples
used for the $A_{\widehat{T}}$ and $\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}$ measurements, with fit
results superimposed, are shown in Fig. 4. From the signal yields, the triple-
product asymmetries are found to be ${A_{\widehat{T}}}=(-2.8\pm 7.2)\times
10^{-2}$ and ${\kern
1.00006pt\overline{\kern-1.00006ptA}_{\widehat{T}}}=(4.0\pm 6.9)\times
10^{-2}$, and the resulting efficiency-uncorrected parity- and
$C\\!P$-violating observables are ${a_{P}^{\widehat{T}\text{-odd}}}=(-3.4\pm
5.0)\times 10^{-2}$ and $a_{C\\!P}^{\widehat{T}\text{-odd}}=(0.6\pm 5.0)\times
10^{-2}$, where again the uncertainties are statistical only.

##  6 Systematic uncertainties

The analysis method depends upon the weighting procedure discussed in Sec. 5
to equalise the kinematic distributions of the protons and kaons between the
signal and control modes. For $\Delta\mathcal{A}_{{C\\!P}}$, the associated
systematic uncertainty is estimated by varying the weights within their
uncertainties and taking the largest deviation, $\pm\;0.15\times 10^{-2}$, as
a systematic uncertainty. No weighting is needed for
$a_{C\\!P}^{\widehat{T}\text{-odd}}$ and $a_{P}^{\widehat{T}\text{-odd}}$, and
therefore no systematic uncertainty is assigned. Instead, the effects of
selection and detector acceptance on the triple-product asymmetries are
estimated by measuring
$a_{C\\!P}^{\widehat{T}\text{-odd}}(p{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}})$ on the control mode, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$. A value of $(0.5\pm 0.7)\times 10^{-2}$ is obtained. For this mode
negligible $\rm CPV$ is expected, and the statistical uncertainty of the
measured asymmetry is assigned as the corresponding systematic uncertainty on
the observables $a_{C\\!P}^{\widehat{T}\text{-odd}}$ and
$a_{P}^{\widehat{T}\text{-odd}}$. The effects of the reconstruction efficiency
on the measured observables are considered by weighting each event by the
inverse of the efficiency extracted from simulated events. This leads to a
change in the central values of $+1.3\times 10^{-2}$ on
$\Delta\mathcal{A}_{{C\\!P}}$, of $+0.6\times 10^{-2}$ on
$a_{C\\!P}^{\widehat{T}\text{-odd}}$ and of $-1.4\times 10^{-2}$ on
$a_{P}^{\widehat{T}\text{-odd}}$. A systematic uncertainty is assigned by
varying the efficiencies within their uncertainties. This amounts to
$\pm\;0.10\times 10^{-2}$ for the $\Delta\mathcal{A}_{{C\\!P}}$ observable and
to $\pm\;0.02\times 10^{-2}$ for $a_{C\\!P}^{\widehat{T}\text{-odd}}$ and
$a_{P}^{\widehat{T}\text{-odd}}$.

The above effects are the dominant sources of systematic uncertainties. Other
possible sources of systematic uncertainties are considered. The experimental
resolution on $C_{\widehat{T}}$ is studied with simulated signal events. The
effect of the fit model choice is studied by fitting simulated
pseudoexperiments with an alternative fit model, in which the Crystal Ball
functions are replaced with bifurcated Gaussian functions and the exponential
background shape is replaced with a polynomial. Systematic effects from
${\mathchar 28931\relax}^{0}_{b}$ polarisation [34], multiple candidates, and
residual physical backgrounds are also studied. These contributions have
negligible impact on the measured asymmetries.

##  7 Conclusions

The first search for $C\\!P$ violation in the process ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{p}{{K}^{-}}{\mu^{+}}{\mu^{-}}$ is performed
with a data sample containing $600\pm 44$ signal decays, this representing the
first observation of this ${\mathchar 28931\relax}^{0}_{b}$ decay mode. Two
different $C\\!P$-violating observables that are sensitive to different
manifestations of $C\\!P$ violation, $\Delta\mathcal{A}_{{C\\!P}}$ and
$a_{C\\!P}^{\widehat{T}\text{-odd}}$, are measured. The parity-violating
observable $a_{P}^{\widehat{T}\text{-odd}}$ is also measured. The values
obtained are

$\displaystyle{\Delta\mathcal{A}_{{C\\!P}}}$ $\displaystyle=(-3.5\pm
5.0\;(\mathrm{stat})\pm 0.2\;(\mathrm{syst}))\times 10^{-2},$ $\displaystyle
a_{C\\!P}^{\widehat{T}\text{-odd}}$ $\displaystyle=(\phantom{-}1.2\pm
5.0\;(\mathrm{stat})\pm 0.7\;(\mathrm{syst}))\times 10^{-2},$
$\displaystyle{a_{P}^{\widehat{T}\text{-odd}}}$ $\displaystyle=(-4.8\pm
5.0\;(\mathrm{stat})\pm 0.7\;(\mathrm{syst}))\times 10^{-2}.$

The results are compatible with $C\\!P$ and parity conservation and agree with
SM predictions for $\rm CPV$ [16, 15], and with experimental results [35, 36]
for decays mediated by $b\rightarrow s\mu^{+}\mu^{-}$ transitions in ${B}^{0}$
and ${{B}^{+}}$ meson decays.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We
acknowledge the computing resources that are provided by CERN, IN2P3 (France),
KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain),
GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland),
IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are
indebted to the communities behind the multiple open source software packages
on which we depend. Individual groups or members have received support from
AvH Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC
(European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU,
Région Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and
GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for
the Exhibition of 1851 and the Leverhulme Trust (United Kingdom).

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, S. Ali43, G. Alkhazov31, P. Alvarez Cartelle55,
A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini18, G.
Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B. Appleby56, F. Archilli43,
P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M. Artuso61, E. Aslanides6, G.
Auriemma26, M. Baalouch5, I. Babuschkin56, S. Bachmann12, J.J. Back50, A.
Badalov38, C. Baesso62, S. Baker55, V. Balagura7,c, W. Baldini17, R.J.
Barlow56, C. Barschel40, S. Barsuk7, W. Barter56, F. Baryshnikov32, M.
Baszczyk27,l, V. Batozskaya29, B. Batsukh61, V. Battista41, A. Bay41, L.
Beaucourt4, J. Beddow53, F. Bedeschi24, I. Bediaga1, L.J. Bel43, V. Bellee41,
N. Belloli21,i, K. Belous37, I. Belyaev32, E. Ben-Haim8, G. Bencivenni19, S.
Benson43, A. Berezhnoy33, R. Bernet42, A. Bertolin23, C. Betancourt42, F.
Betti15, M.-O. Bettler40, M. van Beuzekom43, Ia. Bezshyiko42, S. Bifani47, P.
Billoir8, T. Bird56, A. Birnkraut10, A. Bitadze56, A. Bizzeti18,u, T. Blake50,
F. Blanc41, J. Blouw11,†, S. Blusk61, V. Bocci26, T. Boettcher58, A.
Bondar36,w, N. Bondar31,40, W. Bonivento16, I. Bordyuzhin32, A.
Borgheresi21,i, S. Borghi56, M. Borisyak35, M. Borsato39, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12, M.
Britsch12, T. Britton61, J. Brodzicka56, E. Buchanan48, C. Burr56, A.
Bursche2, J. Buytaert40, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,i, M.
Calvo Gomez38,m, A. Camboni38, P. Campana19, D.H. Campora Perez40, L.
Capriotti56, A. Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A. Cardini16,
P. Carniti21,i, L. Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21,i,
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Chamont7, M. Charles8, Ph. Charpentier40, G. Chatzikonstantinidis47, M.
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K. Müller42, V. Müller10, P. Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57,
I. Nasteva2, M. Needham52, N. Neri22, S. Neubert12, N. Neufeld40, M. Neuner12,
T.D. Nguyen41, C. Nguyen-Mau41,n, S. Nieswand9, R. Niet10, N. Nikitin33, T.
Nikodem12, A. Nogay68, A. Novoselov37, D.P. O’Hanlon50, A. Oblakowska-Mucha28,
V. Obraztsov37, S. Ogilvy19, R. Oldeman16,f, C.J.G. Onderwater70, J.M. Otalora
Goicochea2, A. Otto40, P. Owen42, A. Oyanguren69, P.R. Pais41, A. Palano14,d,
M. Palutan19, A. Papanestis51, M. Pappagallo14,d, L.L. Pappalardo17,g, W.
Parker60, C. Parkes56, G. Passaleva18, A. Pastore14,d, G.D. Patel54, M.
Patel55, C. Patrignani15,e, A. Pearce40, A. Pellegrino43, G. Penso26, M. Pepe
Altarelli40, S. Perazzini40, P. Perret5, L. Pescatore41, K. Petridis48, A.
Petrolini20,h, A. Petrov68, M. Petruzzo22,q, E. Picatoste Olloqui38, B.
Pietrzyk4, M. Pikies27, D. Pinci26, A. Pistone20, A. Piucci12, V. Placinta30,
S. Playfer52, M. Plo Casasus39, T. Poikela40, F. Polci8, A. Poluektov50,36, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, A. Popov37, D. Popov11,40, B.
Popovici30, S. Poslavskii37, C. Potterat2, E. Price48, J.D. Price54, J.
Prisciandaro39,40, A. Pritchard54, C. Prouve48, V. Pugatch46, A. Puig
Navarro42, G. Punzi24,p, W. Qian50, R. Quagliani7,48, B. Rachwal27, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F.
Ratnikov35, G. Raven44, F. Redi55, S. Reichert10, A.C. dos Reis1, C. Remon
Alepuz69, V. Renaudin7, S. Ricciardi51, S. Richards48, M. Rihl40, K.
Rinnert54, V. Rives Molina38, P. Robbe7,40, A.B. Rodrigues1, E. Rodrigues59,
J.A. Rodriguez Lopez66, P. Rodriguez Perez56,†, A. Rogozhnikov35, S. Roiser40,
A. Rollings57, V. Romanovskiy37, A. Romero Vidal39, J.W. Ronayne13, M.
Rotondo19, M.S. Rudolph61, T. Ruf40, P. Ruiz Valls69, J.J. Saborido Silva39,
E. Sadykhov32, N. Sagidova31, B. Saitta16,f, V. Salustino Guimaraes1, C.
Sanchez Mayordomo69, B. Sanmartin Sedes39, R. Santacesaria26, C. Santamarina
Rios39, M. Santimaria19, E. Santovetti25,j, A. Sarti19,k, C. Satriano26,s, A.
Satta25, D.M. Saunders48, D. Savrina32,33, S. Schael9, M. Schellenberg10, M.
Schiller53, H. Schindler40, M. Schlupp10, M. Schmelling11, T. Schmelzer10, B.
Schmidt40, O. Schneider41, A. Schopper40, K. Schubert10, M. Schubiger41, M.-H.
Schune7, R. Schwemmer40, B. Sciascia19, A. Sciubba26,k, A. Semennikov32, A.
Sergi47, N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert21, M. Shapkin37, I.
Shapoval45, Y. Shcheglov31, T. Shears54, L. Shekhtman36,w, V. Shevchenko68,
B.G. Siddi17,40, R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, M. Sirendi49, N. Skidmore48, T. Skwarnicki61, E. Smith55, I.T.
Smith52, J. Smith49, M. Smith55, H. Snoek43, l. Soares Lavra1, M.D.
Sokoloff59, F.J.P. Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, S.
Sridharan40, F. Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55,
O. Steinkamp42, S. Stemmle12, O. Stenyakin37, H. Stevens10, S. Stevenson57, S.
Stoica30, S. Stone61, B. Storaci42, S. Stracka24,p, M. Straticiuc30, U.
Straumann42, L. Sun64, W. Sutcliffe55, K. Swientek28, V. Syropoulos44, M.
Szczekowski29, T. Szumlak28, S. T’Jampens4, A. Tayduganov6, T. Tekampe10, G.
Tellarini17,g, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J. Tilley55, V.
Tisserand4, M. Tobin41, S. Tolk49, L. Tomassetti17,g, D. Tonelli40, S. Topp-
Joergensen57, F. Toriello61, E. Tournefier4, S. Tourneur41, K. Trabelsi41, M.
Traill53, M.T. Tran41, M. Tresch42, A. Trisovic40, A. Tsaregorodtsev6, P.
Tsopelas43, A. Tully49, N. Tuning43, A. Ukleja29, A. Ustyuzhanin35, U. Uwer12,
C. Vacca16,f, V. Vagnoni15,40, A. Valassi40, S. Valat40, G. Valenti15, R.
Vazquez Gomez19, P. Vazquez Regueiro39, S. Vecchi17, M. van Veghel43, J.J.
Velthuis48, M. Veltri18,r, G. Veneziano57, A. Venkateswaran61, M. Vernet5, M.
Vesterinen12, J.V. Viana Barbosa40, B. Viaud7, D. Vieira63, M. Vieites Diaz39,
H. Viemann67, X. Vilasis-Cardona38,m, M. Vitti49, V. Volkov33, A. Vollhardt42,
B. Voneki40, A. Vorobyev31, V. Vorobyev36,w, C. Voß9, J.A. de Vries43, C.
Vázquez Sierra39, R. Waldi67, C. Wallace50, R. Wallace13, J. Walsh24, J.
Wang61, D.R. Ward49, H.M. Wark54, N.K. Watson47, D. Websdale55, A. Weiden42,
M. Whitehead40, J. Wicht50, G. Wilkinson57,40, M. Wilkinson61, M. Williams40,
M.P. Williams47, M. Williams58, T. Williams47, F.F. Wilson51, J. Wimberley60,
J. Wishahi10, W. Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton49, K.
Wraight53, K. Wyllie40, Y. Xie65, Z. Xing61, Z. Xu4, Z. Yang3, Y. Yao61, H.
Yin65, J. Yu65, X. Yuan36,w, O. Yushchenko37, K.A. Zarebski47, M.
Zavertyaev11,c, L. Zhang3, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V.
Zhukov33, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
70Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
†Deceased


on behalf of the PSI muEDM collaboration

# Status of the muEDM experiment at PSI

Kim Siang Khaw<EMAIL_ADDRESS>Tsung-Dao Lee Institute and School of
Physics and Astronomy, Shanghai Jiao Tong University, 201210 Shanghai, China
Cheng Chen  Tsung-Dao Lee Institute and School of Physics and Astronomy,
Shanghai Jiao Tong University, 201210 Shanghai, China  Massimo Giovannozzi
Beams Department, CERN, Esplanade des Particules 1, 1211 Geneva 23,
Switzerland  Tianqi Hu  Tsung-Dao Lee Institute and School of Physics and
Astronomy, Shanghai Jiao Tong University, 201210 Shanghai, China  Meng Lv
Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao
Tong University, 201210 Shanghai, China  Jun Kai Ng  Tsung-Dao Lee Institute
and School of Physics and Astronomy, Shanghai Jiao Tong University, 201210
Shanghai, China  Angela Papa  Paul Scherrer Institut, Forschungsstrasse 111,
5232 Villigen, Switzerland  Istituto Nazionale di Fisica Nucleare, Sez. di
Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy  Dipartimento di Fisica
dell’Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy  Philipp
Schmidt-Wellenburg  Paul Scherrer Institut, Forschungsstrasse 111, 5232
Villigen, Switzerland  Bastiano Vitali  Istituto Nazionale di Fisica Nucleare,
Sez. di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy  Dipartimento di Fisica
dell’Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy
Guan Ming Wong  Tsung-Dao Lee Institute and School of Physics and Astronomy,
Shanghai Jiao Tong University, 201210 Shanghai, China

###### Abstract

Permanent electric dipole moments (EDMs) are excellent probes of physics
beyond the Standard Model, especially on new sources of CP violation. The muon
EDM has recently attracted significant attention due to discrepancies in the
magnetic anomaly of the muon, as well as potential violations of lepton-flavor
universality in B-meson decays. At the Paul Scherrer Institute in Switzerland,
we have proposed a muon EDM search experiment employing the frozen-spin
technique, where a radial electric field is exerted within a storage solenoid
to cancel the muon’s anomalous spin precession. Consequently, the EDM signal
can be inferred from the upstream-downstream asymmetry of the decay positron
count versus time. The experiment is planned to take place in two phases,
anticipating an annual statistical sensitivity of $3\times 10^{-21}$
$e\cdot$cm for Phase I, and $6\times 10^{-23}$ $e\cdot$cm for Phase II. Going
beyond $10^{-21}$ $e\cdot$cm will enable us to probe various Standard Model
extensions.

Electric dipole moment; frozen-spin technique; CP violation; Lepton
universality; Plastic scintillator; Silicon photomultiplier

##  I Introduction

The origin of the imbalance between baryon and anti-baryon in our universe
(BAU) WMAP:2010qai  remains one of the greatest mysteries in cosmology and
particle physics. The size of Charge-Parity (CP) symmetry violation embedded
in the Standard Model (SM) of particle physics is insufficient to explain the
observed BAU Sakharov:1967dj . The existence of a permanent electric dipole
moment (EDM) in any elementary particle inherently violates both the P and T
symmetries Chupp:2017rkp . Assuming CPT symmetry, the latter implies a
violation of the CP symmetry. If an EDM measurement exceeds the SM prediction,
it could suggest physics beyond the Standard Model (BSM) Nakai:2022vgp ;
Dermisek:2022aec ; Crivellin:2018qmi , thus refining our understanding of the
universe’s matter-antimatter asymmetry.

Recently, muon EDM has drawn considerable attention due to discrepancies
between the magnetic anomaly of the muon $a_{\mu}$ Aoyama:2020ynm ;
Muong-2:2021ojo ; Keshavarzi:2021eqa  and the electron $a_{\mathrm{e}}$
Parker:2018vye ; Morel:2020dww ; Fan:2022eto , along with suggestions of
lepton-flavor universality violation in B-meson decay Crivellin:2021sff . Of
all elementary particles, only the muon permits a direct EDM measurement. The
present muon EDM limit, set by the BNL Muon $g-2$ Collaboration, is
$d_{\mu}<1.8\times 10^{-19},e\cdot$cm at a 95% confidence level
Muong-2:2008ebm  while the SM prediction is $1.4\times 10^{-38}\,e\cdot$cm
Pospelov:2013sca ; Yamaguchi:2020eub , way beyond the reach of current
technology. Consequently, the muon EDM remains one of the SM’s least tested
areas, with any detected signal strongly implying BSM physics.

The current muon EDM limit is derived from a ”parasitic” measurement within
the Muon $g-2$ experiment. In this context, the existence of the muon EDM
induces a tilt $\delta=\tan^{-1}\left(\eta\beta/2a_{\mu}\right)$ in the $g-2$
precession plane, where $\eta$ is a dimensionless parameter related to muon
EDM and $|\vec{d}_{\mu}|\approx\eta\times 4.7\times 10^{-14}$. The current BNL
limit implies a plane tilt $\delta$ around a milliradian, corresponding to an
average vertical angle oscillation for emitted positrons of several tens of
µrad. The sensitivity projected for the FNAL and J-PARC experiments is around
the order of $10^{-21}\,e\cdot$cm Chislett:2016jau ; Abe:2019thb .

##  II A frozen-spin-based muon EDM search at PSI

The recently proposed frozen-spin technique Farley:2003wt ; Adelmann:2010zz ;
Adelmann:2021udj  enhances sensitivity in an EDM search by cancelling a muon’s
anomalous spin precession in a storage magnet using a radial electric field
$E_{\mathrm{f}}=a_{\mu}Bc\beta\gamma^{2}$, where $B$ signifies the magnetic
field confining the muon. This technique effectively “freezes” the muon’s spin
in relation to its momentum. If the muon has a permanent EDM, it would induce
a spin rotation out of the orbital plane, leading to an observable upstream-
downstream asymmetry that increases over time. By strategically placing
detectors in the upstream and downstream direction of the muon storage region,
an up-down asymmetry $\alpha$ in positron count can be observed due to
increasing polarization along the direction perpendicular to the muon orbital
plane, as the positron is preferentially emitted in the direction of the
muon’s spin. The sensitivity of the EDM measurement can then be calculated
using:

$\sigma(d_{\mu})=\frac{\hbar\gamma^{2}a_{\mu}}{2PE_{\mathrm{f}}\sqrt{N}\gamma\tau_{\mu}\alpha}$
(1)

where $P$ is the spin polarization, $N$ is the number of detected positrons,
and $\tau_{\mu}$ is the muon lifetime.

Figure 1: A sketch of the Phase I muEDM experiment at PSI. Side view (left)
and front view (right) of the demonstrator device using an existing solenoid
magnet with a field strength of $3$ T.

The proposed muEDM experiment at PSI is planned in two stages. Phase-I will
employ an existing PSC solenoid with a field strength of 3 T to demonstrate
the essential techniques required for a muon EDM search using the frozen-spin
method. As illustrated in Fig. 1, a surface muon beam with approximately 30
MeV/c momentum and a polarization greater than 95% will be directed into a
collimation tube within a superconducting magnetic shield, creating a field-
free condition. The use of correction coils within the solenoid will minimize
the field gradient between the injection region at the collimation tube’s exit
and the storage region at the solenoid’s center, thereby expanding the
acceptable phase space. A coil situated at the solenoid’s center will generate
a weakly focusing field essential for muon storage during the EDM measurement.

An entrance scintillator, operating in anti-coincidence with a set of
scintillators, will produce an entrance signal for muons within the acceptance
phase space. This signal will trigger a pulsed magnetic field at the
solenoid’s center, converting the remaining longitudinal momentum of the
incoming muons into the transverse direction. The muon will then be confined
to a stable orbit of approximately 30 mm radius within the weakly focusing
magnectic field. To establish the frozen-spin condition, a radial electric
field of 3 kV/cm will be applied in the storage orbit region between two co-
axial electrodes.

The experiment will employ a combination of silicon strip and scintillating
fiber ribbon detectors to track the decay positron, enabling the measurement
of the muon’s anomalous precession frequency, $\omega_{a}$. This measurement
will serve as a sensitive probe of the magnetic field. Furthermore, by
plotting $\omega_{a}$ against the applied electric field and interpolating it
to $\omega_{a}(E)=0$, we can adjust the electric field to achieve the frozen-
spin condition. This procedure also enables us to measure the up-down
asymmetry.

In Phase II of the experiment, we plan to employ a muon beam with a higher
momentum of 125 MeV/c and a larger radial electric field of 20 kV/cm. Given
that the anticipated muon orbit will be significantly larger than in Phase I,
we will design a dedicated solenoid magnet specifically for this phase. A
comparison of the conditions in Phase I and Phase II can be found in Table 1.

Parameters | muEDM Phase I | muEDM Phase II
---|---|---
Factor | Event rate [Hz] | Factor | Event rate (Hz)
Muon flux ($\mu^{+}$/s) | - | $4\times 10^{6}$ | - | $1.2\times 10^{8}$
Channel transmission | 0.03 | $1.2\times 10^{5}$ | 0.005 | $6\times 10^{5}$
Injection efficiency | 0.017 | $2.0\times 10^{3}$ | 0.6 | $3.6\times 10^{5}$
$e^{+}$ detection efficiency | 0.25 | $5.0\times 10^{2}$ | 0.25 | $9.0\times 10^{4}$
Detected $e^{+}$ per 200 days | $8.64\times 10^{9}$ | $1.56\times 10^{12}$
Beam momentum (MeV/c) | $\approx 30$ | 125
Gamma factor, $\gamma$ | 1.04 | 1.56
Storage magnetic field, $B$ (T) | 3 | 3
Electric field, $E_{\mathrm{f}}$ (kV/cm) | 3 | 20
Muon decay asymmetry, $\alpha$ | 0.3 | 0.3
Initial polarization, $P_{0}$ | 0.95 | 0.95
Muon EDM Sensitivity ($e\cdot$cm) | $3\times 10^{-21}$ | $6\times 10^{-23}$
Table 1: Calculated event rate, experiment parameters, and annual statistical
sensitivity of the muon EDM measurement for muEDM Phase I and II based on Eq.
(1).

##  III R&D progress at PSI

From 2019 to 2022, we conducted four comprehensive test-beam measurements at
PSI. In 2019, our primary focus was characterizing the phase space of
potential muon beamlines. In 2020, we primarily studied the effects of
multiple Coulomb scattering of low-momentum positrons. We have reported the
details from these test-beam measurements in muonEDMinitiative:2022fmk ;
Sakurai:2022tbk . Currently, we are analyzing the data from the 2021 testbeam,
where we characterized potential electrode materials with positrons and muons.
In 2022, we tested a prototype of the muon tagger/tracker, consisting of a
time projection chamber (TPC) and then tested muon entrance detector
prototypes using a $27.5$ MeV/c muon beam from the $\pi$E1 beamline.

In Fig. 2, a muon-entrance detector based on a thin plastic scintillator (gate
detector) and four GNKD GNKD  plastic scintillating tiles (telescope
detectors), each readout by NDL NDL  silicon photomultipliers (SiPMs)
NDL15-6060S, was developed. The SiPMs were coupled to the scintillators using
BC-603 optical grease. The scintillators and readout electronics were held
together by a 3D-printed holder and a rack made of resin material. This
prototype was recently tested at the $\pi$E1 beamline at PSI. Signal
digitization was done using WaveDAQ Francesconi:2018fkg  based on DRS4
Ritt:2010zz . A total of 0.7 million muon events were collected during the
test beam, and data analysis is ongoing to characterize the efficiency of the
muon-entrance detector.

Figure 2: Left: A detailed three-dimensional CAD model of the muon entrance
detector. Right: An image of the actual prototype entrance detector, developed
for the test beam at PSI. The close-up views (insets) display the SiPM readout
boards designed for the telescope scintillators.”

##  IV Conclusions and outlook

A sensitive search of the muon EDM presents an exciting opportunity to explore
BSM physics within the muon sector. The innovative frozen-spin technique has
the potential to surpass the sensitivity of the existing muon $g-2$ storage
ring approach. By leveraging the current beamlines at the Paul Scherrer
Institute (PSI), it is possible to reach an unprecedented EDM sensitivity of
$6\times 10^{-23}~{}e\cdot$cm. Currently, the development and testing of the
critical components for the experimental setup are in progress, setting the
stage for the Phase-I precursor experiment at PSI.

##  V ACKNOWLEDGEMENTS

We would like to thank our colleagues in the muEDM collaboration for useful
discussions regarding the manuscript. KSK was funded by the National Natural
Science Foundation of China under Grant No. 12075151 and 12050410233.

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