EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-133 LHCb-PAPER-2018-012 20 November 2018

Measurement of the time-integrated $C\\!P$ asymmetry in
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays

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

A measurement of the time-integrated $C\\!P$ asymmetry in
$D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays is reported. The data
correspond to an integrated luminosity of about $2\mbox{\,fb}^{-1}$ collected
in 2015–2016 by the LHCb collaboration in $pp$ collisions at a centre-of-mass
energy of $13\mathrm{\,Te\kern-1.00006ptV}$. The ${D}^{0}$ candidate is
required to originate from a ${{D}^{*+}}\rightarrow D^{0}{{\pi}^{+}}$ decay,
allowing the determination of the flavour of the ${D}^{0}$ meson using the
pion charge. The ${{D}^{0}}\rightarrow K^{+}K^{-}$ decay, which has a well
measured $C\\!P$ asymmetry, is used as a calibration channel. The $C\\!P$
asymmetry for ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ is measured to be

${{\mathcal{A}}^{{C\\!P}}}(D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=(4.3\pm 3.4\pm 1.0)\%,$

where the first uncertainty is statistical and the second is systematic. This
result is combined with the previous LHCb measurement at lower centre-of-mass
energies to obtain

${{\mathcal{A}}^{{C\\!P}}}(D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=(2.3\pm 2.8\pm 0.9)\%.$

Published in JHEP 11 (2018) 048

© 2024 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

##  1 Introduction

In the Standard Model, violation of charge-parity ($C\\!P$) symmetry
originates from the presence of a single phase in the Cabibbo-Kobayashi-
Maskawa (CKM) matrix [1]. Experimental results support the CKM mechanism for
$C\\!P$ violation, but additional sources of $C\\!P$ violation are needed to
explain cosmological observations of the relative abundance of matter and
antimatter in the universe [2]. In the charm sector, $C\\!P$ violation has not
yet been observed, but measurements of $C\\!P$ asymmetries in Cabibbo-
suppressed ${{D}^{0}}\rightarrow h^{+}h^{-}$ decays ($h=\pi,K$) have reached
0.2% and 0.03% precision for time-integrated [3] and indirect $C\\!P$
asymmetries [4], respectively.

The ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decay is a promising discovery
channel for $C\\!P$ violation in charm decays [5]. Only loop-suppressed
amplitudes and exchange diagrams that vanish in the SU(3) flavour limit
contribute to this decay. These amplitudes can have different strong and weak
phases and are of similar size. The time-integrated $C\\!P$ asymmetry,
${{\mathcal{A}}^{{C\\!P}}}$, in
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays may therefore be
enhanced to an observable level [6], and could be as large as 1.1% [5].
Examples of such diagrams are shown in Fig. 1. The most precise measurement of
this asymmetry to date,
${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=(-0.02\pm 1.53\pm 0.17)$%, has
been performed by the Belle collaboration [7]. Earlier measurements were also
performed by the LHCb [8] and CLEO [9] collaborations. This article reports a
new measurement of ${\mathcal{A}}^{{C\\!P}}$ in the decay
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ using LHCb data collected in
2015 and 2016.

$\bar{u}$$c$$s$$\bar{d}$$d$$\bar{s}$$\bar{u}$$c$$s$$\bar{d}$$d$$\bar{s}$

Figure 1: Exchange (left) and penguin annihilation (right) diagrams
contributing to the ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ amplitude. Based on Ref. [5].

The measurement of the $C\\!P$ asymmetry, defined as

${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}})\equiv\dfrac{\Gamma({{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})-\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}})}{\Gamma({{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})+\Gamma({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})},$ (1)

requires knowledge of the flavour of the ${D}^{0}$ meson at production. A
sample of flavour-tagged
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays is obtained by selecting
${D}^{*+}$ mesons that are produced in the primary interaction (hereafter
referred to as prompt), with the subsequent decay
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$.111The inclusion of charge-
conjugate processes is implied throughout this document, unless explicitly
specified. The charge of the pion in this decay identifies the flavour of the
accompanying ${D}^{0}$ meson. The effect of ${{D}^{0}}-{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ mixing [10] is negligible
compared to the precision of this analysis and is not considered further.

The experimentally measured quantity is the raw asymmetry, defined as

${{\mathcal{A}}^{\mathrm{raw}}}\equiv\dfrac{N_{{{D}^{0}}}-N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}}{N_{{{D}^{0}}}+N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}},$ (2)

where $N_{{{D}^{0}}}$ is the measured yield of
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$,
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays and $N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}$ is the measured yield of
${{D}^{*-}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{-}}$, ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays. This observable is
related to the $C\\!P$ asymmetry by the expression, valid for small
asymmetries,

${{\mathcal{A}}^{\mathrm{raw}}}\approx{{\mathcal{A}}^{{C\\!P}}}+{{\mathcal{A}}^{\mathrm{prod}}}+{{\mathcal{A}}^{\mathrm{det}}},$
(3)

where ${\mathcal{A}}^{\mathrm{prod}}$ is the ${D}^{*\pm}$ production
asymmetry, defined as
${{\mathcal{A}}^{\mathrm{prod}}}\equiv\frac{\sigma({{D}^{*+}})-\sigma({{D}^{*-}})}{\sigma({{D}^{*+}})+\sigma({{D}^{*-}})}$,
and ${\mathcal{A}}^{\mathrm{det}}$ is the $\pi_{\mathrm{tag}}^{\pm}$ detection
asymmetry, defined as
${{\mathcal{A}}^{\mathrm{det}}}\equiv\frac{\epsilon(\pi_{\mathrm{tag}}^{+})-\epsilon(\pi_{\mathrm{tag}}^{-})}{\epsilon(\pi_{\mathrm{tag}}^{+})+\epsilon(\pi_{\mathrm{tag}}^{-})}$.
The symbol $\pi_{\mathrm{tag}}^{\pm}$ refers to the pion in the ${D}^{*\pm}$
decay. To a very good approximation, knowledge of
${\mathcal{A}}^{\mathrm{det}}$ and ${\mathcal{A}}^{\mathrm{prod}}$ is
unnecessary when using a calibration channel with the same production and
tagging mechanism. The decay channel ${{D}^{0}}\rightarrow K^{+}K^{-}$ is used
for this purpose. The production and detection asymmetries cancel when taking
the difference of the raw asymmetries:

$\displaystyle\Delta{{\mathcal{A}}^{{C\\!P}}}$ $\displaystyle\equiv$
$\displaystyle{{\mathcal{A}}^{\mathrm{raw}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}})-{{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})$ (4) $\displaystyle=$
$\displaystyle{{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}})-{{\mathcal{A}}^{{C\\!P}}}(K^{+}K^{-}).$ (5)

The quantity ${{\mathcal{A}}^{{C\\!P}}}(K^{+}K^{-})$ has been measured with a
precision of 0.2% [3], thus allowing the determination of
${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})$.

##  2 LHCb detector

The LHCb detector [11, 12] 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 (TT) 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 (RICH)
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 magnetic field deflects oppositely-charged particles in opposite
directions and this can lead to detection asymmetries. Periodically reversing
the magnetic field polarity throughout the data taking almost cancels the
effect. The configuration with the magnetic field pointing upwards
(downwards), MagUp (MagDown), bends positively (negatively) charged particles
in the horizontal plane towards the centre of the LHC ring.

The online event selection is performed by a trigger, 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. At
the hardware trigger stage, events are required to have a muon with high
$p_{\mathrm{T}}$ or a hadron, photon or electron with high transverse-energy
deposit in the calorimeters.

Simulated events are used at various phases of the analysis. In the
simulation, $pp$ collisions are generated using Pythia [13, *Sjostrand:2007gs]
with a specific LHCb configuration [15]. Decays of hadronic particles are
described by EvtGen [16], in which final-state radiation is generated using
Photos [17]. The interaction of the generated particles with the detector, and
its response, are implemented using the Geant4 toolkit [18,
*Agostinelli:2002hh] as described in Ref. [20].

##  3 Event selection

The 2015 and 2016 data samples collected in $pp$ collisions at
$13\mathrm{\,Te\kern-1.00006ptV}$, which correspond to about
$2\mbox{\,fb}^{-1}$ of integrated luminosity, are used in this analysis.
Candidates are reconstructed in the decay
${{D}^{*+}}\rightarrow{{D}^{0}}\pi^{+}$, followed by
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ and then
${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$. The hardware trigger decision is
required to be based either on the transverse energy deposited in the hadronic
calorimeter by a charged particle from the decay of the ${{D}^{0}}$ meson, or
on signatures not associated with the ${{D}^{*+}}$ decay, such as a
high-$p_{\mathrm{T}}$ muon, or a high transverse-energy deposit in the
electromagnetic or hadronic calorimeters. The first stage of the software
trigger selects a sample with enhanced heavy-flavour content by requiring the
presence of a large IP, high-$p_{\mathrm{T}}$ charged particle. In the second
stage of the software trigger, each selected event is required to contain at
least one fully-reconstructed candidate for the
${{D}^{*+}}\rightarrow{{D}^{0}}\pi^{+}$,
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decay.

The decays ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ are reconstructed in two different
categories: the first involving ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$
mesons that decay early enough for the decay products to be reconstructed in
the vertex detector; and the second containing
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates that decay outside the
acceptance of the vertex detector, but within the TT acceptance. These
categories are referred to as _long_ and _downstream_ , respectively. The long
category has better mass, momentum and decay-vertex resolution than the
downstream category. In this analysis at least one
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ in each ${D}^{0}$ decay is required
to be of the long type. There are therefore two subsamples used: one where
both ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates are long and the
other where one is long and the other is downstream. These are referred to as
the LL and LD subsamples, and are analysed separately, since they exhibit
different resolutions. One or more of the charged decay products from a long
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ meson is required to activate the
first stage of the software trigger. The pion candidates used in the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ reconstruction are required to be
high-quality tracks, using the $\chi^{2}$/ndf of the track fit and the output
${\cal P}_{\rm fake}$ of a multivariate classifier, trained to identify fake
tracks, that combines information from the particle identification and
tracking systems. To ensure that pion candidates do not originate from the PV,
they are required to satisfy $\chi^{2}_{\text{IP}}>36$. The quantity
$\chi^{2}_{\text{IP}}$ for a given particle is defined as the difference in
the vertex fit $\chi^{2}$ of the PV associated to the particle, reconstructed
with and without the particle being considered. For downstream
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates, the pions are required
to satisfy $p>3$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$\mbox{$p_{\mathrm{T}}$}>175$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

Two oppositely charged pions are used to form
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates. The vertex fit is
required to satisfy $\chi^{2}<30$ and the $\chi^{2}_{\text{IP}}$ is required
to be greater than 9 (4) for long (downstream)
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates. Furthermore, long
(downstream) ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates are required
to satisfy $\mbox{$p_{\mathrm{T}}$}>500\
(750)$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.

Two reconstructed ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates are
paired to form ${D}^{0}$ candidates, requiring $\chi^{2}<10$ for the vertex
fit. The sum of the $p_{\mathrm{T}}$ of the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates is required to exceed
1500 (2000) ${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ for LL (LD) candidates. The
angle between the ${D}^{0}$ momentum and the vector connecting the PV to the
${D}^{0}$ decay vertex is required to be less than 34.6 mrad. The measured
decay time of the ${D}^{0}$ meson is required to be greater than 0.2 ps.
Finally, the ${D}^{0}$ mass is required to be within 20
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known value [10].

A pion candidate ($\pi_{\mathrm{tag}}^{+}$) is added to a reconstructed
${D}^{0}$ meson to form a ${D}^{*+}$ candidate, with a ${D}^{*+}$ vertex fit
which is required to have $\chi^{2}<25$. The $\pi_{\mathrm{tag}}^{+}$
candidate is required to have $\mbox{$p_{\mathrm{T}}$}>100$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, and to pass through regions of the
detector that are known to have a small detector asymmetry [8]. A small
fraction of $\pi_{\mathrm{tag}}^{\pm}$ candidates are reconstructed with the
wrong charge assignment, and are removed by a selection on track quality.

An important source of background is due to the presence of
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays, where the ${\pi}^{+}$ ${\pi}^{-}$ pair
satisfies the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ selection. In
principle, the contribution of this channel can be substantial, due to its
large branching fraction, but it is effectively reduced by placing a
requirement on the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ flight distance
(FD) and on the mass of the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$
candidates. The quantity $\chi^{2}_{\text{FD}}$ is the square of the measured
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ flight distance divided by the
square of its uncertainty. Figure 2 shows a two-dimensional plot of the value
of the quantity $\log\chi^{2}_{\text{FD}}$ for
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ pairs in the LL sample. In the
figure, four separate regions are visible. The upper right part of the plot,
where both ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates have
significant flight distances, is the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ signal, while the upper left
and lower right regions correspond to
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays. The lower left is populated by
${{D}^{0}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays and
combinatorial background.

Figure 2: Two-dimensional distribution of the logarithm of the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ flight distance significance
($\log\chi^{2}_{\text{FD}}$) for the two ${K}^{0}_{\mathrm{\scriptscriptstyle
S}}$ candidates in the LL subsample of
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays. The
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ signal can be observed in the
upper right region of the plot. The contour corresponds to Eq. 6.

A requirement on $\chi^{2}_{\text{FD}}$ is only necessary for long
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates, since downstream
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates decay far from the PV by
construction. For the LL subsample the requirement on the two
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates
(${{K}^{0}_{\mathrm{\scriptscriptstyle S}\mathrm{1}}}$ and
${{K}^{0}_{\mathrm{\scriptscriptstyle S}\mathrm{2}}}$) is

$[\log\chi^{2}_{\text{FD}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{1}}})-10]^{2}+[\log\chi^{2}_{\text{FD}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{2}}})-10]^{2}<16,$ (6)

while for the LD sample
$\log\chi^{2}_{\text{FD}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{L}}})>2.5$ is imposed on the long
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidate.

The ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass requirements are

$\sqrt{[m({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{1}}})-m_{K^{0}}]^{2}+[m({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{2}}})-m_{K^{0}}]^{2}}<10.5\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$
(7)

for LL candidates, with
$m_{K^{0}}=497.6\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [10], and

$\sqrt{\left[\frac{m({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{L}}})-m_{K^{0}}}{10.5{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}\right]^{2}+\left[\frac{m({{K}^{0}_{\mathrm{\scriptscriptstyle
S}\mathrm{D}}})-m_{K^{0}}}{15{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}\right]^{2}}<1,$
(8)

for LD candidates. This selection takes into account the difference in
resolution between $m({{K}^{0}_{\mathrm{\scriptscriptstyle S}\mathrm{L}}})$
and $m({{K}^{0}_{\mathrm{\scriptscriptstyle S}\mathrm{D}}})$. The
$\log\chi^{2}_{\text{FD}}({{K}^{0}_{\mathrm{\scriptscriptstyle S}}})$ and
$m({{K}^{0}_{\mathrm{\scriptscriptstyle S}}})$ regions corresponding to signal
and peaking-background candidates are identified using simulations. They are
further optimised on charge-integrated data by minimising the expected
statistical uncertainty on ${\mathcal{A}}^{\mathrm{raw}}$.

Events in which the ${D}^{*+}$ meson is not produced in the primary
interaction, but instead is the product of a $b$-hadron decay, are
characterised by a different production asymmetry and are treated as
background. These so-called secondary ${D}^{*+}$ candidates tend to have
larger values of $\chi^{2}_{\text{IP}}({{D}^{0}})$ than prompt ${D}^{*+}$
candidates and are suppressed by requiring
$\log\chi^{2}_{\text{IP}}({{D}^{0}})<3.0$ (3.5) for the LL (LD) subsample. The
requirement $\log\chi^{2}_{\text{IP}}(\pi_{\mathrm{tag}}^{+})<2.5$ is imposed
on both subsamples. Simulated events are used to estimate the residual
secondary fraction in the LL and LD subsamples to be 9% and 13%, respectively.

A multivariate classifier, based on the k-nearest neighbours (kNN) algorithm
[21], is used to further suppress combinatorial background. The kNN algorithm
classifies events according to the fraction of signal events among its $k$
nearest neighbours (taken from the training sample of signal and background
events), where the distance is calculated in the $n$-dimensional space of the
input variables and $k$ is a positive integer. The training sample uses
simulated events for the signal and data events from the ${D}^{0}$ mass
sidebands for the background. A wide range of input variables based on track
and vertex quality, the transverse momenta of
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ and ${D}^{0}$ candidates, helicity
angles of the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ and ${D}^{0}$ decays
and particle identification information on the pions in the ${D}^{0}$ decays
was initially considered. Variables depending on the
$\pi_{\mathrm{tag}}^{\pm}$ track are not included in the classifier to avoid
introducing possible bias on the asymmetry measurement. The actual variables
used, the value of $k$, and the selection on the classifier output are
optimised separately for the LL and LD subsamples, using the expected
statistical uncertainty on the raw asymmetry as a figure of merit.

For the ${{D}^{0}}\rightarrow K^{+}K^{-}$ control channel, an attempt is made
to keep the selection similar to the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ channel, although some
selections made at the software trigger level are different for the two
channels. Charged tracks positively identified as kaons in the RICH detectors
are selected to reconstruct ${D}^{0}$ candidates. The kaons are required to
satisfy $\chi^{2}_{\text{IP}}>4$. For the ${D}^{0}$ candidates, at least one
of the kaons is required to have $\mbox{$p_{\mathrm{T}}$}>1$
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The sum of the kaon momenta is
required to exceed 5 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and the ${D}^{0}$
$p_{\mathrm{T}}$ is required to be at least 1
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Furthermore, the angle between the
${D}^{0}$ momentum vector and the vector connecting the primary and decay
vertices is required to be less than 17.3 mrad. The following selections are
the same as for the ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ channel:
$\pi_{\mathrm{tag}}^{\pm}$ fiducial cuts, fake-track probability and
$\chi^{2}_{\text{IP}}$ selection; and requirements on ${D}^{0}$
$\chi^{2}_{\text{IP}}$ and invariant mass.

##  4 Asymmetry measurement

The raw asymmetry for
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ is determined by separating the
selected candidates into subsets tagged by positively and negatively charged
pions. A simultaneous unbinned maximum likelihood fit to their $\Delta m$
distributions is performed, where $\Delta m$ is the difference of the
reconstructed invariant mass of the ${D}^{*+}$ and the ${D}^{0}$ candidates.
The calculation of $\Delta m$ is made after the full decay chain has been
reconstructed using a mass constraint on the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidates and constraining the
${D}^{*+}$ candidate to originate from the PV.

The signal shape is modelled using the Johnson $S_{\mathrm{U}}$ distribution
[22], which consists of a core Gaussian-like shape but allows for an
asymmetric tail

$S(x;\mu,\sigma,\delta,\gamma)\propto\left[1+\left(\frac{x-\mu}{\sigma}\right)^{2}\right]^{-\frac{1}{2}}\times\exp\left\\{-\frac{1}{2}\left[\gamma+\delta\sinh^{-1}\left(\frac{x-\mu}{\sigma}\right)\right]^{2}\right\\}.$
(9)

The background shape is described with an exponential function multiplied by a
threshold factor and is zero below a fixed endpoint, which is set to the pion
mass $m_{\pi}$

$B(x;m_{\pi},\chi)\propto\sqrt{x-m_{\pi}}\times\exp{\left(\chi\frac{x}{m_{\pi}}\right)}.$
(10)

The likelihood function is parametrised in terms of ${\mathcal{A}}^{{C\\!P}}$
and the expected total number of events
$N_{\mathrm{exp}}=n_{\mathrm{sig}}+n_{\mathrm{bkg}}$

$\mathcal{L}=\dfrac{e^{-N_{\mathrm{exp}}}}{N_{\mathrm{obs}}!}\prod_{i}\left[n_{\mathrm{sig}}\dfrac{1+q_{i}{{\mathcal{A}}^{\mathrm{raw}}_{\mathrm{sig}}}}{2}S({\mbox{$\Delta
m$}})+n_{\mathrm{bkg}}\dfrac{1+q_{i}{{\mathcal{A}}^{\mathrm{raw}}_{\mathrm{bkg}}}}{2}B_{q_{i}}({\mbox{$\Delta
m$}})\right],$ (11)

where $n_{\mathrm{sig}}$ and $n_{\mathrm{bkg}}$ are the signal and background
yields, respectively, and the parameter $q_{i}=\pm 1$ is the charge of the
$D^{\ast\pm}$ candidate and $N_{\mathrm{obs}}$ is the total number of
candidates. The signal raw asymmetry
${\mathcal{A}}^{\mathrm{raw}}_{\mathrm{sig}}$ is a free parameter in the fit.
The free parameter ${\mathcal{A}}^{\mathrm{raw}}_{\mathrm{bkg}}$ allows for a
possible asymmetry in the combinatorial background. The four parameters in Eq.
9 defining the signal probability distribution function (PDF) are common to
the ${D}^{*+}$ and ${D}^{*-}$ samples, while the parameter describing the
background shape is allowed to differ between the two subsamples. For the LL
sample, there are ten free parameters. To achieve convergence of the fit in
the smaller LD sample, it is necessary to fix the two parameters that describe
the asymmetric tail in the signal PDF to the values obtained from the charge-
integrated LL subsample. Based on studies of simulated events, the tail
parameters of the LL and LD subsamples are expected to be compatible. Separate
fits are performed for the two magnet polarities.

Table 1 shows the results of the simultaneous fits to the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ candidates. The results on each
subset of the data are compatible with each other. The fit is shown in Fig. 3
for the samples collected with the MagUp magnetic field configuration.

Table 1: Fit results on the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ LL and LD samples for each
magnet polarity, where $N_{\mathrm{obs}}$ represents the number of candidates
fitted. The purity is determined in the range $144.5<{\mbox{$\Delta
m$}}<146.5\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. For each sample, a
$\chi^{2}$ test statistic for the fitted model and binned data for positively
and negatively charged candidates is constructed. The quantity
$\mathcal{P}_{\rm fit}$ is the probability of observing a $\chi^{2}$ value
greater than that observed in the fit to real data, determined using simulated
pseudoexperiments sampled from the fitted model.

| ${\mathcal{A}}^{\mathrm{raw}}_{\mathrm{sig}}$ | $n_{\mathrm{sig}}$ | ${\mathcal{A}}^{\mathrm{raw}}_{\mathrm{bkg}}$ | Purity | $\mathcal{P}_{\rm fit}(\%)$ | $N_{\mathrm{obs}}$
---|---|---|---|---|---|---
LL MagUp | $\phantom{-}0.008\pm 0.057$ | $346\pm 21$ | $-0.097\pm 0.069$ | 0.92 | 48 | 589
LL MagDown | $\phantom{-}0.103\pm 0.052$ | $413\pm 24$ | $-0.098\pm 0.068$ | 0.92 | 43 | 675
LD MagUp | $-0.046\pm 0.102$ | $156\pm 18$ | $-0.021\pm 0.044$ | 0.67 | 93 | 758
LD MagDown | $-0.078\pm 0.107$ | $152\pm 19$ | $-0.040\pm 0.038$ | 0.60 | 14 | 950

(a)(b)
(c)(d)

Figure 3: Results of fits to $\Delta m$ distributions of
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ candidates for MagUp magnet
polarity. The fit to (a) $D^{\ast+}\rightarrow{{D}^{0}}{{\pi}^{+}}$ and (b)
$D^{\ast-}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{-}}$ candidates for the
LL sample and the fit to (c) $D^{\ast+}\rightarrow{{D}^{0}}{{\pi}^{+}}$ and
(d) $D^{\ast-}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{-}}$ candidates for the
LD sample are shown. The black crosses represent the data points, the solid
blue curve is the total fit function, and the dashed blue curve is the
background component of the fit.

For the ${{D}^{0}}\rightarrow K^{+}K^{-}$ channel, binned $\chi^{2}$ fits are
performed to the $\Delta m$ distributions of the positively and negatively
tagged ${D}^{0}$ decays. The sample consists of $8.25\times 10^{5}$ selected
candidates for the MagDown magnet polarity and $5.61\times 10^{5}$ candidates
for the MagUp magnet polarity. The signal is modelled with a Johnson
$S_{\mathrm{U}}$ distribution plus a Gaussian distribution, while the
background shape is described by a fourth-degree polynomial multiplied by a
$\sqrt{{\mbox{$\Delta m$}}-m_{\pi}}$ threshold factor. There are 12 free
parameters, and 150 bins, in each $\Delta m$ fit. The $\chi^{2}$ probabilities
associated to the fits are 28% (20%) for the negatively (positively) tagged
${D}^{0}$ decays, and 23% (3%) for the negatively (positively) tagged
${D}^{0}$ decays, in the MagUp and MagDown magnet polarities, respectively.
Figure 4 shows the results for the MagUp magnet polarity fit. The results
obtained for the two magnet polarities are

$\displaystyle{{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})_{\mathrm{MagUp\phantom{wn}}}$
$\displaystyle=$ $\displaystyle-0.0188\pm 0.0020,$ (12)
$\displaystyle{{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})_{\mathrm{MagDown}}$
$\displaystyle=$ $\displaystyle\phantom{+}0.0030\pm 0.0017,$

where the uncertainties are statistical.

(a)(b)

Figure 4: Results of fits to $\Delta m$ distributions of ${{D}^{0}}\rightarrow
K^{+}K^{-}$ candidates for the MagUp magnet polarity. The fits to (a)
$D^{\ast+}\rightarrow{{D}^{0}}{{\pi}^{+}}$ candidates and (b)
$D^{\ast-}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{-}}$ candidates are
shown. The black points represent the data, the dashed blue and solid blue
curves represent the background component and the total fit function,
respectively.

The difference in the MagUp and MagDown values of
${{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})$ is an indication of a significant
$\pi_{\mathrm{tag}}^{\pm}$ detection asymmetry, which depends on the magnetic
field orientation.

##  5 Systematic uncertainties

The main source of systematic uncertainty arises from the determination of
${\mathcal{A}}^{\mathrm{raw}}$ on the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ sample. Possible bias in the
fitting procedure is evaluated using simulated pseudoexperiments. In
particular, the uncertainty related to the choice of the signal model is
evaluated by using the nominal model to fit samples generated with two
alternative models for the signal PDF: either a sum of two Gaussians with a
common mean (for the LL sample) or a single Gaussian (for the LD sample). The
background PDF is varied by modifying its behaviour at threshold. Systematic
uncertainties of $5\times 10^{-3}$ and 0.01 for the LL and LD samples,
respectively, are assigned based on this study. As a cross-check, the
background shapes are constrained to be the same for the ${D}^{*+}$ and
${D}^{*-}$ samples, and the resulting asymmetry is compatible with the
nominal. For the ${{D}^{0}}\rightarrow K^{+}K^{-}$ fit, an alternative
procedure is used to evaluate the systematic uncertainty associated with the
signal PDF. In this case, the signal region ($\pm 2.5$
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the signal mean) is excluded
and only the background shape is fit. The yield is then determined by
estimating the background in the signal region by interpolating the fitted
background function. Additionally, alternative background shapes are tried,
varying the degree of the polynomial. Based on these studies a systematic
uncertainty of $2\times 10^{-3}$ is assigned to
${{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})$.

The contribution of the residual background of
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\pi^{+}\pi^{-}$
decays to the fitted LL and LD signal yields is estimated to be $(3.5\pm
0.7)\%$ and $(5.5\pm 4.6)\%$, respectively. These values are combined with the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$ background
asymmetry, determined from background-dominated regions of the
$\chi^{2}_{\text{FD}}$ distributions, to estimate contributions to the
systematic uncertainty of $4\times 10^{-3}$ and $5\times 10^{-3}$, for the LL
and LD samples. Another contribution comes from the residual fraction of
secondary decays, which leads to a systematic uncertainty for this source of
$2\times 10^{-3}$ and $3\times 10^{-3}$ for the LL and LD samples. In this
case an upper limit of 0.02 for the maximum difference in the production
asymmetries of ${D}^{*\pm}$ mesons and $b$-hadrons is assumed [23, 24, 25].

Potential trigger biases are studied using tagged
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}$ decays, by comparing the raw
asymmetries obtained in the subsample in which the trigger decision is based
on the charged particles from the decay of the ${{D}^{0}}$ meson, and in the
subsample in which the trigger decision is not associated with the
${{D}^{*+}}$ decay. The sum in quadrature of the difference (albeit not
statistically significant) and of its statistical uncertainty is assigned as a
systematic uncertainty, which accounts for residual trigger-induced biases in
the difference of measured asymmetries for signal and control channels. This
uncertainty amounts to $5\times 10^{-3}$ for both the LL and LD samples. The
small probability of assigning the wrong charge to the
$\pi_{\mathrm{tag}}^{\pm}$ candidate results in a systematic uncertainty of
$2\times 10^{-3}$ for both the LL and LD samples. This is obtained by varying
the selection on the ${\cal P}_{\rm fake}$ value of $\pi_{\mathrm{tag}}^{\pm}$
candidates. This uncertainty cancels for $\Delta{{\mathcal{A}}^{{C\\!P}}}$.
For each neutral kaon in the final state, asymmetries arising from
regeneration and from mixing and $C\\!P$ violation in the ${{K}^{0}}-{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ system are suppressed at the
${\cal O}(10^{-3})$ level [26]. Since they are expected to affect
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ and ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays by the same amount, they
cancel in ${\mathcal{A}}^{\mathrm{raw}}$ and therefore do not contribute to
the systematic uncertainty.

The cancellation of the production and detection asymmetries in the
computation of ${\Delta\mathcal{A}}^{{C\\!P}}$ may not be perfect due to
differences in the kinematics of the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ candidates and the
${{D}^{0}}\rightarrow K^{+}K^{-}$ candidates. The offline selection of the two
channels aims to keep the kinematics as similar as possible, but the different
trigger selections on the final states can introduce differences. The
associated systematic uncertainty is evaluated by considering four kinematic
variables: the transverse momentum and the pseudorapidity of the ${{D}^{*+}}$
candidate and the $\pi_{\mathrm{tag}}^{+}$ candidate, respectively. For each
variable a one-dimensional weighting is performed on the ${{D}^{0}}\rightarrow
K^{+}K^{-}$ events such that they have the same distribution as the
${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ sample. Then
${{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})$ is determined from the weighted
sample. This is repeated for each of the four kinematic variables. The largest
change in ${{\mathcal{A}}^{\mathrm{raw}}}(K^{+}K^{-})$ is taken as the
systematic uncertainty and this is found to be $2\times 10^{-3}$ for both the
LL and LD samples. The systematic uncertainties are summarised in Table 2.

Table 2: Systematic uncertainties on the quantities ${\mathcal{A}}^{\mathrm{raw}}$ and $\Delta{{\mathcal{A}}^{{C\\!P}}}$. The total systematic uncertainties in the last row are obtained by summing the corresponding contributions in each column in quadrature. Uncertainties are expressed in units of $10^{-3}$.  Source | ${{\mathcal{A}}^{\mathrm{raw}}}({\rm LL})$ | ${{\mathcal{A}}^{\mathrm{raw}}}({\rm LD})$ | $\Delta{{\mathcal{A}}^{{C\\!P}}}({\rm LL})$ | $\Delta{{\mathcal{A}}^{{C\\!P}}}({\rm LD})$
---|---|---|---|---
Fit procedure | 5 | 10 | 5 | 10
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$ background | 4 | 5 | 4 | 5
Secondaries | 2 | 3 | 2 | 3
Wrong $\pi_{\mathrm{tag}}^{\pm}$ charge | 2 | 2 | – | –
Trigger selection | 5 | 5 | 5 | 5
$K^{+}K^{-}$ fit procedure | – | – | 2 | 2
Residual detection | – | – | 2 | 2
asymmetry
Total | 9 | 13 | 9 | 13

##  6 Results

The procedure described in Sect. 1 is used to combine the results for the raw
asymmetries to obtain
${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})$ for each of the LL and LD
subsamples. For each of the subsamples, the difference
${\Delta\mathcal{A}}^{{C\\!P}}$ is calculated separately for the different
magnet polarities using the fitted values of ${\mathcal{A}}^{\mathrm{raw}}$
(Table 1 and Eq. 12). The values of ${\Delta\mathcal{A}}^{{C\\!P}}$
corresponding to the two magnet polarities, which are found to be in good
agreement (Fig. 5), are averaged by weighting with their statistical
uncertainties.

Figure 5: Values of ${\Delta\mathcal{A}}^{{C\\!P}}$ obtained for both magnet
polarities on the LL and LD samples, along with the average of these
measurements. Only statistical uncertainties are shown.

The systematic uncertainties are taken from Table 2. Using the LHCb
measurement of ${{\mathcal{A}}^{{C\\!P}}}(K^{+}K^{-})=(0.04\pm 0.12\pm 0.10)$%
[3] results in

$\displaystyle{{\mathcal{A}}^{{C\\!P}}}(\mathrm{LL})$ $\displaystyle=$
$\displaystyle\phantom{-}0.067\pm 0.038\pm 0.009,$
$\displaystyle{{\mathcal{A}}^{{C\\!P}}}(\mathrm{LD})$ $\displaystyle=$
$\displaystyle-0.053\pm 0.074\pm 0.013,$

where the first uncertainty is statistical and the second is systematic. These
results are combined by performing an average weighted by the total
uncertainties and assuming that the systematic uncertainties are fully
correlated. The final result is

${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=0.043\pm 0.034\pm 0.010.$

This measurement is systematically independent of the LHCb Run 1 measurement,
${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=-0.029\pm 0.052\pm 0.022$ [8],
and is compatible with it. An average, weighted by the total uncertainties, of
the two measurements is performed to obtain

${{\mathcal{A}}^{{C\\!P}}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}})=0.023\pm 0.028\pm 0.009.$

These results are compatible with the expectations of the Standard Model [5]
and with previous measurements [9, 7].

## 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); NWO (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 (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), ANR, Labex P2IO and OCEVU,
and Région Auvergne-Rhône-Alpes (France), Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China), RFBR, RSF
and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund,
the Royal Society, the English-Speaking Union and the Leverhulme Trust (United
Kingdom).

## References

  * [1] M. Kobayashi and T. Maskawa, _CP-violation in the renormalizable theory of weak interaction_ , Prog. Theor. Phys. 49 (1973) 652
  * [2] M. Dine and A. Kusenko, _The origin of the matter - antimatter asymmetry_ , Rev. Mod. Phys. 76 (2003) 1, arXiv:hep-ph/0303065
  * [3] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ asymmetry in ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}$ decays_, Phys. Lett. B767 (2017) 177, arXiv:1610.09476
  * [4] LHCb collaboration, R. Aaij et al., _Measurement of the $C\\!P$ violation parameter $A_{\Gamma}$ in ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}$ and ${{D}^{0}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decays_, Phys. Rev. Lett. 118 (2017) 261803, arXiv:1702.06490
  * [5] U. Nierste and S. Schacht, _CP violation in $D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$_, Phys. Rev. D92 (2015) 054036, arXiv:1508.00074
  * [6] J. Brod, A. L. Kagan, and J. Zupan, _Size of direct CP violation in singly Cabibbo-suppressed D decays_ , Phys. Rev. D86 (2012) 014023, arXiv:1111.5000
  * [7] Belle collaboration, N. Dash et al., _Search for $C\\!P$ violation and measurement of the branching fraction in the decay ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$_, Phys. Rev. Lett. 119 (2017) 171801, arXiv:1705.05966
  * [8] LHCb collaboration, R. Aaij et al., _Measurement of the time-integrated ${C\\!P}$ asymmetry in ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays_, JHEP 10 (2015) 055, arXiv:1508.06087
  * [9] CLEO collaboration, G. Bonvicini et al., _Search for CP violation in $D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\pi^{0}$ and $D^{0}\rightarrow\pi^{0}\pi^{0}$ and $D^{0}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ decays_, Phys. Rev. D63 (2001) 071101, arXiv:hep-ex/0012054
  * [10] Particle Data Group, C. Patrignani et al., _Review of particle physics_ , Chin. Phys. C40 (2016) 100001, and 2017 update
  * [11] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [12] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [13] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [14] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [15] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [16] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [17] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [18] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [19] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [20] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [21] I. Narsky and F. C. Porter, Statistical analysis techniques in particle physics, Wiley-VCH, Weinheim, Germany, 2014
  * [22] N. L. Johnson, _Systems of frequency curves generated by methods of translation_ , Biometrika 36 (1949) 149
  * [23] LHCb collaboration, R. Aaij et al., _Measurement of the $D^{\pm}$ production asymmetry in 7 TeV pp collisions_, Phys. Lett. B718 (2013) 902, arXiv:1210.4112
  * [24] LHCb collaboration, R. Aaij et al., _Measurement of the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$–${{B}^{0}}$ and ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$–${{B}^{0}_{s}}$ production asymmetries in ${p}{p}$ collisions at $\sqrt{s}=7$$~{}T\kern-0.50003pteV$_, Phys. Lett. B739 (2014) 218, arXiv:1408.0275
  * [25] LHCb collaboration, R. Aaij et al., _Measurement of $B^{0}$, $B^{0}_{s}$, $B^{+}$ and $\Lambda^{0}_{b}$ production asymmetries in 7 and 8 TeV proton-proton collisions_, Phys. Lett. B774 (2017) 139, arXiv:1703.08464
  * [26] C. P. Enz and R. R. Lewis, _On the phenomenological description of CP violation for K mesons and its consequences_ , Helv. Phys. Acta 38 (1965) 860

LHCb collaboration

R. Aaij27, B. Adeva41, M. Adinolfi48, C.A. Aidala73, Z. Ajaltouni5, S. Akar59,
P. Albicocco18, J. Albrecht10, F. Alessio42, M. Alexander53, A. Alfonso
Albero40, S. Ali27, G. Alkhazov33, P. Alvarez Cartelle55, A.A. Alves Jr59, S.
Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G. Andreassi43, M.
Andreotti16,g, J.E. Andrews60, R.B. Appleby56, F. Archilli27, P. d’Argent12,
J. Arnau Romeu6, A. Artamonov39, M. Artuso61, K. Arzymatov37, E. Aslanides6,
M. Atzeni44, S. Bachmann12, J.J. Back50, S. Baker55, V. Balagura7,b, W.
Baldini16, A. Baranov37, R.J. Barlow56, S. Barsuk7, W. Barter56, F.
Baryshnikov70, V. Batozskaya31, B. Batsukh61, V. Battista43, A. Bay43, J.
Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61, L.J. Bel27, N. Beliy63, V.
Bellee43, N. Belloli20,i, K. Belous39, I. Belyaev34,42, E. Ben-Haim8, G.
Bencivenni18, S. Benson27, S. Beranek9, A. Berezhnoy35, R. Bernet44, D.
Berninghoff12, E. Bertholet8, A. Bertolin23, C. Betancourt44, F. Betti15,42,
M.O. Bettler49, M. van Beuzekom27, Ia. Bezshyiko44, S. Bifani47, P. Billoir8,
A. Birnkraut10, A. Bizzeti17,u, M. Bjørn57, T. Blake50, F. Blanc43, S.
Blusk61, D. Bobulska53, V. Bocci26, O. Boente Garcia41, T. Boettcher58, A.
Bondar38,w, N. Bondar33, S. Borghi56,42, M. Borisyak37, M. Borsato41,42, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock54, C. Bozzi16,42, S. Braun12, M.
Brodski42, J. Brodzicka29, D. Brundu22, E. Buchanan48, A. Buonaura44, C.
Burr56, A. Bursche22, J. Buytaert42, W. Byczynski42, S. Cadeddu22, H. Cai64,
R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo Gomez40,m, A.
Camboni40,m, P. Campana18, D.H. Campora Perez42, L. Capriotti56, A.
Carbone15,e, G. Carboni25, R. Cardinale19,h, A. Cardini22, P. Carniti20,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina20, M. Cattaneo42, G.
Cavallero19,h, R. Cenci24,p, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier42, G. Chatzikonstantinidis47, M. Chefdeville4, V. Chekalina37, C.
Chen3, S. Chen22, S.-G. Chitic42, V. Chobanova41, M. Chrzaszcz42, A.
Chubykin33, P. Ciambrone18, X. Cid Vidal41, G. Ciezarek42, P.E.L. Clarke52, M.
Clemencic42, H.V. Cliff49, J. Closier42, V. Coco42, J. Cogan6, E. Cogneras5,
L. Cojocariu32, P. Collins42, T. Colombo42, A. Comerma-Montells12, A. Contu22,
G. Coombs42, S. Coquereau40, G. Corti42, M. Corvo16,g, C.M. Costa Sobral50, B.
Couturier42, G.A. Cowan52, D.C. Craik58, A. Crocombe50, M. Cruz Torres1, R.
Currie52, C. D’Ambrosio42, F. Da Cunha Marinho2, C.L. Da Silva74, E.
Dall’Occo27, J. Dalseno48, A. Danilina34, A. Davis3, O. De Aguiar Francisco42,
K. De Bruyn42, S. De Capua56, M. De Cian43, J.M. De Miranda1, L. De Paula2, M.
De Serio14,d, P. De Simone18, C.T. Dean53, D. Decamp4, L. Del Buono8, B.
Delaney49, H.-P. Dembinski11, M. Demmer10, A. Dendek30, D. Derkach37, O.
Deschamps5, F. Dettori54, B. Dey65, A. Di Canto42, P. Di Nezza18, S.
Didenko70, H. Dijkstra42, F. Dordei42, M. Dorigo42,y, A. Dosil Suárez41, L.
Douglas53, A. Dovbnya45, K. Dreimanis54, L. Dufour27, G. Dujany8, P.
Durante42, J.M. Durham74, D. Dutta56, R. Dzhelyadin39, M. Dziewiecki12, A.
Dziurda42, A. Dzyuba33, S. Easo51, U. Egede55, V. Egorychev34, S.
Eidelman38,w, S. Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53,
S. Ely61, A. Ene32, S. Escher9, S. Esen27, H.M. Evans49, T. Evans57, A.
Falabella15, N. Farley47, S. Farry54, D. Fazzini20,42,i, L. Federici25, G.
Fernandez40, P. Fernandez Declara42, A. Fernandez Prieto41, F. Ferrari15, L.
Ferreira Lopes43, F. Ferreira Rodrigues2, M. Ferro-Luzzi42, S. Filippov36,
R.A. Fini14, M. Fiorini16,g, M. Firlej30, C. Fitzpatrick43, T. Fiutowski30, F.
Fleuret7,b, M. Fontana22,42, F. Fontanelli19,h, R. Forty42, V. Franco Lima54,
M. Frank42, C. Frei42, J. Fu21,q, W. Funk42, C. Färber42, M. Féo Pereira
Rivello Carvalho27, E. Gabriel52, A. Gallas Torreira41, D. Galli15,e, S.
Gallorini23, S. Gambetta52, M. Gandelman2, P. Gandini21, Y. Gao3, L.M. Garcia
Martin72, B. Garcia Plana41, J. García Pardiñas44, J. Garra Tico49, L.
Garrido40, D. Gascon40, C. Gaspar42, L. Gavardi10, G. Gazzoni5, D. Gerick12,
E. Gersabeck56, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì43, V.
Gibson49, O.G. Girard43, L. Giubega32, K. Gizdov52, V.V. Gligorov8, D.
Golubkov34, A. Golutvin55,70, A. Gomes1,a, I.V. Gorelov35, C. Gotti20,i, E.
Govorkova27, J.P. Grabowski12, R. Graciani Diaz40, L.A. Granado Cardoso42, E.
Graugés40, E. Graverini44, G. Graziani17, A. Grecu32, R. Greim27, P.
Griffith22, L. Grillo56, L. Gruber42, B.R. Gruberg Cazon57, O. Grünberg67, C.
Gu3, E. Gushchin36, Yu. Guz39,42, T. Gys42, C. Göbel62, T. Hadavizadeh57, C.
Hadjivasiliou5, G. Haefeli43, C. Haen42, S.C. Haines49, B. Hamilton60, X.
Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57, S.T. Harnew48, C.
Hasse42, M. Hatch42, J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K.
Hennessy54, L. Henry72, E. van Herwijnen42, M. Heß67, A. Hicheur2, D. Hill57,
M. Hilton56, P.H. Hopchev43, W. Hu65, W. Huang63, Z.C. Huard59, W.
Hulsbergen27, T. Humair55, M. Hushchyn37, D. Hutchcroft54, D. Hynds27, P.
Ibis10, M. Idzik30, P. Ilten47, K. Ivshin33, R. Jacobsson42, J. Jalocha57, E.
Jans27, A. Jawahery60, F. Jiang3, M. John57, D. Johnson42, C.R. Jones49, C.
Joram42, B. Jost42, N. Jurik57, S. Kandybei45, M. Karacson42, J.M. Kariuki48,
S. Karodia53, N. Kazeev37, M. Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49,
T. Ketel28, E. Khairullin37, B. Khanji12, C. Khurewathanakul43, K.E. Kim61, T.
Kirn9, S. Klaver18, K. Klimaszewski31, T. Klimkovich11, S. Koliiev46, M.
Kolpin12, R. Kopecna12, P. Koppenburg27, S. Kotriakhova33, M. Kozeiha5, L.
Kravchuk36, M. Kreps50, F. Kress55, P. Krokovny38,w, W. Krupa30, W.
Krzemien31, W. Kucewicz29,l, M. Kucharczyk29, V. Kudryavtsev38,w, A.K.
Kuonen43, T. Kvaratskheliya34,42, D. Lacarrere42, G. Lafferty56, A. Lai22, D.
Lancierini44, G. Lanfranchi18, C. Langenbruch9, T. Latham50, C. Lazzeroni47,
R. Le Gac6, A. Leflat35, J. Lefrançois7, R. Lefèvre5, F. Lemaitre42, O.
Leroy6, T. Lesiak29, B. Leverington12, P.-R. Li63, T. Li3, Z. Li61, X.
Liang61, T. Likhomanenko69, R. Lindner42, F. Lionetto44, V. Lisovskyi7, X.
Liu3, D. Loh50, A. Loi22, I. Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M.
Lucio Martinez41, A. Lupato23, E. Luppi16,g, O. Lupton42, A. Lusiani24, X.
Lyu63, F. Machefert7, F. Maciuc32, V. Macko43, P. Mackowiak10, S. Maddrell-
Mander48, O. Maev33,42, K. Maguire56, D. Maisuzenko33, M.W. Majewski30, S.
Malde57, B. Malecki29, A. Malinin69, T. Maltsev38,w, G. Manca22,f, G.
Mancinelli6, D. Marangotto21,q, J. Maratas5,v, J.F. Marchand4, U. Marconi15,
C. Marin Benito40, M. Marinangeli43, P. Marino43, J. Marks12, G.
Martellotti26, M. Martin6, M. Martinelli43, D. Martinez Santos41, F. Martinez
Vidal72, A. Massafferri1, R. Matev42, A. Mathad50, Z. Mathe42, C. Matteuzzi20,
A. Mauri44, E. Maurice7,b, B. Maurin43, A. Mazurov47, M. McCann55,42, A.
McNab56, R. McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N.
Meinert67, D. Melnychuk31, M. Merk27, A. Merli21,q, E. Michielin23, D.A.
Milanes66, E. Millard50, M.-N. Minard4, L. Minzoni16,g, D.S. Mitzel12, A.
Mogini8, J. Molina Rodriguez1,z, T. Mombächer10, I.A. Monroy66, S. Monteil5,
M. Morandin23, G. Morello18, M.J. Morello24,t, O. Morgunova69, J. Moron30,
A.B. Morris6, R. Mountain61, F. Muheim52, M. Mulder27, D. Müller42, J.
Müller10, K. Müller44, V. Müller10, P. Naik48, T. Nakada43, R. Nandakumar51,
A. Nandi57, T. Nanut43, I. Nasteva2, M. Needham52, N. Neri21, S. Neubert12, N.
Neufeld42, M. Neuner12, T.D. Nguyen43, C. Nguyen-Mau43,n, S. Nieswand9, R.
Niet10, N. Nikitin35, A. Nogay69, D.P. O’Hanlon15, A. Oblakowska-Mucha30, V.
Obraztsov39, S. Ogilvy18, R. Oldeman22,f, C.J.G. Onderwater68, A. Ossowska29,
J.M. Otalora Goicochea2, P. Owen44, A. Oyanguren72, P.R. Pais43, A. Palano14,
M. Palutan18,42, G. Panshin71, A. Papanestis51, M. Pappagallo52, L.L.
Pappalardo16,g, W. Parker60, C. Parkes56, G. Passaleva17,42, A. Pastore14, M.
Patel55, C. Patrignani15,e, A. Pearce42, A. Pellegrino27, G. Penso26, M. Pepe
Altarelli42, S. Perazzini42, D. Pereima34, P. Perret5, L. Pescatore43, K.
Petridis48, A. Petrolini19,h, A. Petrov69, M. Petruzzo21,q, B. Pietrzyk4, G.
Pietrzyk43, M. Pikies29, D. Pinci26, J. Pinzino42, F. Pisani42, A.
Pistone19,h, A. Piucci12, V. Placinta32, S. Playfer52, J. Plews47, M. Plo
Casasus41, F. Polci8, M. Poli Lener18, A. Poluektov50, N. Polukhina70,c, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce42, A. Popov39, D.
Popov47,11, S. Poslavskii39, C. Potterat2, E. Price48, J. Prisciandaro41, C.
Prouve48, V. Pugatch46, A. Puig Navarro44, H. Pullen57, G. Punzi24,p, W.
Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal30, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas41, M.S. Rangel2, F. Ratnikov37,x, G.
Raven28, M. Ravonel Salzgeber42, M. Reboud4, F. Redi43, S. Reichert10, A.C.
dos Reis1, F. Reiss8, C. Remon Alepuz72, Z. Ren3, V. Renaudin7, S.
Ricciardi51, S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B.
Rodrigues43, E. Rodrigues59, J.A. Rodriguez Lopez66, A. Rogozhnikov37, S.
Roiser42, A. Rollings57, V. Romanovskiy39, A. Romero Vidal41, M. Rotondo18,
M.S. Rudolph61, T. Ruf42, J. Ruiz Vidal72, J.J. Saborido Silva41, N.
Sagidova33, B. Saitta22,f, V. Salustino Guimaraes62, C. Sanchez Gras27, C.
Sanchez Mayordomo72, B. Sanmartin Sedes41, R. Santacesaria26, C. Santamarina
Rios41, M. Santimaria18, E. Santovetti25,j, G. Sarpis56, A. Sarti18,k, C.
Satriano26,s, A. Satta25, M. Saur63, D. Savrina34,35, S. Schael9, M.
Schellenberg10, M. Schiller53, H. Schindler42, M. Schmelling11, T.
Schmelzer10, B. Schmidt42, O. Schneider43, A. Schopper42, H.F. Schreiner59, M.
Schubiger43, M.H. Schune7, R. Schwemmer42, B. Sciascia18, A. Sciubba26,k, A.
Semennikov34, E.S. Sepulveda8, A. Sergi47,42, N. Serra44, J. Serrano6, L.
Sestini23, P. Seyfert42, M. Shapkin39, Y. Shcheglov33,†, T. Shears54, L.
Shekhtman38,w, V. Shevchenko69, E. Shmanin70, B.G. Siddi16, R. Silva
Coutinho44, L. Silva de Oliveira2, G. Simi23,o, S. Simone14,d, N. Skidmore12,
T. Skwarnicki61, E. Smith9, I.T. Smith52, M. Smith55, M. Soares15, l. Soares
Lavra1, M.D. Sokoloff59, F.J.P. Soler53, B. Souza De Paula2, B. Spaan10, P.
Spradlin53, F. Stagni42, M. Stahl12, S. Stahl42, P. Stefko43, S. Stefkova55,
O. Steinkamp44, S. Stemmle12, O. Stenyakin39, M. Stepanova33, H. Stevens10, S.
Stone61, B. Storaci44, S. Stracka24, M.E. Stramaglia43, M. Straticiuc32, U.
Straumann44, S. Strokov71, J. Sun3, L. Sun64, K. Swientek30, V. Syropoulos28,
T. Szumlak30, M. Szymanski63, S. T’Jampens4, Z. Tang3, A. Tayduganov6, T.
Tekampe10, G. Tellarini16, F. Teubert42, E. Thomas42, J. van Tilburg27, M.J.
Tilley55, V. Tisserand5, M. Tobin43, S. Tolk42, L. Tomassetti16,g, D.
Tonelli24, D.Y. Tou8, R. Tourinho Jadallah Aoude1, E. Tournefier4, M.
Traill53, M.T. Tran43, A. Trisovic49, A. Tsaregorodtsev6, G. Tuci24,p, A.
Tully49, N. Tuning27,42, A. Ukleja31, A. Usachov7, A. Ustyuzhanin37, U.
Uwer12, C. Vacca22,f, A. Vagner71, V. Vagnoni15, A. Valassi42, S. Valat42, G.
Valenti15, R. Vazquez Gomez42, P. Vazquez Regueiro41, S. Vecchi16, M. van
Veghel27, J.J. Velthuis48, M. Veltri17,r, G. Veneziano57, A. Venkateswaran61,
T.A. Verlage9, M. Vernet5, M. Vesterinen57, J.V. Viana Barbosa42, D. Vieira63,
M. Vieites Diaz41, H. Viemann67, X. Vilasis-Cardona40,m, A. Vitkovskiy27, M.
Vitti49, V. Volkov35, A. Vollhardt44, B. Voneki42, A. Vorobyev33, V.
Vorobyev38,w, C. Voß9, J.A. de Vries27, C. Vázquez Sierra27, R. Waldi67, J.
Walsh24, J. Wang61, M. Wang3, Y. Wang65, Z. Wang44, D.R. Ward49, H.M. Wark54,
N.K. Watson47, D. Websdale55, A. Weiden44, C. Weisser58, M. Whitehead9, J.
Wicht50, G. Wilkinson57, M. Wilkinson61, M.R.J. Williams56, M. Williams58, T.
Williams47, F.F. Wilson51,42, J. Wimberley60, M. Winn7, J. Wishahi10, W.
Wislicki31, M. Witek29, G. Wormser7, S.A. Wotton49, K. Wyllie42, D. Xiao65, Y.
Xie65, A. Xu3, M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z. Yang3, Z. Yang60, Y.
Yao61, H. Yin65, J. Yu65,ab, X. Yuan61, O. Yushchenko39, K.A. Zarebski47, M.
Zavertyaev11,c, D. Zhang65, L. Zhang3, W.C. Zhang3,aa, Y. Zhang7, A.
Zhelezov12, Y. Zheng63, X. Zhu3, V. Zhukov9,35, J.B. Zonneveld52, 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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, 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
14INFN Sezione di Bari, Bari, Italy
15INFN Sezione di Bologna, Bologna, Italy
16INFN Sezione di Ferrara, Ferrara, Italy
17INFN Sezione di Firenze, Firenze, Italy
18INFN Laboratori Nazionali di Frascati, Frascati, Italy
19INFN Sezione di Genova, Genova, Italy
20INFN Sezione di Milano-Bicocca, Milano, Italy
21INFN Sezione di Milano, Milano, Italy
22INFN Sezione di Cagliari, Monserrato, Italy
23INFN Sezione di Padova, Padova, Italy
24INFN Sezione di Pisa, Pisa, Italy
25INFN Sezione di Roma Tor Vergata, Roma, Italy
26INFN Sezione di Roma La Sapienza, Roma, Italy
27Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
28Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
29Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
30AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
31National Center for Nuclear Research (NCBJ), Warsaw, Poland
32Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
33Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
34Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
35Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
36Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
37Yandex School of Data Analysis, Moscow, Russia
38Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
39Institute for High Energy Physics (IHEP), Protvino, Russia
40ICCUB, Universitat de Barcelona, Barcelona, Spain
41Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
42European Organization for Nuclear Research (CERN), Geneva, Switzerland
43Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
44Physik-Institut, Universität Zürich, Zürich, Switzerland
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
68Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 27
69National Research Centre Kurchatov Institute, Moscow, Russia, associated to
34
70National University of Science and Technology ”MISIS”, Moscow, Russia,
associated to 34
71National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
34
72Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 40
73University of Michigan, Ann Arbor, United States, associated to 61
74Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

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, Vietnam
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
vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
ySezione INFN di Trieste, Trieste, Italy
zEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
aaSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
abPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased