EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-194 LHCb-PAPER-2014-046 October 1, 2014

Search for $C\\!P$ violation using $T$-odd correlations in
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays

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

A search for $C\\!P$ violation using $T$-odd correlations is performed using
the four-body ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$
decay, selected from semileptonic $B$ decays. The data sample corresponds to
integrated luminosities of 1.0$\mbox{\,fb}^{-1}$ and 2.0$\mbox{\,fb}^{-1}$
recorded at the centre-of-mass energies of 7$\mathrm{\,Te\kern-1.00006ptV}$
and 8$\mathrm{\,Te\kern-1.00006ptV}$, respectively. The $C\\!P$-violating
asymmetry $a_{{C\\!P}}^{\text{$T$-odd}}$ is measured to be $(0.18\pm
0.29\mathrm{\,(stat)}\pm 0.04\mathrm{\,(syst)})\%$. Searches for $C\\!P$
violation in different regions of phase space of the four-body decay, and as a
function of the ${D}^{0}$ decay time, are also presented. No significant
deviation from the $C\\!P$ conservation hypothesis is found.

Published in JHEP

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

##  1 Introduction

Violation of the $C\\!P$ symmetry in charm decays is expected to be very small
in the Standard Model (SM) [1, 2], however, asymmetries at a few times 10-3
within the SM cannot be excluded according to recent calculations [3, 4, 5]. A
significant excess of $C\\!P$ violation ($C\\!PV$) with respect to the
theoretical predictions would be a signature of physics beyond the SM. The
study of $C\\!PV$ in singly Cabibbo-suppressed charm decays is uniquely
sensitive to physics beyond the SM, in particular through new contributions in
strong penguin and chromomagnetic dipole operators [2]. The analysis of singly
Cabibbo-suppressed
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ 111 Throughout
this paper the use of charge conjugate reactions is implied, unless otherwise
indicated. decays allows localised $C\\!PV$ in different regions of phase
space to be probed. This approach enhances the sensitivity due to several
interfering amplitudes with different relative strong phases contributing to
the decay.

The analysis in Ref. [6] quotes a $p$-value of 9.1% for the compatibility with
the $C\\!P$ conservation hypothesis, using $D^{*}$-tagged promptly-produced
${D}^{0}$ mesons. In the present analysis, a sample of
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays,
selected from semileptonic $B$ decays, is used to measure a $C\\!P$-violating
parameter based on $T$-odd correlations characterised by different sensitivity
to $C\\!PV$ [7, 8]. Using triple products of final state particle momenta in
the ${D}^{0}$ centre-of-mass frame,
$C_{T}\equiv\vec{p}_{{{K}^{+}}}\cdot(\vec{p}_{{{\pi}^{+}}}\times\vec{p}_{{{\pi}^{-}}})$
for ${D}^{0}$ and
$\overline{C}_{T}\equiv\vec{p}_{{{K}^{-}}}\cdot(\vec{p}_{{{\pi}^{-}}}\times\vec{p}_{{{\pi}^{+}}})$
for ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decays, two $T$-odd
observables,

$A_{T}\equiv\frac{\Gamma_{{{D}^{0}}}(C_{T}>0)-\Gamma_{{{D}^{0}}}(C_{T}<0)}{\Gamma_{{{D}^{0}}}(C_{T}>0)+\Gamma_{{{D}^{0}}}(C_{T}<0)},\quad\quad\overline{A}_{T}\equiv\frac{\Gamma_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(-\overline{C}_{T}>0)-\Gamma_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(-\overline{C}_{T}<0)}{\Gamma_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(-\overline{C}_{T}>0)+\Gamma_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(-\overline{C}_{T}<0)},$ (1)

can be studied [9], where $\Gamma_{{{D}^{0}}}$ ($\Gamma_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}$) is the partial decay width
of ${D}^{0}$ (${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$) decays
to ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ in the indicated $C_{T}$
($\overline{C}_{T}$) range. However, because final state interaction (FSI)
effects could introduce fake asymmetries [9, 10], these are not theoretically
clean $C\\!P$-violating observables. A well defined $C\\!P$-violating
observable is

$a_{{C\\!P}}^{\text{$T$-odd}}\equiv\frac{1}{2}(A_{T}-\overline{A}_{T}),$ (2)

as FSI effects cancel out in the difference. In contrast to the asymmetry
between the phase-space integrated rates in a ${{D}^{0}}\rightarrow
V_{1}V_{2}$ decay (where $V_{i}$ indicates a vector meson),
$a_{{C\\!P}}^{\text{$T$-odd}}$ is sensitive to $C\\!P$ violation in
interference between even- and odd- partial waves of the $V_{1}V_{2}$
system[7].

Previous measurements of $a_{{C\\!P}}^{\text{$T$-odd}}$ are compatible with no
$C\\!PV$: FOCUS measured $a_{{C\\!P}}^{\text{$T$-odd}}=(1.0\pm 5.7\pm 3.7)\%$
[11], and BaBar measured $a_{{C\\!P}}^{\text{$T$-odd}}=(0.10\pm 0.51\pm
0.44)\%$ [12]. The physics observables, $A_{T}$, $\overline{A}_{T}$, and
$a_{{C\\!P}}^{\text{$T$-odd}}$ are by construction insensitive to
${D}^{0}$/${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ production
asymmetries, detector- and reconstruction-induced charge asymmetries. The
measurement described in this paper determines the $C\\!P$-violating
observable $a_{{C\\!P}}^{\text{$T$-odd}}$ with an improved precision. For the
first time, $a_{{C\\!P}}^{\text{$T$-odd}}$ is measured in different regions of
phase space and in bins of ${D}^{0}$ decay time, allowing to probe for $C\\!P$
violation both in the decay amplitude and in its interference with the mixing
amplitude.

##  2 Detector

The LHCb detector [13] 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 $p$ $p$
interaction region [14], a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\rm\,Tm}$, and three
stations of silicon-strip detectors and straw drift tubes [15] placed
downstream of the magnet. The tracking system provides a measurement of
momentum, $p$, with a relative uncertainty that varies from 0.4% at low
momentum to 0.6% at $100{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter, is measured
with a resolution of
($15+(29{\mathrm{\,Ge\kern-1.00006ptV\\!/}c})/\mbox{$p_{\rm T}$}$)${\,\upmu\rm
m}$, where $p_{\rm T}$ is the component of $p$ transverse to the beam.
Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov (RICH) detectors [16]. Photon, electron and hadron
candidates 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 [17]. The trigger [18] 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.

Events are required to pass both hardware and software trigger selections. The
software trigger identifies
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ (signal) and
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ (control
sample) events from ${B}\rightarrow{{D}^{0}}{\mu^{-}}X$ decays, where $X$
indicates any system composed of charged and neutral particles, by requiring a
four-track secondary vertex with a scalar sum of $p_{\rm T}$ of the tracks
greater than $1.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The ${D}^{0}$ daughter
tracks are required to have $\mbox{$p_{\rm
T}$}>0.3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and momentum
$p>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The muon track is selected with
$\mbox{$p_{\rm T}$}>1.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$p>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Tracks have to be compatible with
detached decay vertices of $B$ and ${{D}^{0}}$ decays. Therefore, a
requirement is imposed for all the tracks in the signal candidate on the
$\chi^{2}_{\text{IP}}$, i.e. the difference in $\chi^{2}$ of a given primary
vertex reconstructed with and without the considered particle, to be greater
than 9. The invariant mass of the ${{D}^{0}}\mu$ system is required to be less
than $6.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

In the simulation, $p$ $p$ collisions are generated using Pythia [19, 20] with
a specific LHCb configuration [21]. Decays of hadronic particles are described
by EvtGen [22]. The interaction of the generated particles with the detector
and its response are implemented using the Geant4 toolkit [23, 24] as
described in Ref. [25].

##  3 Selection

The analysis is based on data recorded by the LHCb experiment, at center-of-
mass energies of $7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$, corresponding to integrated luminosities of
$1.0\mbox{\,fb}^{-1}$ and $2.0\mbox{\,fb}^{-1}$, respectively.

The ${D}^{0}$ candidates are formed from combinations of kaon and pion
candidate tracks and then combined with a muon candidate track to reconstruct
the semileptonic $B$ decay. The flavour of the ${D}^{0}$ is identified by the
charge of the muon, i.e. a negative charge identifies a ${D}^{0}$ meson and a
positive charge identifies a ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ meson. The information from the
RICH system is used to distinguish between kaons and pions, while the
information from the muon system is used to identify muon candidates. The
${D}^{0}$ meson decay vertex is required to be downstream of the $B$ decay
vertex. The invariant mass of the ${{D}^{0}}\mu$ system is required to be in
the range $[2.6,5.2]{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.

Two main sources of peaking background in
$m({{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}})$, the reconstructed invariant
mass of ${D}^{0}$ candidates, are present and consist of
${{D}^{0}}\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$
decays, and ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$
decays from ${D}^{0}$ mesons that originate at the interaction point, referred
to as “prompt” charm decays in the following. The small component of
${{D}^{0}}\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$
events is vetoed by requiring the invariant mass of the ${\pi}^{+}$
${\pi}^{-}$ system to be more than $3\sigma$ away from the known
${K}^{0}_{\rm\scriptscriptstyle S}$ mass [26], where
$\sigma=4.5{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is the resolution
determined from the fit to data. The contribution of prompt charm decays is
estimated by fitting the distribution of the logarithm of the
$\chi^{2}_{\textrm{IP}}$ of the ${D}^{0}$ meson. The prompt component and the
signal component from semileptonic $B$ decays accumulate at 0 and at 5,
respectively. The fraction of prompt ${D}^{0}$ decays in our sample is
measured to be $f_{\textrm{prompt}}=(1.20\pm 0.08)\%$ and the effect of its
presence is accounted for as a systematic uncertainty. The distributions of
${D}^{0}$ decays where pions and kaons have not been correctly identified have
been studied and do not peak in $m({{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}})$.
When multiple candidates are reconstructed, one candidate per event is
retained, by random choice. This happens in 0.7% of the events. The signal
yield for ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ from
${B}\rightarrow{{D}^{0}}{\mu^{-}}X$ decays, obtained from an extended maximum
likelihood fit to the $m({{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}})$
distribution, is $(171.3\pm 0.6)\times 10^{3}$ events with a sample purity of
about 75%.

By using identical kinematic selection criteria as for the signal, Cabibbo-
favoured ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$
decays are also reconstructed with a signal yield of about of $6.211\times
10^{6}$ and a purity of about 95%. These decays are used for control checks
and for assessing systematic uncertainties.

##  4 Asymmetry measurements

The selected data sample is split into four subsamples according to the charge
of the muon candidate, which determines the flavour of the ${D}^{0}$, and the
sign of $C_{T}$ ($\overline{C}_{T}$). The reconstruction efficiencies are
equal, within their uncertainties, for $C_{T}>0$ ($-\overline{C}_{T}>0$) and
for $C_{T}<0$ ($-\overline{C}_{T}<0$) according to studies based on simulated
events and on the
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ control
sample. A simultaneous maximum likelihood fit to the
$m({{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}})$ distribution of the four
subsamples is used to determine the number of signal and background events,
and the asymmetries $A_{T}$ and $\overline{A}_{T}$. The fit model consists of
two Gaussian functions with common mean for the signal and an exponential
function for the background. The two asymmetries $A_{T}$ and
$\overline{A}_{T}$ are included in the fit model as

$\displaystyle N_{{{D}^{0}},C_{T}>0}$
$\displaystyle=\frac{1}{2}N_{{{D}^{0}}}(1+A_{T}),$ (3) $\displaystyle
N_{{{D}^{0}},C_{T}<0}$ $\displaystyle=\frac{1}{2}N_{{{D}^{0}}}(1-A_{T}),$
$\displaystyle N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}},-\overline{C}_{T}>0}$
$\displaystyle=\frac{1}{2}N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(1+\overline{A}_{T}),$
$\displaystyle N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}},-\overline{C}_{T}<0}$
$\displaystyle=\frac{1}{2}N_{{{\kern
1.39998pt\overline{\kern-1.39998ptD}{}}{}^{0}}}(1-\overline{A}_{T}).$

The $C\\!P$-violating asymmetry $a_{{C\\!P}}^{\text{$T$-odd}}$ is then
calculated from $A_{T}$ and $\overline{A}_{T}$. Negligible correlation is
found between these two asymmetries. The results of the fit are shown in Fig.
1.

Figure 1: Distributions of the ${{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$
invariant mass in the four samples defined by ${D}^{0}$ (${\kern
1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$) flavour and the sign of
$C_{T}$ ($\overline{C}_{T}$). The results of the fit are overlaid as a solid
line, and a dashed line is used for representing the background. The
normalised residuals (pulls) of the difference between the fit results and the
data points, divided by their uncertainties, are shown on top of each
distribution.

The number of signal decays for each subsample are listed in Table 1.

Table 1: Number of signal decays obtained from the fit to data for each of the four samples defined by the ${D}^{0}$/${\kern 1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$ flavour and the sign of $C_{T}$ or $\overline{C}_{T}$. Sample | Signal Decays
---|---
${D}^{0}$, $\phantom{-}C_{T}>0$ | $39\,628\pm 256$
${D}^{0}$, $\phantom{-}C_{T}<0$ | $45\,762\pm 272$
${\kern 1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$, $-\overline{C}_{T}>0$ | $39\,709\pm 256$
${\kern 1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$, $-\overline{C}_{T}<0$ | $46\,162\pm 274$

Three different approaches have been followed to search for $C\\!PV$: a
measurement integrated over the phase space, measurements in different regions
of phase space, and measurements as a function of the ${D}^{0}$ decay time.
The results of the first approach are obtained by fitting the full data sample
and are $A_{T}=(-7.18\pm 0.41)\%$, and $\overline{A}_{T}=(-7.55\pm 0.41)\%$,
where the uncertainties are statistical only. The $C\\!P$-violating asymmetry
calculated from the two partial asymmetries is
$a_{{C\\!P}}^{\text{$T$-odd}}=(0.18\pm 0.29)\%$.

The relatively large asymmetries observed in $A_{T}$ and $\overline{A}_{T}$
are due to FSI effects [9, 10], which are known to be relevant in charm mesons
decays. These effects are difficult to predict, since they involve non-
perturbative strong interactions [27]. However, experimental measurements
provide solid anchor points for future calculations.

The measurement in different regions of the phase space is performed by
dividing the sample using a binning scheme based on the Cabibbo-Maksimowicz
[28] variables $m_{{{K}^{+}}{{K}^{-}}}$, $m_{{{\pi}^{+}}{{\pi}^{-}}}$,
$\cos(\theta_{{{K}^{+}}})$, $\cos(\theta_{{{\pi}^{+}}})$, $\Phi$, defined as
the ${{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ invariant masses, the
cosine of the angle of the ${K}^{+}$ (${\pi}^{+}$) with respect to the
opposite direction to the ${D}^{0}$ momentum in the ${{K}^{+}}{{K}^{-}}$
(${{\pi}^{+}}{{\pi}^{-}}$) rest frame, and the angle between the planes
described by the two kaons and pions in the ${D}^{0}$ rest frame,
respectively.

The background-subtracted distributions for ${D}^{0}$ (${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$) events with $C_{T}>0$ and
$C_{T}<0$ ($-\overline{C}_{T}>0$ and $-\overline{C}_{T}<0$) in
$m_{{{\pi}^{+}}{{\pi}^{-}}}$ and $m_{{{K}^{+}}{{K}^{-}}}$ are shown in Fig. 2.
The background subtraction is performed using
$m({{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}})$ sidebands. Clear indications of
$\rho^{0}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ and
$\phi\rightarrow{{K}^{+}}{{K}^{-}}$ resonances are seen in the data. The
distributions of $\cos(\theta_{{{K}^{+}}})$, $\cos(\theta_{{{\pi}^{+}}})$, and
$\Phi$ variables are shown in Fig. 3, where FSI-induced differences are
clearly evident [29]. Effects of $C\\!PV$ would lead to different
distributions for ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ events.

Figure 2: Sideband-subtracted distributions of ${D}^{0}$ (${\kern
1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$) candidates in variables of (a,
b) $m_{{{\pi}^{+}}{{\pi}^{-}}}$ and (c, d) $m_{{{K}^{+}}{{K}^{-}}}$ for
different values of $C_{T}$ ($\overline{C}_{T}$). The veto for
${{D}^{0}}\rightarrow{{K}^{0}_{\rm\scriptscriptstyle S}}{{K}^{+}}{{K}^{-}}$
decays is visible in the $m_{{{\pi}^{+}}{{\pi}^{-}}}$ distribution.

Figure 3: Sideband-subtracted distributions of ${D}^{0}$ (${\kern
1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}$) candidates in variables of (a,
b) $\cos(\theta_{{{K}^{+}}})$, (c, d) $\cos(\theta_{{{\pi}^{+}}})$, and (e, f)
$\Phi$ for different values of $C_{T}$ ($\overline{C}_{T}$). The asymmetric
distributions with respect to 0 for $\cos(\theta_{{{K}^{+}}})$ and
$\cos(\theta_{{{\pi}^{+}}})$ variables, and with respect to $\pi/2$ for the
$\Phi$ variable, are due to the dynamics of the four-body decay.

The phase space is divided in 32 regions such that the number of signal events
is similar in each region; the definition of the 32 regions is reported in
Table 3 in Appendix A.

The same fit model used for the integrated measurement is separately fitted to
data in each bin. The signal shapes are consistent among different bins, while
significant variations are found in the distribution of the combinatorial
background. The distributions of the measured asymmetries in the 32-region
binning scheme are shown in Fig. 4 and the results are reported in Table 4 in
Appendix A.

Figure 4: Distributions of the asymmetry parameters (a) $A_{T}$, (b)
$\overline{A}_{T}$ and (c) $a_{{C\\!P}}^{\text{$T$-odd}}$ in 32 regions of the
phase space.

The compatibility with the $C\\!P$ conservation hypothesis is tested by means
of a $\chi^{2}$ test, where the $\chi^{2}$ is defined as $R^{T}V^{-1}R$, where
$R$ is the array of $a_{{C\\!P}}^{\text{$T$-odd}}$ measurements, and $V^{-1}$
is the inverse of the covariance matrix $V$, defined as the sum of the
statistical and systematic covariance matrices. An average systematic
uncertainty, whose evaluation is discussed in Sec. 5, is assumed for the
different bins. The statistical uncertainties are considered uncorrelated
among the bins, while systematic uncertainties are assumed to be fully
correlated. The contribution of systematic uncertainties is small compared to
the statistical ones, as shown in Table 2. The results are consistent with the
$C\\!P$ conservation hypothesis with a $p$-value of 74%, based on
$\chi^{2}/\mathrm{ndf}=26.4/32$, where ndf is the number of degrees of
freedom. Four alternative binning schemes, one with 8 regions and three with
16 regions, are also tested. These are described in Appendix A. Results are
compatible with the $C\\!P$ conservation hypothesis with a $p$-value of 24%
for the case of 8 regions and 28%, 62%, 82% for the three different phase
space divisions in 16 regions. The $A_{T}$ and $\overline{A}_{T}$ asymmetries
are significantly different among the different regions. This effect can be
explained by the rich resonant structure of the hadronic four-body decay [30]
that produces different FSI effects over the phase space.

The $a_{{C\\!P}}^{\text{$T$-odd}}$ distribution in ${D}^{0}$ decay time is
shown in Fig. 5 and the results for the different decay time bins are reported
in Table 5 in Appendix B.

Figure 5: Distributions of the asymmetry parameters (a) $A_{T}$, (b)
$\overline{A}_{T}$ and (c) $a_{{C\\!P}}^{\text{$T$-odd}}$ as a function of the
${D}^{0}$ decay time. For $a_{{C\\!P}}^{\text{$T$-odd}}$, the value of the
$\chi^{2}/\mathrm{ndf}$ for the $C\\!P$ conservation hypothesis, represented
by a dashed line, is also quoted. The scale is broken for the first and last
bin.

The compatibility with the $C\\!P$ conservation hypothesis is verified by
means of a $\chi^{2}$ test considering statistical and systematic
uncertainties as in the previous case; a value of
$\chi^{2}/\mathrm{ndf}=1.3/4$ is obtained, corresponding to a $p$-value of
86%. Consistent results are obtained when using different divisions of the
decay time in 3 and 5 intervals compatible with the $C\\!P$ conservation
hypothesis with $p$-values of 92% and 83%, respectively. This result is
consistent with no time-dependent $C\\!PV$. The $A_{T}$ and $\overline{A}_{T}$
asymmetry parameters do not show any significant dependence as a function of
the decay time, and the results are compatible with constant functions with
$p$-values of 80% and 38%, respectively.

##  5 Systematic uncertainties

The sources of systematic uncertainty and their relative contributions to the
total uncertainty are listed in Table 2.

Table 2: Considered sources of systematic uncertainty and their relative contributions to the total uncertainty. Contribution | $\Delta A_{T}(\%)$ | $\Delta\overline{A}_{T}(\%)$ | $\Delta a_{{C\\!P}}^{\text{$T$-odd}}(\%)$
---|---|---|---
Prompt background | $\pm 0.09$ | $\pm 0.08$ | $\pm 0.00$
Detector bias | $\pm 0.04$ | $\pm 0.04$ | $\pm 0.04$
$C_{T}$ resolution | $\pm 0.02$ | $\pm 0.03$ | $\pm 0.01$
Fit model | $\pm 0.01$ | $\pm 0.01$ | $\pm 0.01$
Flavour misidentification | $\pm 0.08$ | $\pm 0.07$ | $\pm 0.00$
Total | $\pm 0.13$ | $\pm 0.12$ | $\pm 0.04$

The contamination from prompt ${D}^{0}$ decays affects the asymmetry $A$
according to $A\rightarrow A(1-f)+fA^{d}$, where $f$ is the fraction of the
contamination in the selected sample and $A^{d}$ is its own asymmetry. The
uncertainties are evaluated by using as input the fraction $f_{\text{prompt}}$
and the asymmetries of the prompt charm sample. These events correspond to
random combinations of muons with ${D}^{0}$ originating at the primary vertex
and show no significant evidence of correlation between the flavour of the
${D}^{0}$ and the charge of the muon. Assuming that the flavour mistag rate
for the prompt ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ samples is 0.5, these are
related to the signal asymmetries as:
$A_{T}^{d}=a_{{C\\!P}}^{\text{$T$-odd}}$,
$\overline{A}_{T}^{d}=-a_{{C\\!P}}^{\text{$T$-odd}}$, and
${a_{{C\\!P}}^{\text{$T$-odd}}}^{d}=a_{{C\\!P}}^{\text{$T$-odd}}$.

The detector bias is tested by measuring
$a_{{C\\!P}}^{\text{$T$-odd}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}})$
on the ${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
control sample. In this case, a kinematic selection is required between the
pair of pions with identical charge to define the $C_{T}$ and
$\overline{C}_{T}$ triple products. The pion with higher momentum is used to
calculate the triple product. Since this is a Cabibbo-favoured decay, the
$C\\!P$-violating effects are assumed to be negligible, and any significant
deviation from zero is considered as a bias introduced by the experimental
technique and the detector reconstruction. The asymmetry obtained on the
control sample is compatible with no bias,
$a_{{C\\!P}}^{\text{$T$-odd}}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}})=(0.05\pm
0.04)\%$. A systematic uncertainty equal to the statistical uncertainty of
this measurement is assigned. The test was repeated for different regions of
phase space with consistent results.

The systematic uncertainty from detector resolution on $C_{T}$ is estimated
from a simulated sample of
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays where
neither FSI nor $C\\!P$-violating effects are present. The difference between
the reconstructed and generated asymmetry is considered as a systematic
uncertainty due to this effect.

The fit models for signal and background are modified, ensuring good fit
quality, to account for model-dependent uncertainties. The signal shape is
described with a Gaussian function plus a second Gaussian function with a low-
mass power-law tail. The background is described with a third-order polynomial
function. Alternative models are fitted to the data and for each model 1000
simulated samples are generated according to fit results. The nominal model is
then fitted to the simulated samples and the asymmetry parameters are
extracted. Since the bias is not significantly different from zero, its
statistical uncertainty is taken as the systematic uncertainty due to this
source.

Wrongly identified muon candidates could affect the $C\\!P$-violating
asymmetry as

$\displaystyle a_{{C\\!P}}^{\text{$T$-odd}}$ $\displaystyle\rightarrow
a_{{C\\!P}}^{\text{$T$-odd}}-\Delta\omega/2(A_{T}+\overline{A}_{T}),$ (4)

where $\Delta\omega\equiv\omega^{+}-\omega^{-}$ is the difference between the
probability of assigning a wrong ${D}^{0}$ ($\omega^{+}$) and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ ($\omega^{-}$) flavour. Similar
considerations enable the estimation of the uncertainty on $A_{T}$
($\overline{A}_{T}$) as $(A_{T}+\overline{A}_{T})\omega^{+}$
($(A_{T}+\overline{A}_{T})\omega^{-}$). The mistag probabilities are measured
by reconstructing the double-tagged decay channel
${B}\rightarrow{{D}^{*+}}\mu^{-}X$, with
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ and
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$, and
calculating the fraction of events for which the charge of the muon is
identical to the charge of the soft pion from ${D}^{*+}$ decay. Mistag
probabilities of $\omega^{+}=(5.2\pm 1.0)\times 10^{-3}$ and
$\omega^{-}=(4.7\pm 1.0)\times 10^{-3}$ are measured for ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ flavour, respectively.

Since the various contributions to the systematic uncertainty are independent,
the total uncertainty is obtained by summing them in quadrature, and it is
very small. In particular, the $a_{{C\\!P}}^{\text{$T$-odd}}$ observable is
insensitive to the production asymmetry of ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ and to reconstruction-induced
charge asymmetries. Further cross-checks are made for establishing the
stability of the results with respect to the different periods of data taking,
different magnet polarities, the choice made in the selection of multiple
candidates, and the effect of selection through particle identification
criteria. All these tests reported effects compatible to statistical
fluctuations, and therefore are not included in the systematic uncertainty.

The total systematic uncertainties reported in Table 2 are used for the
measurement of the asymmetries in all regions of phase space and in all bins
of ${D}^{0}$ decay time.

##  6 Conclusions

In conclusion, a search for $C\\!PV$ in
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays produced
in ${B}\rightarrow{{D}^{0}}\mu^{-}X$ transitions has been performed. The data
sample consists of about $171\,300$ signal decays. Three different approaches
have been followed to exploit the full potential of the data: a measurement
integrated over the phase space, measurements in different regions of the
phase space, and measurements as a function of the ${D}^{0}$ decay time.

The results from the phase space integrated measurement,

$\displaystyle A_{T}$ $\displaystyle=(-7.18\pm 0.41(\text{stat})\pm
0.13(\text{syst}))\%,$ $\displaystyle\overline{A}_{T}$
$\displaystyle=(-7.55\pm 0.41(\text{stat})\pm 0.12(\text{syst}))\%,$
$\displaystyle a_{{C\\!P}}^{\text{$T$-odd}}$
$\displaystyle=(\phantom{-}0.18\pm 0.29(\text{stat})\pm 0.04(\text{syst}))\%,$

are consistent with those measured in Ref. [12], with significantly improved
statistical and systematic uncertainties. The evaluation of the systematic
uncertainties is based mostly on high statistics control samples.

An analysis of the asymmetries in different regions of the phase space is made
for the first time and the results are consistent with $C\\!P$ conservation.
Relatively large variations of $A_{T}$ and $\overline{A}_{T}$ over the phase
space are measured, which are due to FSI effects produced in the rich resonant
structure of the decay [29, 30]. For the first time the
$a_{{C\\!P}}^{\text{$T$-odd}}$ asymmetry is measured as a function of the
${D}^{0}$ decay time and does not show any significant structure at the
observed sensitivity. These results further constrain extensions of the SM
[2].

Appendices

##  Appendix A Measured asymmetries in regions of phase space

The definitions of the 32 regions of phase space of the four-body
${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decay are
reported in Table 3. The measurements in each region of phase space for the
$a_{{C\\!P}}^{\text{$T$-odd}}$, $A_{T}$, and $\overline{A}_{T}$ are reported
in Table 4.

Table 3: Definition of the 32 regions of the five-dimensional phase space of the four-body ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decay. Region | $\Phi$ |  $m_{{{\pi}^{+}}{{\pi}^{-}}}$ (${\mathrm{\,Ge\kern-0.90005ptV\\!/}c^{2}}$) |  $m_{{{K}^{+}}{{K}^{-}}}$ (${\mathrm{\,Ge\kern-0.90005ptV\\!/}c^{2}}$) | $\cos(\theta_{{{\pi}^{+}}})$ | $\cos(\theta_{{{K}^{+}}})$
---|---|---|---|---|---
1 | (0.00, 1.99) | (0.20, 0.65) | (0.60, 1.08) |  ($-$1.00, $-$0.22) |  ($-$1.00, $-$0.28)
2 | (0.00, 1.99) | (0.20, 0.65) | (1.08, 1.70) |  ($-$1.00, $-$0.24) |  ($-$1.00, $-$0.14)
3 | (0.00, 1.99) | (0.65, 1.00) | (0.60, 1.02) |  ($-$1.00, $-$0.09) |  ($-$1.00, $-$0.03)
4 | (0.00, 1.99) | (0.65, 1.00) | (1.02, 1.70) |  ($-$1.00, $-$0.09) |  ($-$1.00, $-$0.26)
5 | (1.99, 3.14) | (0.20, 0.68) | (0.60, 1.12) |  ($-$1.00, $-$0.02) |  ($-$1.00, $-$0.04)
6 | (1.99, 3.14) | (0.20, 0.68) | (1.12, 1.70) |  ($-$1.00, $-$0.01) |  ($-$1.00, $-$0.07)
7 | (1.99, 3.14) | (0.68, 1.00) | (0.60, 1.04) |  ($-$1.00, $-$0.28) |  ($-$1.00, $-$0.05)
8 | (1.99, 3.14) | (0.68, 1.00) | (1.04, 1.70) |  ($-$1.00, $-$0.27) |  ($-$1.00, $-$0.08)
9 | (0.00, 1.99) | (0.20, 0.65) | (0.60, 1.08) |  ($-$0.22, $-$1.00) |  ($-$1.00, $-$0.28)
10 | (0.00, 1.99) | (0.20, 0.65) | (1.08, 1.70) |  ($-$0.24, $-$1.00) |  ($-$1.00, $-$0.15)
11 | (0.00, 1.99) | (0.65, 1.00) | (0.60, 1.02) |  ($-$0.09, $-$1.00) |  ($-$1.00, $-$0.03)
12 | (1.99, 3.14) | (0.20, 0.68) | (0.60, 1.12) |  ($-$0.02, $-$1.00) |  ($-$1.00, $-$0.04)
13 | (1.99, 3.14) | (0.20, 0.68) | (1.12, 1.70) |  ($-$0.01, $-$1.00) |  ($-$1.00, $-$0.07)
14 | (1.99, 3.14) | (0.68, 1.00) | (0.60, 1.04) |  ($-$0.28, $-$1.00) |  ($-$1.00, $-$0.05)
15 | (1.99, 3.14) | (0.68, 1.00) | (1.04, 1.70) |  ($-$0.27, $-$1.00) |  ($-$1.00, $-$0.08)
16 | (0.00, 1.99) | (0.20, 0.65) | (0.60, 1.08) |  ($-$1.00, $-$0.10) |  ($-$0.28, $-$1.00)
17 | (0.00, 1.99) | (0.20, 0.65) | (1.08, 1.70) |  ($-$1.00, $-$0.01) |  ($-$0.15, $-$1.00)
18 | (0.00, 1.99) | (0.65, 1.00) | (0.60, 1.02) |  ($-$1.00, $-$0.28) |  ($-$0.03, $-$1.00)
19 | (0.00, 1.99) | (0.65, 1.00) | (1.02, 1.70) |  ($-$1.00, $-$0.12) |  ($-$0.26, $-$1.00)
20 | (1.99, 3.14) | (0.20, 0.68) | (0.60, 1.12) |  ($-$1.00, $-$0.07) |  ($-$0.04, $-$1.00)
21 | (1.99, 3.14) | (0.20, 0.68) | (1.12, 1.70) |  ($-$1.00, $-$0.11) |  ($-$0.07, $-$1.00)
22 | (1.99, 3.14) | (0.68, 1.00) | (0.60, 1.04) |  ($-$1.00, $-$0.13) |  ($-$0.05, $-$1.00)
23 | (1.99, 3.14) | (0.68, 1.00) | (1.04, 1.70) |  ($-$1.00, $-$0.15) |  ($-$0.08, $-$1.00)
24 | (0.00, 1.99) | (0.20, 0.65) | (0.60, 1.08) |  ($-$0.10, $-$1.00) |  ($-$0.28, $-$1.00)
25 | (0.00, 1.99) | (0.20, 0.65) | (1.08, 1.70) |  ($-$0.01, $-$1.00) |  ($-$0.15, $-$1.00)
26 | (0.00, 1.99) | (0.65, 1.00) | (0.60, 1.02) |  ($-$0.28, $-$1.00) |  ($-$0.03, $-$1.00)
27 | (0.00, 1.99) | (0.65, 1.00) | (1.02, 1.70) |  ($-$0.12, $-$1.00) |  ($-$0.26, $-$1.00)
28 | (1.99, 3.14) | (0.20, 0.68) | (0.60, 1.12) |  ($-$0.07, $-$1.00) |  ($-$0.04, $-$1.00)
29 | (1.99, 3.14) | (0.20, 0.68) | (1.12, 1.70) |  ($-$0.11, $-$1.00) |  ($-$0.07, $-$1.00)
30 | (1.99, 3.14) | (0.68, 1.00) | (0.60, 1.04) |  ($-$0.13, $-$1.00) |  ($-$0.05, $-$1.00)
31 | (0.00, 1.99) | (0.65, 1.00) | (1.02, 1.70) |  ($-$0.10, $-$1.00) |  ($-$1.00, $-$0.26)
32 | (1.99, 3.14) | (0.68, 1.00) | (1.04, 1.70) |  ($-$0.15, $-$1.00) |  ($-$0.08, $-$1.00)
Table 4: Measurements of $a_{{C\\!P}}^{\text{$T$-odd}}$, $A_{T}$ and $\overline{A}_{T}$ in each region of phase space. The uncertainties are statistical only. A common systematic uncertainty of 0.13%, 0.12% and 0.04% should be added to the asymmetries $A_{T}$, $\overline{A}_{T}$ and $a_{{C\\!P}}^{\text{$T$-odd}}$, respectively. This uncertainty is considered fully correlated among the bins. | Region 1 | Region 2 | Region 3 | Region 4 | Region 5
---|---|---|---|---|---
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $-0.51\pm 1.53$ | $\phantom{-}0.43\pm 1.84$ | $\phantom{2}1.36\pm 1.42$ | $-0.77\pm 1.48$ | $\phantom{-1}1.91\pm 1.62$
$A_{T}$ .11(%) | $\phantom{-}6.25\pm 2.21$ | $\phantom{-}5.54\pm 2.59$ | $20.51\pm 1.98$ | $\phantom{-}5.33\pm 2.10$ | $-12.54\pm 2.37$
$\overline{A}_{T}$ .11(%) | $\phantom{-}7.28\pm 2.10$ | $\phantom{-}4.68\pm 2.61$ | $17.79\pm 2.04$ | $\phantom{-}6.87\pm 2.09$ | $-16.37\pm 2.22$
| Region 6 | Region 7 | Region 8 | Region 9 | Region 10
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $\phantom{}-0.73\pm 1.81$ | $\phantom{-1}0.01\pm 1.43$ | $\phantom{-1}0.32\pm 1.45$ | $\phantom{-}1.26\pm 1.60$ | $-0.13\pm 2.02$
$A_{T}$ .11(%) | $-26.04\pm 2.54$ | $-16.27\pm 2.03$ | $-17.99\pm 2.06$ | $-1.74\pm 2.27$ | $-8.32\pm 2.86$
$\overline{A}_{T}$ .11(%) | $-24.59\pm 2.58$ | $-16.30\pm 2.03$ | $-18.63\pm 2.04$ | $-4.25\pm 2.25$ | $-8.06\pm 2.86$
| Region 11 | Region 12 | Region 13 | Region 14 | Region 15
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $-0.01\pm 1.48$ | $\phantom{-1}0.02\pm 1.56$ | $\phantom{}-0.32\pm 1.59$ | $\phantom{-1}4.03\pm 1.84$ | $\phantom{}-2.64\pm 1.43$
$A_{T}$ .11(%) | $\phantom{.}15.32\pm 2.07$ | $-11.92\pm 2.24$ | $-33.55\pm 2.26$ | $-20.03\pm 2.55$ | $-18.45\pm 2.00$
$\overline{A}_{T}$ .11(%) | $\phantom{.}15.35\pm 2.11$ | $-11.96\pm 2.18$ | $-32.91\pm 2.22$ | $-28.09\pm 2.64$ | $-13.17\pm 2.04$
| Region 16 | Region 17 | Region 18 | Region 19 | Region 20
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $\phantom{-}0.31\pm 1.45$ | $-2.43\pm 1.64$ | $-1.18\pm 2.08$ | $-1.19\pm 1.45$ | $\phantom{-1}0.56\pm 1.53$
$A_{T}$ .11(%) | $-7.63\pm 2.06$ | $\phantom{-}7.42\pm 2.28$ | $-5.60\pm 2.89$ | $\phantom{.}16.15\pm 2.05$ | $-10.57\pm 2.19$
$\overline{A}_{T}$ .11(%) | $-8.25\pm 2.05$ | $\phantom{.}12.28\pm 2.35$ | $-3.23\pm 3.00$ | $\phantom{.}18.53\pm 2.04$ | $-11.69\pm 2.15$
| Region 21 | Region 22 | Region 23 | Region 24 | Region 25
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $\phantom{-1}0.82\pm 1.57$ | $\phantom{-1}2.52\pm 1.82$ | $\phantom{-1}0.55\pm 1.41$ | $\phantom{-}1.06\pm 1.49$ | $-0.29\pm 1.66$
$A_{T}$ .11(%) | $-11.50\pm 2.22$ | $-10.81\pm 2.59$ | $-15.90\pm 1.96$ | $-7.27\pm 2.11$ | $\phantom{-}4.95\pm 2.34$
$\overline{A}_{T}$ .11(%) | $-13.15\pm 2.21$ | $-15.85\pm 2.55$ | $-17.00\pm 2.02$ | $-9.40\pm 2.11$ | $\phantom{-}5.53\pm 2.34$
| Region 26 | Region 27 | Region 28 | Region 29 | Region 30
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $-0.17\pm 2.05$ | $\phantom{1}0.37\pm 1.42$ | $\phantom{-}0.46\pm 1.59$ | $\phantom{-1}0.18\pm 1.62$ | $\phantom{-1}3.45\pm 1.73$
$A_{T}$ .11(%) | $-3.47\pm 2.94$ | $23.09\pm 2.01$ | $-3.37\pm 2.26$ | $-25.11\pm 2.32$ | $-27.24\pm 2.53$
$\overline{A}_{T}$ .11(%) | $-3.13\pm 2.87$ | $22.34\pm 2.02$ | $-4.30\pm 2.25$ | $-25.47\pm 2.25$ | $-34.15\pm 2.36$
| Region 31 | Region 32 |  |  |
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $\phantom{}-2.30\pm 1.45$ | $\phantom{}-1.88\pm 1.47$ |  |  |
$A_{T}$ .11(%) | $-18.51\pm 2.06$ | $-21.65\pm 2.05$ |  |  |
$\overline{A}_{T}$ .11(%) | $-13.91\pm 2.04$ | $-17.89\pm 2.12$ |  |  |

The alternative binning schemes with 8 and 16 bins have been defined by
integrating over $\cos(\theta_{{{K}^{+}}})$ and $\cos(\theta_{{{\pi}^{+}}})$
(8 bins), $\cos(\theta_{{{K}^{+}}})$ (16 bins), $\cos(\theta_{{{\pi}^{+}}})$
(16 bins), and by using mass variables ($m_{{{K}^{-}}{{\pi}^{+}}}$,
$m_{{{K}^{+}}{{K}^{-}}{{\pi}^{+}}}$, $m_{{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}}$) in
place of the angular variables (16 bins).

##  Appendix B Measured asymmetries in intervals of ${D}^{0}$ decay time

The values measured in 4 different intervals of the ${D}^{0}$ decay time for
$a_{{C\\!P}}^{\text{$T$-odd}}$, $A_{T}$, and $\overline{A}_{T}$ are reported
in Table 5.

Table 5: Measurements of $a_{{C\\!P}}^{\text{$T$-odd}}$, $A_{T}$ and $\overline{A}_{T}$ in different intervals of ${D}^{0}$ decay time, $t$, expressed in ${\rm\,ps}$. The uncertainties are statistical only. A common systematic uncertainty of 0.13%, 0.12% and 0.04% should be added to the asymmetries $A_{T}$, $\overline{A}_{T}$ and $a_{{C\\!P}}^{\text{$T$-odd}}$, respectively. This uncertainty is considered fully correlated among the bins. | $[-1.00,0.05]$ | $[0.05,0.10]$ | $[0.10,0.19]$ | $[0.19,4.00]$
---|---|---|---|---
$a_{{C\\!P}}^{\text{$T$-odd}}$ (%) | $\phantom{-}0.51\pm 0.62$ | $-0.12\pm 0.58$ | $-0.02\pm 0.56$ | $\phantom{-}0.42\pm 0.56$
$A_{T}$ .11(%) | $-7.49\pm 0.88$ | $-6.67\pm 0.81$ | $-7.64\pm 0.80$ | $-6.84\pm 0.79$
$\overline{A}_{T}$ .11(%) | $-8.51\pm 0.87$ | $-6.44\pm 0.82$ | $-7.60\pm 0.79$ | $-7.68\pm 0.79$

## 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); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

## References

  * [1] S. Bianco, F. L. Fabbri, D. Benson, and I. Bigi, A Cicerone for the physics of charm, Riv. Nuovo Cim. 26N7 (2003) 1, arXiv:hep-ex/0309021
  * [2] Y. Grossman, A. L. Kagan, and Y. Nir, New physics and $C\\!P$ violation in singly Cabibbo suppressed D decays, Phys. Rev. D75 (2007) 036008, arXiv:hep-ph/0609178
  * [3] T. Feldmann, S. Nandi, and A. Soni, Repercussions of flavour symmetry breaking on $C\\!P$ violation in $D$-meson decays, JHEP 06 (2012) 007, arXiv:1202.3795
  * [4] 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
  * [5] B. Bhattacharya, M. Gronau, and J. L. Rosner, $C\\!P$ asymmetries in singly-Cabibbo-suppressed $D$ decays to two pseudoscalar mesons, Phys. Rev. D85 (2012) 054014, arXiv:1201.2351
  * [6] LHCb collaboration, R. Aaij et al., Model-independent search for $C\\!P$ violation in ${{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ and ${{D}^{0}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ decays, Phys. Lett. B726 (2013) 623, arXiv:1308.3189
  * [7] G. Valencia, Angular correlations in the decay $B\rightarrow VV$ and CP violation, Phys. Rev. D39 (1989) 3339
  * [8] A. Datta and D. London, Triple-product correlations in $B\rightarrow V_{1}V_{2}$ decays and new physics, Int. J. Mod. Phys. A19 (2004) 2505, arXiv:hep-ph/0303159
  * [9] I. Bigi, Charm physics: like Botticelli in the Sistine Chapel, arXiv:hep-ph/0107102, Invited talk given at KAON 2001, the 3th International Conference on $C\\!P$ Violation, Pisa, Italy, June 12 - 17, 2001
  * [10] M. Gronau and J. L. Rosner, Triple-product asymmetries in $K$, $D_{(s)}$, and $B_{(s)}$ decays, Phys. Rev. D84 (2011) 096013, arXiv:1107.1232
  * [11] FOCUS collaboration, J. M. Link et al., Search for $T$ violation in charm meson decays, Phys. Lett. B622 (2005) 239, arXiv:hep-ex/0506012
  * [12] BaBar collaboration, P. del Amo Sanchez et al., Search for $C\\!P$ violation using $T$-odd correlations in $D^{0}\rightarrow K^{+}K^{-}\pi^{+}\pi^{-}$ decays, Phys. Rev. D81 (2010) 111103, arXiv:1003.3397
  * [13] LHCb collaboration, A. A. Alves Jr. et al., The LHCb detector at the LHC, JINST 3 (2008) S08005
  * [14] R. Aaij et al., Performance of the LHCb Vertex Locator, arXiv:1405.7808
  * [15] R. Arink et al., Performance of the LHCb Outer Tracker, JINST 9 (2014) P01002, arXiv:1311.3893
  * [16] M. Adinolfi et al., Performance of the LHCb RICH detector at the LHC, Eur. Phys. J. C73 (2013) 2431, arXiv:1211.6759
  * [17] A. A. Alves Jr. et al., Performance of the LHCb muon system, JINST 8 (2013) P02022, arXiv:1211.1346
  * [18] R. Aaij et al., The LHCb trigger and its performance in 2011, JINST 8 (2013) P04022, arXiv:1211.3055
  * [19] T. Sjöstrand, S. Mrenna, and P. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [20] T. Sjöstrand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [21] I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, Nuclear Science Symposium Conference Record (NSS/MIC) IEEE (2010) 1155
  * [22] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A 462 (2001) 152
  * [23] Geant4 collaboration, J. Allison et al., Geant4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [24] Geant4 collaboration, S. Agostinelli et al., Geant4: a simulation toolkit, Nucl. Instrum. Meth. A 506 (2003) 250
  * [25] M. Clemencic et al., The LHCb simulation application, Gauss: design, evolution and experience, J. Phys. Conf. Ser. 331 (2011) 032023
  * [26] Particle Data Group, J. Beringer et al., Review of particle physics, Phys. Rev. D86 (2012) 010001, and 2013 partial update for the 2014 edition
  * [27] M. Gronau, Resonant two-body D decays, Phys. Rev. Lett. 83 (1999) 4005, arXiv:hep-ph/9908237
  * [28] N. Cabibbo and A. Maksymowicz, Angular correlations in Ke-4 decays and determination of low-energy $\pi-\pi$ phase shifts, Phys. Rev. 137 (1965) B438
  * [29] J. F. Donoghue, Is $D^{0}\rightarrow\phi{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}$ really a clear signal for the annihilation diagram?, Phys. Rev. D33 (1986) 1516
  * [30] CLEO collaboration, M. Artuso et al., Amplitude analysis of $D^{0}\rightarrow K^{+}K^{-}\pi^{+}\pi^{-}$, Phys. Rev. D85 (2012) 122002, arXiv:1201.5716

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle37, A.A. Alves Jr25,38, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, W. Baldini16, R.J. Barlow54, C.
Barschel38, S. Barsuk7, W. Barter47, V. Batozskaya28, V. Battista39, A. Bay39,
L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1, S. Belogurov31, K.
Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, M.-O. Bettler47, M. van Beuzekom41, A.
Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, P.M. Bjørnstad54, T. Blake48,
F. Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30,38,
W. Bonivento15,38, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E.
Bowen40, C. Bozzi16, T. Brambach9, J. Bressieux39, D. Brett54, M. Britsch10,
T. Britton59, J. Brodzicka54, N.H. Brook46, H. Brown52, A. Bursche40, G.
Busetto22,r, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M.
Calvo Gomez36,p, P. Campana18,38, D. Campora Perez38, A. Carbone14,d, G.
Carboni24,l, R. Cardinale19,38,j, A. Cardini15, L. Carson50, K. Carvalho
Akiba2, G. Casse52, L. Cassina20, L. Castillo Garcia38, M. Cattaneo38, Ch.
Cauet9, R. Cenci58, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S.
Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, K. Ciba38, X. Cid
Vidal38, G. Ciezarek53, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J.
Closier38, V. Coco38, J. Cogan6, E. Cogneras5, L. Cojocariu29, P. Collins38,
A. Comerma-Montells11, A. Contu15, A. Cook46, M. Coombes46, S. Coquereau8, G.
Corti38, M. Corvo16,f, I. Counts56, B. Couturier38, G.A. Cowan50, D.C.
Craik48, M. Cruz Torres60, S. Cunliffe53, R. Currie50, C. D’Ambrosio38, J.
Dalseno46, P. David8, P.N.Y. David41, A. Davis57, K. De Bruyn41, S. De
Capua54, M. De Cian11, J.M. De Miranda1, L. De Paula2, W. De Silva57, P. De
Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. Déléage4, D.
Derkach55, O. Deschamps5, F. Dettori38, A. Di Canto38, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A.
Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P. Durante38, R.
Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V.
Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L.
Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, H.-M. Evans47, T.
Evans55, A. Falabella14, C. Färber11, C. Farinelli41, N. Farley45, S. Farry52,
RF Fay52, D. Ferguson50, V. Fernandez Albor37, F. Ferreira Rodrigues1, M.
Ferro-Luzzi38, S. Filippov33, M. Fiore16,f, M. Fiorini16,f, M. Firlej27, C.
Fitzpatrick39, T. Fiutowski27, P. Fol53, M. Fontana10, F. Fontanelli19,j, R.
Forty38, O. Francisco2, M. Frank38, C. Frei38, M. Frosini17,38,g, J. Fu21,38,
E. Furfaro24,l, A. Gallas Torreira37, D. Galli14,d, S. Gallorini22, S.
Gambetta19,j, M. Gandelman2, P. Gandini59, Y. Gao3, J. García Pardiñas37, J.
Garofoli59, J. Garra Tico47, L. Garrido36, C. Gaspar38, R. Gauld55, L.
Gavardi9, G. Gavrilov30, A. Geraci21,v, E. Gersabeck11, M. Gersabeck54, T.
Gershon48, Ph. Ghez4, A. Gianelle22, S. Gianì39, V. Gibson47, L. Giubega29,
V.V. Gligorov38, C. Göbel60, D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a,
C. Gotti20, M. Grabalosa Gándara5, R. Graciani Diaz36, L.A. Granado Cardoso38,
E. Graugés36, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P.
Griffith45, L. Grillo11, O. Grünberg62, B. Gui59, E. Gushchin33, Yu. Guz35,38,
T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S.
Hall53, B. Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N.
Harnew55, S.T. Harnew46, J. Harrison54, J. He38, T. Head38, V. Heijne41, K.
Hennessy52, P. Henrard5, L. Henry8, J.A. Hernando Morata37, E. van
Herwijnen38, M. Heß62, A. Hicheur1, D. Hill55, M. Hoballah5, C. Hombach54, W.
Hulsbergen41, P. Hunt55, N. Hussain55, D. Hutchcroft52, D. Hynds51, M.
Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, P.
Jaton39, A. Jawahery58, F. Jing3, M. John55, D. Johnson55, C.R. Jones47, C.
Joram38, B. Jost38, N. Jurik59, M. Kaballo9, S. Kandybei43, W. Kanso6, M.
Karacson38, T.M. Karbach38, S. Karodia51, M. Kelsey59, I.R. Kenyon45, T.
Ketel42, B. Khanji20, C. Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O.
Kochebina7, M. Kolpin11, I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M.
Korolev32, A. Kozlinskiy41, L. Kravchuk33, K. Kreplin11, M. Kreps48, G.
Krocker11, P. Krokovny34, F. Kruse9, W. Kucewicz26,o, M. Kucharczyk20,26,38,k,
V. Kudryavtsev34, K. Kurek28, T. Kvaratskheliya31, V.N. La Thi39, D.
Lacarrere38, G. Lafferty54, A. Lai15, D. Lambert50, R.W. Lambert42, G.
Lanfranchi18, C. Langenbruch48, B. Langhans38, T. Latham48, C. Lazzeroni45, R.
Le Gac6, J. van Leerdam41, J.-P. Lees4, R. Lefèvre5, A. Leflat32, J.
Lefrançois7, S. Leo23, O. Leroy6, T. Lesiak26, B. Leverington11, Y. Li3, T.
Likhomanenko63, M. Liles52, R. Lindner38, C. Linn38, F. Lionetto40, B. Liu15,
S. Lohn38, I. Longstaff51, J.H. Lopes2, N. Lopez-March39, P. Lowdon40, H. Lu3,
D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A.
Malinin63, G. Manca15,e, G. Mancinelli6, A. Mapelli38, J. Maratas5, J.F.
Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,t, R. Märki39, J.
Marks11, G. Martellotti25, A. Martens8, A. Martín Sánchez7, M. Martinelli39,
D. Martinez Santos42, F. Martinez Vidal64, D. Martins Tostes2, A.
Massafferri1, R. Matev38, Z. Mathe38, C. Matteuzzi20, A. Mazurov45, M.
McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. McSkelly52, B.
Meadows57, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes8, M.-N. Minard4,
N. Moggi14, J. Molina Rodriguez60, S. Monteil5, M. Morandin22, P. Morawski27,
A. Mordà6, M.J. Morello23,t, J. Moron27, A.-B. Morris50, R. Mountain59, F.
Muheim50, K. Müller40, M. Mussini14, B. Muster39, P. Naik46, T. Nakada39, R.
Nandakumar49, I. Nasteva2, M. Needham50, N. Neri21, S. Neubert38, N.
Neufeld38, M. Neuner11, A.D. Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, M.
Nicol7, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A. Novoselov35, D.P.
O’Hanlon48, A. Oblakowska-Mucha27, V. Obraztsov35, S. Oggero41, S. Ogilvy51,
O. Okhrimenko44, R. Oldeman15,e, G. Onderwater65, M. Orlandea29, J.M. Otalora
Goicochea2, P. Owen53, A. Oyanguren64, B.K. Pal59, A. Palano13,c, F.
Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49,38, M. Pappagallo51,
L.L. Pappalardo16,f, C. Parkes54, C.J. Parkinson9,45, G. Passaleva17, G.D.
Patel52, M. Patel53, C. Patrignani19,j, A. Pazos Alvarez37, A. Pearce54, A.
Pellegrino41, M. Pepe Altarelli38, S. Perazzini14,d, E. Perez Trigo37, P.
Perret5, M. Perrin-Terrin6, L. Pescatore45, E. Pesen66, K. Petridis53, A.
Petrolini19,j, E. Picatoste Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25,
A. Pistone19, S. Playfer50, M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E.
Polycarpo2, A. Popov35, D. Popov10, B. Popovici29, C. Potterat2, E. Price46,
J.D. Price52, J. Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A.
Puig Navarro39, G. Punzi23,s, W. Qian4, B. Rachwal26, J.H. Rademacker46, B.
Rakotomiaramanana39, M. Rama18, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G.
Raven42, F. Redi53, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S.
Ricciardi49, S. Richards46, M. Rihl38, K. Rinnert52, V. Rives Molina36, P.
Robbe7, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V.
Romanovsky35, A. Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, H.
Ruiz36, P. Ruiz Valls64, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B.
Saitta15,e, V. Salustino Guimaraes2, C. Sanchez Mayordomo64, B. Sanmartin
Sedes37, R. Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A.
Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, M. Savrie16,f, D.
Savrina31,32, M. Schiller42, H. Schindler38, M. Schlupp9, M. Schmelling10, B.
Schmidt38, O. Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B.
Sciascia18, A. Sciubba25, M. Seco37, A. Semennikov31, I. Sepp53, N. Serra40,
J. Serrano6, L. Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y.
Shcheglov30, T. Shears52, L. Shekhtman34, V. Shevchenko63, A. Shires9, R.
Silva Coutinho48, G. Simi22, M. Sirendi47, N. Skidmore46, T. Skwarnicki59,
N.A. Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41,
M.D. Sokoloff57, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2,
B. Spaan9, A. Sparkes50, P. Spradlin51, S. Sridharan38, F. Stagni38, M.
Stahl11, S. Stahl11, O. Steinkamp40, O. Stenyakin35, S. Stevenson55, S.
Stoica29, S. Stone59, B. Storaci40, S. Stracka23,38, M. Straticiuc29, U.
Straumann40, R. Stroili22, V.K. Subbiah38, L. Sun57, W. Sutcliffe53, K.
Swientek27, S. Swientek9, V. Syropoulos42, M. Szczekowski28, P. Szczypka39,38,
D. Szilard2, T. Szumlak27, S. T’Jampens4, M. Teklishyn7, G. Tellarini16,f, F.
Teubert38, C. Thomas55, E. Thomas38, J. van Tilburg41, V. Tisserand4, M.
Tobin39, S. Tolk42, L. Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N.
Torr55, E. Tournefier4, S. Tourneur39, M.T. Tran39, M. Tresch40, A.
Tsaregorodtsev6, P. Tsopelas41, N. Tuning41, M. Ubeda Garcia38, A. Ukleja28,
A. Ustyuzhanin63, U. Uwer11, C. Vacca15, V. Vagnoni14, G. Valenti14, A.
Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez Sierra37, S.
Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M. Vesterinen11, B.
Viaud7, D. Vieira2, M. Vieites Diaz37, X. Vilasis-Cardona36,p, A. Vollhardt40,
D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß62, H.
Voss10, J.A. de Vries41, R. Waldi62, C. Wallace48, R. Wallace12, J. Walsh23,
S. Wandernoth11, J. Wang59, D.R. Ward47, N.K. Watson45, D. Websdale53, M.
Whitehead48, J. Wicht38, D. Wiedner11, G. Wilkinson55, M.P. Williams45, M.
Williams56, H.W. Wilschut65, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W.
Wislicki28, M. Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38,
Y. Xie61, Z. Xing59, Z. Xu39, Z. Yang3, X. Yuan3, O. Yushchenko35, M.
Zangoli14, M. Zavertyaev10,b, L. Zhang59, W.C. Zhang12, Y. Zhang3, A.
Zhelezov11, A. Zhokhov31, L. Zhong3, A. Zvyagin38.

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 de Savoie, 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
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
63National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
64Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
65KVI - University of Groningen, Groningen, The Netherlands, associated to 41
66Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy