EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-084 LHCb-PAPER-2018-009

Measurement of $C\\!P$ violation in ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$
decays

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

A measurement of the $C\\!P$ asymmetries $S_{f}$ and $S_{\bar{f}}$ in
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays is reported. The decays are
reconstructed in a dataset collected with the LHCb experiment in proton-proton
collisions at centre-of-mass energies of 7 and
8$\mathrm{\,Te\kern-1.00006ptV}$ and corresponding to an integrated luminosity
of 3.0$\mbox{\,fb}^{-1}$. The $C\\!P$ asymmetries are measured to be
$\mbox{$S_{f}$}=\mbox{$0.058$}\pm\mbox{$0.020$}\mathrm{\,(stat)}\pm\mbox{$0.011$}\mathrm{\,(syst)}$
and
$\mbox{$S_{\bar{f}}$}=\mbox{$0.038$}\pm\mbox{$0.020$}\mathrm{\,(stat)}\pm\mbox{$0.007$}\mathrm{\,(syst)}$.
These results are in agreement with, and more precise than, previous
determinations. They are used to constrain angles of the unitarity triangle,
$|\sin\left(2\beta+\gamma\right)|$ and $\gamma$, to intervals that are
consistent with the current world-average values.

Published in JHEP 06 (2018) 084

© 2018 CERN for the benefit of the LHCb Collaboration. CC-BY-4.0 licence.

##  1 Introduction

In the Standard Model, the decays ${{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}}$
and ${{B}^{0}}\rightarrow{{D}^{+}}{{\pi}^{-}}$ proceed through the
$\bar{b}\rightarrow\bar{c}u\bar{d}$ and $\bar{b}\rightarrow\bar{u}c\bar{d}$
quark transitions, respectively.111Inclusion of charge conjugate modes is
implied unless explicitly stated. The relative weak phase between these two
decay amplitudes is $\gamma\equiv\arg(-V_{ud}V_{ub}^{*}/V_{cd}V_{cb}^{*})$.
The ${B}^{0}$ meson can undergo a flavour oscillation before the decay. The
amplitude of the direct decay and that of a decay preceded by an oscillation
have a total relative phase difference of $2\beta+\gamma$, where
$\beta\equiv\arg(-V_{cd}V_{cb}^{*}/V_{td}V_{tb}^{*})$. The phases $\beta$ and
$\gamma$ are angles of the unitary triangle. Measurements of $C\\!P$ violation
in ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays provide information on
these angles.

Decay-time-dependent $C\\!P$ asymmetries in
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays can be measured by analysing
the decay rates as a function of the decay time of ${B}^{0}$ mesons of known
initial flavour [1, 2, 3]. The ratio of the decay amplitudes,
$r_{D\pi}=|A({{B}^{0}}\rightarrow{{D}^{+}}{{\pi}^{-}})/A({{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}})|$,
is around $2\%$, and limits the size of the $C\\!P$ asymmetries. Given its
small value, this ratio needs to be determined from independent measurements,
for example using the branching ratio of
${{B}^{0}}\rightarrow{{D}^{+}_{s}}\pi^{-}$ decays under the assumption of
SU(3) flavour symmetry [4, 5].

The decay rates of initially produced ${{B}^{0}}$ mesons to the final states
$f={{D}^{-}}{{\pi}^{+}}$ and $\bar{f}={{D}^{+}}{{\pi}^{-}}$ as a function of
the ${{B}^{0}}$-meson decay time, $t$, are given by

$\displaystyle\Gamma_{{{B}^{0}}\rightarrow f}(t)$ $\displaystyle\propto
e^{-\Gamma t}\left[1+C_{f}\cos(\Delta m\,t)-\mbox{$S_{f}$}\sin(\Delta
m\,t)\right]\,,$ (1) $\displaystyle\Gamma_{{{B}^{0}}\rightarrow\bar{f}}(t)$
$\displaystyle\propto e^{-\Gamma t}\left[1+C_{\bar{f}}\cos(\Delta
m\,t)-S_{\bar{f}}\sin(\Delta m\,t)\right]\,,$

where $\Gamma$ is the average ${B}^{0}$ decay width and $\Delta m$ is the
${B}^{0}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ oscillation
frequency. For an initially produced ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ meson, the same equations hold
except for a change of sign of the coefficients in front of the sine and
cosine functions. No $C\\!P$ violation in the decay is assumed, i.e. only
tree-level processes contribute to the decay amplitudes. It is also assumed
that $|q/p|=1$, where $q$ and $p$ are the complex coefficients defining the
heavy and light mass eigenstates of the ${B}^{0}$ system, and
$\Delta\Gamma=0$, where $\Delta\Gamma$ is the decay-width difference between
the two mass eigenstates. These assumptions follow from the known values of
these quantities [6]. Under these assumptions, the coefficients of the cosine
and sine terms of Eq. (1) are given by

$\displaystyle C_{f}$
$\displaystyle=\frac{1-r_{D\pi}^{2}}{1+r_{D\pi}^{2}}=-C_{\bar{f}}\,,$ (2)
$S_{f}$
$\displaystyle=-\frac{2r_{D\pi}\sin\left[\delta-(2\beta+\gamma)\right]}{1+r_{D\pi}^{2}}\,,$
(3) $S_{\bar{f}}$
$\displaystyle=\frac{2r_{D\pi}\sin\left[\delta+(2\beta+\gamma)\right]}{1+r_{D\pi}^{2}}\,,$
(4)

where $\delta$ is the $C\\!P$-conserving phase difference between the
$\bar{b}\rightarrow\bar{c}u\bar{d}$ and $\bar{b}\rightarrow\bar{u}c\bar{d}$
decay amplitudes. Due to the small value of $r_{D\pi}$, terms of
$\mathcal{O}(r_{D\pi}^{2})$ are neglected in this analysis, fixing
$C_{f}=-C_{\bar{f}}=1$.

A measurement of the $C\\!P$ asymmetries $S_{f}$ and $S_{\bar{f}}$ can be
interpreted in terms of $2\beta+\gamma$ by using the value of $r_{D\pi}$ as
input. Additionally, using the known value of $\beta$ [6], the angle $\gamma$
can be evaluated. The determination of $\gamma$ from tree-level decays is
important because processes beyond the Standard Model are not expected to
contribute. Constraints from the analysis of
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays can be combined with other
measurements to improve the ultimate sensitivity to this angle [7].

Measurements of $S_{f}$ and $S_{\bar{f}}$ using ${{B}^{0}}\rightarrow
D^{(*)\mp}\pi^{\pm}$ and ${{B}^{0}}\rightarrow D^{\mp}\rho^{\pm}$ decays have
been reported by the BaBar [8, 9] and Belle [10, 11] collaborations. This
paper presents a measurement of $S_{f}$ and $S_{\bar{f}}$ with
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays reconstructed in a dataset
collected with the LHCb experiment in proton-proton collisions at centre-of-
mass energies of $7$ and $8$$\mathrm{\,Te\kern-1.00006ptV}$ and corresponding
to an integrated luminosity of 3.0$\mbox{\,fb}^{-1}$. This is the first
measurement of $S_{f}$ and $S_{\bar{f}}$ at a hadron collider.

##  2 Detector and simulation

The LHCb detector [12, 13] is a single-arm forward spectrometer covering the
pseudorapidity range 2–5, 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 [14], a large-area silicon-strip detector located upstream of a dipole
magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three stations of
silicon-strip detectors and straw drift tubes [15] placed downstream of the
magnet. The tracking system provides a measurement of the momentum, $p$, of
charged particles with a relative uncertainty that varies from $0.5\%$ at low
momentum to $1.0\%$ at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex (PV), the impact parameter (IP), is
measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

In the simulation, $pp$ collisions are generated using Pythia [16,
*Sjostrand:2007gs] with a specific LHCb configuration [18]. Decays of hadronic
particles are described by EvtGen [19], in which final-state radiation is
generated using Photos [20]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [21,
*Agostinelli:2002hh] as described in Ref. [23].

##  3 Candidate selection

The online event selection is performed by a trigger, which consists of a
hardware stage, using information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.
Events containing a muon with high $p_{\mathrm{T}}$ or a hadron, photon or
electron with high transverse energy in the calorimeters are considered at the
hardware trigger stage. Events selected by the trigger using hadrons from the
signal decay represent $70\%$ of the sample used in this analysis, the rest
being collected using trigger criteria satisfied by other properties of the
event.

The software trigger requires a two-, three-, or four-track secondary vertex
with a significant displacement from the primary $pp$ interaction vertices. At
least one charged particle must have
$\mbox{$p_{\mathrm{T}}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and be
inconsistent with originating from a PV. A multivariate algorithm is used for
the identification of secondary vertices consistent with the decay of a ${b}$
hadron [24].

The selection of ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ candidates is
performed by reconstructing
${{{D}^{-}}\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}}$ candidates from
charged particle tracks with high momentum and transverse momentum, and
originating from a common displaced vertex. Particle identification (PID)
information is used to select kaon and pion candidates, and the
${{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ invariant mass is required to be within
$35{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known value of the
${{D}^{-}}$ mass [25]. These candidates are combined with a fourth charged
particle, referred to as the _companion_ , to form the ${{B}^{0}}$ vertex,
which must be displaced from any PV. The PV with respect to which the
${{B}^{0}}$ candidate has the smallest $\chi^{2}_{\text{IP}}$ is considered as
the production vertex. The $\chi^{2}_{\text{IP}}$ is defined as the difference
in the vertex-fit $\chi^{2}$ of a given PV reconstructed with and without the
${B}^{0}$ candidate. No PID requirement is applied to the companion track at
this stage.

The ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ candidates are required to match
the secondary vertices found in the software trigger, to have a proper decay
time larger than $0.2\text{\,}\mathrm{p}\mathrm{s}$, and to have a momentum
vector aligned with the vector formed by joining the PV and the ${B}^{0}$
decay vertex. The decay time is determined from a kinematic fit in which the
${{B}^{0}}$ candidate is constrained to originate from the PV to improve the
decay-time resolution, while the ${{B}^{0}}$-candidate mass is computed
assigning the known value [25] to the mass of the ${{D}^{-}}$ candidate to
improve the mass resolution [26]. A combination of PID information and mass-
range vetoes is used to suppress to a negligible level cross-feed backgrounds
such as ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}(\rightarrow p{{K}^{-}}{{\pi}^{+}}){{\pi}^{-}}$ and
${{B}^{0}_{s}}\rightarrow{{D}^{-}_{s}}(\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{-}}){{\pi}^{+}}$,
due to the misidentification of protons and kaons as pions.

A boosted decision tree (BDT) [27, 28] is used to increase the signal purity
by suppressing background from random combinations of particles. Candidates
reconstructed from simulated ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays
are used as signal in the training of the BDT, and data candidates with an
invariant mass larger than $5.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ are
used as background. A set of $16$ variables are combined into a single
response, which is used to categorise the ${B}^{0}$ candidates. The most
relevant variables entering the BDT are the quality of the fit of the
${B}^{0}$ vertex and that of the kinematic fit to calculate the ${B}^{0}$
decay time, the transverse momentum of the $D^{-}$ candidate, and the quality
of the fit of the companion-particle track. The requirement placed on the BDT
response is chosen to maximise the expected sensitivity to $S_{f}$ and
$S_{\bar{f}}$ as derived from a set of simulated samples of signal plus
background that are passed through the entire analysis. The data sample is
further required to consist of ${{B}^{0}}$ candidates whose initial flavour
has been determined by means of the flavour tagging algorithms described in
Sec. 5.

##  4 Sample composition

The data sample after the selection is split into two disjoint subsets
according to the PID information of the companion particle: a sample referred
to as _pion-like_ consisting mostly of genuine
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays, and a sample referred to as
_kaon-like_ consisting mostly of genuine
${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$ decays. The binned ${{B}^{0}}$-mass
distributions of these two samples are fitted simultaneously in order to
determine the sample compositions. The mass distributions span the range
5090–6000${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and are shown in Fig. 1
with fit projections overlaid.

Figure 1: Invariant mass distributions of the (left) pion-like and (right)
kaon-like samples with fit projections overlaid. The simultaneous fit of the
two distributions is described in the text and yields a $\chi^{2}$ per degree
of freedom of 1.18. The $B\rightarrow{{D}^{\mp}}\rho$ component includes both
${{B}^{0}}\rightarrow{{D}^{\mp}}\rho^{\pm}$ and
${{B}^{\mp}}\rightarrow{{D}^{\mp}}\rho^{0}$ decays.

The mass distribution of ${{B}^{0}}$ candidates in the pion-like sample
features a peak at the known ${{B}^{0}}$ mass with a width of about ,
corresponding to ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ signal decays, and
is modelled with the sum of a double-sided Hypatia function [29] and a Johnson
SU function [30]. The combinatorial background is modelled using the sum of
two exponential functions. At values lower than , broad structures
corresponding to partially reconstructed decays, such as
${{B}^{0}}\rightarrow{{D}^{-}}\rho^{+}(\rightarrow\pi^{+}\pi^{0})$,
${{{B}^{-}}}\rightarrow{{D}^{-}}\rho^{0}(\rightarrow{{\pi}^{+}}{{\pi}^{-}})$
and ${{B}^{0}}\rightarrow D^{*-}(\rightarrow{{D}^{-}}\pi^{0}){{\pi}^{+}}$
where the additional pion is not reconstructed, are present; the shapes of
these backgrounds are determined from simulation. Cross-feed
${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$ decays, due to kaon-to-pion
misidentification, contaminating the left tail of the signal peak, are
described with a double-sided Hypatia function with parameters determined from
simulated decays.

The ${{B}^{0}}$-mass distribution of the kaon-like sample contains analogous
components: the ${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$ signal peak is modelled
with a single-sided Hypatia function; the combinatorial background with an
exponential function; partially reconstructed
${{B}^{0}}\rightarrow{{D}^{-}}\rho^{+}(\rightarrow\pi^{+}\pi^{0})$,
${{B}^{0}}\rightarrow D^{*-}(\rightarrow{{D}^{-}}\pi^{0}){{\pi}^{+}}$,
${{B}^{0}}\rightarrow D^{*-}(\rightarrow{{D}^{-}}\pi^{0})K^{+}$ and
${{B}^{0}}\rightarrow{{D}^{-}}K^{*+}(\rightarrow\pi^{0}K^{+})$ decays, where
the charged pion is misidentified as a kaon and the neutral pion is not
reconstructed, are modelled using simulation. Cross-feed
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays from pion-to-kaon
misidentification in the kaon-like sample peaks to the right of the
${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$ signal region, with a long tail towards
the high-mass region; the shape of this distribution, a double-sided Hypatia
function, is taken from simulation.

The yields of all components are floating parameters of the fit. The yield of
the ${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$ cross-feed decays in the pion-like
sample is constrained to that of the ${{B}^{0}}\rightarrow{D}^{\mp}K^{\pm}$
signal decays in the kaon-like sample using the kaon-to-pion misidentification
probability and the kaon identification efficiency of the PID requirement on
the companion particle. In a similar manner, the yield of the
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ cross-feed decays in the kaon-like
sample is constrained to that of ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$
signal decays in the pion-like sample scaled by the pion-to-kaon
misidentification probability and the pion identification efficiency. The
misidentification probabilities and the identification efficiencies are
determined from a large sample of $D^{*+}\rightarrow D^{0}(\rightarrow
K^{-}{{\pi}^{+}}){{\pi}^{+}}$ decays in which the charged tracks are weighted
in momentum and pseudorapidity to match those of the companion particle in
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays [31].

An unbinned maximum-likelihood fit to the ${{B}^{0}}$-mass distribution of the
pion-like sample is performed to determine _sWeights_ [32], which are used to
statistically subtract the background in the decay-time analysis of Sec. 6.
This unbinned fit contains the same components as the binned fit, but applied
in a smaller mass window, 5220–5600${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
to suppress the background contamination. All backgrounds entering this mass
region are combined to form a single shape according to the fractions found in
the previous fit. The shape parameters of the signal and background components
are also fixed to the values found in the preceding fit. The
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ signal yield is found to be
$479\,000\pm 700$ and that of the background to be $34\,400\pm 300$.

##  5 Flavour tagging

A combination of tagging algorithms is used to determine the flavour of the
${B}^{0}$ candidates at production. Each algorithm provides a decision (tag),
$d$, which determines the flavour, and an estimate, $\eta$, of the probability
that the decision is incorrect (mistag probability). The decision takes the
value of $d=1$ for a candidate tagged as a ${B}^{0}$, and $d=-1$ for a
candidate tagged as ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$.
The mistag probability is defined only between 0 and 0.5, since $\eta>0.5$
corresponds to an opposite tag with a mistag probability of $(1-\eta)$.

Two classes of flavour tagging algorithms are used: opposite-side, OS, and
same-side, SS, taggers. The OS tagger exploits the dominant production
mechanism of ${b}$ hadrons, the incoherent production of ${{b}{\overline{b}}}$
pairs, by identifying signatures of the ${b}$ hadron produced together with
the signal ${{B}^{0}}$ meson. The time evolution of the signal ${{B}^{0}}$
meson is independent from that of the accompanying ${b}$ hadron. The OS tagger
uses the charge of the electron or muon from semileptonic ${b}$-hadron decays,
the charge of the kaon from a $b\rightarrow c\rightarrow s$ decay chain, the
charge of a reconstructed secondary charm hadron, and the charge of particles
associated with a secondary vertex distinct from the signal decay; further
details are given in Refs. [33, 34].

The SS tagger selects pions and protons related to the hadronisation process
of the signal ${{B}^{0}}$ meson by means of BDT classifiers that determine the
tag decision and mistag probability, as described in Ref. [35]. Unlike Ref.
[35], where ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ decays are used assuming
$S_{f}=S_{\bar{f}}=0$, the BDT classifiers of the SS algorithm exploited in
this analysis are trained on a control sample of flavour-specific
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*0}}$
decays, whose distributions of $p_{\mathrm{T}}$, pseudorapidity, azimuthal
angle of the ${{B}^{0}}$ candidate, as well as number of tracks and PVs in the
event, are weighted to match those of the
${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ signal decay.

Around $37\%$ of the ${B}^{0}$ candidates are tagged by the OS tagger, $79\%$
by the SS tagger, and $31\%$ by both algorithms. About $15\%$ of the ${B}^{0}$
candidates are not tagged by either of the algorithms and are discarded. Each
tagging decision is weighted by the estimated mistag probability $\eta$, which
dilutes the sensitivity to the $C\\!P$ asymmetry. To correct for potential
biases in $\eta$, a function $\omega\hskip 1.42262pt(\eta)$ is used to
calibrate the mistag probability which provides an unbiased estimate of the
mistag fraction $\omega$ ($\bar{\omega}$), i.e. the fraction of incorrectly
tagged candidates for a ${B}^{0}$ (${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$) meson, for any value of
$\eta$.

Charged particles used for flavour tagging, such as the kaons from the
$b\rightarrow c\rightarrow s$ decay chain exploited in the OS tagger, can have
different interaction cross-sections with the detector material and therefore
different reconstruction efficiencies. This can result in different tagging
efficiencies and mistag probabilities for initial ${{B}^{0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ mesons. Asymmetries in the
tagging efficiency are found to be consistent with zero in simulation and data
for both taggers and are therefore neglected in the baseline fit, but
considered as a source of systematic uncertainty. This is not the case for the
asymmetries of the mistag probability, which can bias the determination of the
${C\\!P}$ asymmetries and must be corrected for. Therefore, the calibration
functions depend on the initial flavour of the ${B}^{0}$ candidate:
$\omega(\eta)$ for $d=+1$ and $\overline{\omega}(\eta)$ for $d=-1$. They are
expressed as generalised linear models (GLMs) of the form

$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{11.00008pt}{0.51212pt})} \\\
[-.7ex]
$\kern-0.50003pt\omega$}{}(\eta)=g\big{(}h(\eta)\big{)}=g\bigg{(}g^{-1}(\eta)+\sum\limits_{i=1}^{N}\left(p_{i}\shortstack{{\tiny$(-)$}
\\\ [-.7ex] $+$}\frac{\Delta p_{i}}{2}\right)f_{i}(\eta)\bigg{)}\,,$ (5)

where $p_{i}$ and $\Delta p_{i}$ are free parameters, $f_{i}$ are the basis
functions, and $g$ is the link function [36].

The calibration function of the OS tagger is a GLM using natural splines as
the basis functions [37] with five _knots_ , $N=5$. For the SS tagger, a GLM
using first-order polynomial basis functions and $N=2$ is used. In both cases
a modified logistic function, $g(x)=\frac{1}{2}(1+e^{x})^{-1}$, is used as the
link function. To account for the tagging decision and mistag probability, the
following substitutions occur in Eq. (1):

$\begin{split}S_{f}&\rightarrow(\Delta^{-}-\Delta^{+})S_{f}\,,\\\
C_{f}&\rightarrow(\Delta^{-}-\Delta^{+})C_{f}\,.\end{split}$ (6)

Similar equations hold for $S_{\bar{f}}$ and $C_{\bar{f}}$. The calibration
functions enter the coefficients $\Delta^{\pm}$ along with the tagging
efficiencies $\varepsilon_{\text{OS}}$ and $\varepsilon_{\text{SS}}$ of the OS
and SS taggers, according to

$\displaystyle\Delta^{\pm}$
$\displaystyle=\frac{1}{2}\varepsilon_{\text{\tiny{OS}}}\bigg{[}1-\varepsilon_{\text{\tiny{SS}}}+d_{\text{\tiny{OS}}}\Big{(}1-\varepsilon_{\text{\tiny{SS}}}-2\omega(\eta_{\text{\tiny{OS}}})\big{(}1+\varepsilon_{\text{\tiny{SS}}}\big{)}\Big{)}\bigg{]}$
$\displaystyle\pm\frac{1}{2}\varepsilon_{\text{\tiny{OS}}}\bigg{[}1-\varepsilon_{\text{\tiny{SS}}}+d_{\text{\tiny{OS}}}\Big{(}1-\varepsilon_{\text{\tiny{SS}}}-2\overline{\omega}(\eta_{\text{\tiny{OS}}})\big{(}1+\varepsilon_{\text{\tiny{SS}}}\big{)}\Big{)}\bigg{]}\,,$
(7)

for candidates tagged by the OS algorithm and not by the SS algorithm (and
vice-versa, exchanging the OS and SS indexes), and

$\displaystyle\Delta^{\pm}$
$\displaystyle=\frac{1}{4}\varepsilon_{\text{\tiny{OS}}}\varepsilon_{\text{\tiny
SS}}\left[1+\sum\limits_{j=\text{\tiny OS},\text{\tiny
SS}}d_{j}\Big{(}1-2\omega(\eta_{j})\Big{)}+d_{\text{\tiny OS}}d_{\text{\tiny
SS}}\Big{(}1-2\omega(\eta_{j})+2\omega(\eta_{\text{\tiny
OS}})\omega(\eta_{\text{\tiny SS}})\Big{)}\right]$
$\displaystyle\pm\frac{1}{4}\varepsilon_{\text{\tiny{OS}}}\varepsilon_{\text{\tiny
SS}}\left[1+\sum\limits_{j=\text{\tiny OS},\text{\tiny
SS}}d_{j}\Big{(}1-2\overline{\omega}(\eta_{j})\Big{)}+d_{\text{\tiny
OS}}d_{\text{\tiny
SS}}\Big{(}1-2\overline{\omega}(\eta_{j})+2\overline{\omega}(\eta_{\text{\tiny
OS}})\overline{\omega}(\eta_{\text{\tiny SS}})\Big{)}\right]\,,$ (8)

for candidates tagged by both algorithms. The form of the $\Delta^{\pm}$
coefficients and of the substitutions of Eq. (6) is convenient to also account
for other spurious asymmetries considered in Sect. 6.

The seven pairs of calibration parameters $(p_{i},\Delta p_{i})$ are left free
in the fit from which the $S_{f}$ and $S_{\bar{f}}$ observables are extracted.
This is possible because the $C_{f}$ and $C_{\bar{f}}$ coefficients are fixed
parameters, so that the cosine terms of the decay rates permit the calibration
parameters to be measured. This procedure has been validated with
pseudoexperiments and possible deviations of $C_{f}$ and $C_{\bar{f}}$ from
unity are taken into account in the systematic uncertainties. To account for
possible mismodelling of the calibration functions, systematic uncertainties
are assigned to $S_{f}$ and $S_{\bar{f}}$. The calibration functions obtained
in the data are shown in Fig. 2, where the measured mistag fraction is
presented as a function of the predicted mistag probability of the tagger.

Considering only candidates retained for the analysis, i.e. those with a
flavour tag, the statistical uncertainties of $S_{f}$ and $S_{\bar{f}}$ are
inversely proportional to $\sqrt{\langle\mathcal{D}^{2}\rangle}$. Here,
$\langle\mathcal{D}^{2}\rangle$ is the average of the squared dilution of the
signal, calculated as
$\frac{1}{\mathcal{N}_{\mathrm{tag}}}\sum_{i=1}^{N_{\mathrm{tag}}}w_{i}\left[1-2\omega(\eta_{i})\right]^{2}$,
where $N_{\mathrm{tag}}$ is the number of candidates, $w_{i}$ is the $sWeight$
of the candidate $i$ determined in the fit of the sample composition, and
$\mathcal{N}_{\mathrm{tag}}=\sum_{i=1}^{N_{\mathrm{tag}}}w_{i}$. The total
dilution squared of the sample is found to be $(6.554\pm 0.017)\%$.
Considering also the number of discarded candidates because no tagging
decision is determined by either tagger, $N_{\mathrm{untag}}$ and
$\mathcal{N}_{\mathrm{untag}}=\sum_{i=1}^{N_{\mathrm{untag}}}w_{i}$, the
tagging efficiency $\varepsilon_{\rm
tag}\equiv\mathcal{N}_{\mathrm{tag}}/(\mathcal{N}_{\mathrm{tag}}+\mathcal{N}_{\mathrm{untag}})$
is found to be $(85.23\pm 0.05)\%$. Hence, the effective tagging efficiency of
the initial sample is $\varepsilon_{\rm
tag}\langle\mathcal{D}^{2}\rangle=(5.59\pm 0.01)\%$. All quoted uncertainties
are statistical only. The effective tagging efficiency is similar to that of
the measurement of $C\\!P$ violation in
${{B}^{0}_{s}}\rightarrow{{D}^{\mp}_{s}}K^{\pm}$ decays [38].

Figure 2: Measured mistag fraction $\omega$ versus predicted mistag
probability $\eta$ of the combination of (left) OS and (right) SS taggers as
determined in signal decays with the fit described in Sect. 6. The black
histograms are the distributions of the mistag probabilities in arbitrary
units. The shaded areas correspond to the 68% and 95% confidence-level regions
of the calibration functions and do not include systematic uncertainties on
the parameters. The calibration functions and the distributions of mistag
probabilities are shown summing over candidates tagged as either ${B}^{0}$ or
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$.

##  6 Decay-time fit

The ${C\\!P}$ asymmetries $S_{f}$ and $S_{\bar{f}}$ are determined from a
multidimensional maximum-likelihood fit to the unbinned distributions of the
signal candidates weighted with the _sWeights_. The probability density
function (PDF) describing the signal decay to a final state $F$ equal to $f$
or $\bar{f}$, at the reconstructed decay time $t$, and given the tags
$\vec{d}=(d_{\mathrm{OS}},d_{\mathrm{SS}})$ and mistag probabilities
$\vec{\eta}=(\eta_{\mathrm{OS}},\eta_{\mathrm{SS}})$, is

$P(t,F,\vec{d}\>|\>\vec{\eta})\propto\epsilon(t)\left(\mathcal{P}(t^{\prime},F,\vec{d}\>|\>\vec{\eta})\otimes\mathcal{R}(t^{\prime}-t)\right)\,,$
(9)

where $\mathcal{P}(t^{\prime},F,\vec{d}\>|\>\vec{\eta})$ is the function
describing the distribution of true decay times $t^{\prime}$,
$\mathcal{R}(t^{\prime}-t)$ is the decay time resolution, and $\epsilon(t)$
describes the decay-time-dependent efficiency of reconstructing and selecting
the signal decays. The function
$\mathcal{P}(t^{\prime},F,\vec{d}\>|\>\vec{\eta})$ corresponds to one of the
decay rates of Eq. (1), according to the final state $F$, and with the
substitutions of Eq. (6) to include the flavour tagging.

A production asymmetry, $A_{\text{P}}$, and a final-state detection asymmetry,
$A_{\text{D}}$, must also be taken into account. These are defined as

$A_{\rm{P}}=\frac{\sigma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}})-\sigma({{B}^{0}})}{\sigma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}})+\sigma({{B}^{0}})}\,,\qquad
A_{\rm{D}}=\frac{\varepsilon(f)-\varepsilon(\bar{f})}{\varepsilon(f)+\varepsilon(\bar{f})}\,,$
(10)

where $\varepsilon$ is the decay-time-integrated efficiency in reconstructing
and selecting the final state $\bar{f}$ or $f$, and $\sigma$ is the production
cross-section of the given ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ or ${B}^{0}$ meson. The
asymmetry $A_{\rm{P}}$ arises from the different production cross-sections of
${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${B}^{0}$ mesons in
proton-proton collisions and is measured to be at the percent level at LHC
energies [39]. The detection asymmetry is also measured to be at the percent
level and to be independent of the decay time. Therefore, Eq. (6) is further
modified as follows:

$\begin{split}(\Delta^{-}-\Delta^{+})S_{f}&\rightarrow(\Delta^{-}-A_{\rm{P}}\Delta^{+})(1+A_{\rm{D}})S_{f}\,,\\\
(\Delta^{-}-\Delta^{+})C_{f}&\rightarrow(\Delta^{-}-A_{\rm{P}}\Delta^{+})(1+A_{\rm{D}})C_{f}\,,\end{split}$
(11)

where $C_{f}$ is fixed to 1. Similar equations hold for $S_{\bar{f}}$ and
$C_{\bar{f}}$ (fixed to $-1$) with $A_{\rm{D}}\rightarrow-A_{\rm{D}}$.

The decay-time resolution is determined from a sample of fake ${{B}^{0}}$
candidates formed from a genuine ${{D}^{-}}$ meson and a charged track
originating from the same PV and consistent with being a pion of opposite
charge. These candidates are subjected to a selection similar to that of the
signal decays except for all decay-time biasing requirements, which are
removed. The decay-time distribution of these candidates is therefore expected
to peak at zero with a Gaussian shape given by the resolution function. Its
width is determined in bins of the uncertainty on the decay time provided by
the kinematic fit of the decay chain. A second-order polynomial is used to
describe the measured width as a function of the decay-time uncertainty. The
average resolution of $54.9\pm 0.4\text{\,}\mathrm{fs}$ is used as the width
of the Gaussian resolution function $\mathcal{R}(t^{\prime}-t)$. The
efficiency function $\epsilon(t)$ is modelled by segments of cubic b-splines
[40] with nine free parameters in total.

The free parameters of the fit are the $S_{f}$ and $S_{\bar{f}}$ coefficients,
the detection and production asymmetries $A_{\rm{D}}$ and $A_{\rm{P}}$, the
seven pairs of parameters $(p_{i},\Delta p_{i})$ for the calibration functions
of the OS and SS taggers, their efficiencies $\varepsilon_{\text{OS}}$ and
$\varepsilon_{\text{SS}}$, and the nine parameters of $\epsilon(t)$. The
average ${B}^{0}$ decay width, $\Gamma$ in Eq. (1), is constrained by means of
a Gaussian function whose mean is the world average value and whose width is
the uncertainty [6]. Similarly, the ${B}^{0}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mixing frequency, $\Delta m$,
is constrained to the value measured in Ref. [41].

The fit determines $\mbox{$S_{f}$}=\mbox{$0.058$}\pm 0.021$ and
$\mbox{$S_{\bar{f}}$}=\mbox{$0.038$}\pm 0.021$ where the uncertainties include
the contributions from the constraints on the decay width and mixing
frequency. When the fit is repeated by fixing ${\Delta m}$ and $\Gamma$ to the
central values used in the constraints, the central values for $S_{f}$ and
$S_{\bar{f}}$ do not change and their uncertainties decrease to $0.020$. This
is considered as the statistical uncertainty for both $S_{f}$ and
$S_{\bar{f}}$. The statistical correlation between $S_{f}$ and $S_{\bar{f}}$
is 60%. This correlation is introduced by the flavour tagging and by the
production asymmetry. The distribution of the decay time with the overlaid
projection of the fit is shown in Fig. 3.

Figure 3:  Background-subtracted decay-time distribution for tagged
candidates. The solid blue curve is the projection of the signal PDF. The red
dotted curve indicates the efficiency function $\varepsilon\left(t\right)$ in
arbitrary units.

The values reported for $S_{f}$ and $S_{\bar{f}}$ result in a significance of
$2.7\sigma$ for the $C\\!P$-violation hypothesis, according to Wilks’ theorem.
Figure 4 reports the decay-time-dependent signal-yield asymmetries between
candidates tagged as ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$, for the decays split according
to the favoured (F) $\bar{b}\rightarrow\bar{c}u\bar{d}$ and the suppressed (S)
$\bar{b}\rightarrow\bar{u}c\bar{d}$ transitions

$\displaystyle A_{\text{F}}$ $\displaystyle=\frac{\Gamma_{{{B}^{0}}\rightarrow
f}(t)-\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}\rightarrow\bar{f}}(t)}{\Gamma_{{{B}^{0}}\rightarrow
f}(t)+\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}\rightarrow\bar{f}}(t)}$ (12)
$\displaystyle A_{\text{S}}$ $\displaystyle=\frac{\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}\rightarrow
f}(t)-\Gamma_{{{B}^{0}}\rightarrow\bar{f}}(t)}{\Gamma_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}}\rightarrow
f}(t)+\Gamma_{{{B}^{0}}\rightarrow\bar{f}}(t)}.$ (13)

The fit projections are overlaid to the asymmetries of the data, along with
the curves expected when $\mbox{$S_{\bar{f}}$}=-\mbox{$S_{f}$}$ is imposed,
i.e. in the hypothesis of no $C\\!P$ violation.

Figure 4:  Decay-time-dependent signal-yield asymmetries for (left) the
favoured and (right) the suppressed decays. The signal-yield asymmetries are
defined in Eq. (12) and Eq. (13). The blue solid curve is the projection of
the signal PDF, the red dotted curve indicates the projection of the fit when
$C\\!P$ conservation is imposed.

Several consistency checks are made by performing the fit on subsets of the
data sample split according to different data-taking conditions, tagging
algorithms, number of tracks in the event, and trigger requirements. These
fits show good agreement with the result presented here. The stability of the
result is also analysed in bins of the transverse momentum of the ${B}^{0}$
meson and in bins of the difference of pseudorapidity between the ${D}^{-}$
candidate and the companion pion.

The production asymmetry and the detection asymmetry are compared with results
of independent LHCb measurements. The values found in this analysis are
$A_{\rm{P}}=(-0.64\pm 0.28)\%$ and $A_{\rm{D}}=(0.86\pm 0.19)\%$, where the
uncertainties are statistical, in agreement with those derived from Ref. [39],
when accounting for the different kinematics of the signals.

The values of the flavour-tagging parameters are also determined in control
samples. The ${{B}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{+}}$ decay is used for
the OS tagger. As the quarks that accompany the ${b}$ quark in ${{B}^{+}}$ and
${{B}^{0}}$ mesons differ, the SS calibration function is studied with
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*0}}$
decays from a sample that is disjoint to that used in the training of the BDT
classifiers. In both cases, distributions of $p_{\mathrm{T}}$ and
pseudorapidity of the ${{B}^{0}}$ candidate, number of tracks and PVs in the
event, and the composition of software trigger decisions are weighted to match
those of the ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ signal sample. In the
case of the ${{B}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{+}}$ mode, the decay-
time distribution of the ${B}^{+}$ and ${D}^{0}$ mesons are also weighted to
match those of the ${B}^{0}$ and ${D}^{-}$ mesons of the signal decays, while
in the case of the ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*0}}$ decay the azimuthal angle of the ${B}^{0}$ is weighted to
match that of the ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ signal sample. The
charged pion produced in ${{B}^{+}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{+}}$ decays directly
identifies the ${B}^{+}$ flavour at production. Therefore, the calibration of
the OS tagger is achieved by counting the number of correctly and incorrectly
tagged signal candidates. In contrast, the SS tagger calibration with
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*0}}$
decays requires the ${{B}^{0}}$–${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ flavour oscillations to be
resolved by using the decay time as an additional observable, since the
amplitude of the observed oscillation is related to the mistag fraction [35].
The values of the calibration parameters found in the control decays are in
agreement with those determined in the fit to the signal, with the largest
deviation being of $2$ standard deviations for two of the $\Delta p_{i}$
parameters.

##  7 Systematic uncertainties

Systematic uncertainties due to external measurements used in the fit are
accounted for through Gaussian constraints in the likelihood function. These
parameters are the mixing frequency, ${\Delta m}$, and the ${B}^{0}$ decay
width, $\Gamma$. In order to disentangle these contributions from the
statistical uncertainty of $S_{f}$ and $S_{\bar{f}}$, the fit is repeated by
fixing ${\Delta m}$ and $\Gamma$ to the central values used in the
constraints. The systematic uncertainty due to the constraint on $\Gamma$ is
found to be negligible, and that due to $\Delta m$ is $0.0073$ and $0.0061$
for $S_{f}$ and $S_{\bar{f}}$, respectively. These are the largest systematic
uncertainties of $S_{f}$ and $S_{\bar{f}}$ and are found to be fully
anticorrelated. The correlation of $\Delta m$ with $S_{f}$ is $-34\%$ and that
with $S_{\bar{f}}$ is $29\%$.

Validation of the entire analysis using ensembles of simulated signal
candidates shows that the values of $S_{f}$ and $S_{\bar{f}}$ are biased up to
$0.0068$ and $0.0018$, respectively. The size of these potential biases are
small and so are taken as a systematic uncertainty. The correlation of these
systematic uncertainties is $40\%$.

Variation of the fit to the ${{D}^{-}}{{\pi}^{+}}$ invariant-mass distribution
used to calculate the _sWeights_ for the background subtraction leads to
systematic uncertainties on $S_{f}$ and $S_{\bar{f}}$ of $0.0042$ and
$0.0023$, respectively. Their correlation is 70%.

The remaining systematic uncertainties are much smaller than those reported
above. Hence, the correlation between the systematic uncertainty of $S_{f}$
and $S_{\bar{f}}$ for the sources that follow are neglected. The systematic
uncertainties associated with the PID efficiencies used in the fit to the
${{D}^{-}}{{\pi}^{+}}$ invariant mass are also propagated by means of Gaussian
constraints. These uncertainties take into account the size of the calibration
samples and the dependence of the results on the binning scheme adopted for
weighting the kinematic distributions of the particles of the control decays
to match those of the companion tracks. They contribute an uncertainty of
$0.0008$ to both $S_{f}$ and $S_{\bar{f}}$.

The other sources of systematic uncertainty are calculated by means of
pseudoexperiments, where samples of the same size as the data are generated by
sampling the PDF with parameters fixed to the value found in data. In the
generation of the pseudoexperiments the PDF is modified to consider
alternative models according to the source of systematic uncertainty under
investigation. The generated sample is then fit with the nominal model. For
each parameter, the mean of the distribution of the residuals is considered,
$(S_{i}^{\textrm{gen}}-S_{i}^{\textrm{fit}})$, from $1000$ pseudoexperiments
as the systematic uncertainty. If the mean differs from zero by less than one
standard deviation, the error on the mean is taken as the systematic
uncertainty.

To test the impact of the choice of the calibration models, pseudoexperiments
are generated using for the SS calibration the nominal model, while for the OS
the degree of the polynomial used in the model is reduced by one unit compared
to the nominal model. In the fit for both taggers the degrees of the
calibration models are increased by one degree compared to that used to
generate the pseudoexperiments. The systematic uncertainties are determined to
be $0.0008$ and $0.0016$ for $S_{f}$ and $S_{\bar{f}}$, respectively.

Assuming values for the flavour-tagging efficiency asymmetries different from
zero, based on what is found in simulation, leads to systematic uncertainties
of $0.0012$ and $0.0015$ for $S_{f}$ and $S_{\bar{f}}$, respectively.

A different decay-time acceptance model is used in generation by considering
new boundaries of the subranges of the spline functions. This results in a
systematic uncertainty of $0.0007$ for both $S_{f}$ and $S_{\bar{f}}$.

Mismodelling of the decay-time resolution is also considered by increasing and
decreasing the nominal resolution by $20\mathrm{\,fs}$. The largest residuals
are considered as the systematic uncertainties, and are $0.0012$ and $0.0008$
for $S_{f}$ and $S_{\bar{f}}$, respectively.

A value for $C_{f}=-C_{\bar{f}}$ different from 1, based on the value of
$r_{D\pi}$ from Refs. [4, 5] is assumed, resulting in a variation of $0.0006$
for both $S_{f}$ and $S_{\bar{f}}$. By assigning to $\Delta\Gamma$ a value
different from zero and equal to the world-average value plus its uncertainty
[6] leads to a systematic uncertainty of $0.0007$ on both $S_{f}$ and
$S_{\bar{f}}$.

The sources of systematic uncertainties are summarised in Table 1. They total
$0.011$ and $0.007$ for $S_{f}$ and $S_{\bar{f}}$, respectively, with a
correlation of $-41\%$.

Table 1: Systematic uncertainties on the $C\\!P$ asymmetries $S_{f}$ and $S_{\bar{f}}$. The total uncertainty is the sum in quadrature of the individual contributions. Source | $S_{f}$ | $S_{\bar{f}}$
---|---|---
uncertainty of $\Delta m$ | $0.0073$ | $0.0061$
fit biases | $0.0068$ | $0.0018$
background subtraction | $0.0042$ | $0.0023$
PID efficiencies | $0.0008$ | $0.0008$
flavour-tagging models | $0.0011$ | $0.0015$
flavour-tagging efficiency asymmetries | $0.0012$ | $0.0015$
$\epsilon(t)$ model | $0.0007$ | $0.0007$
assumption on $\Delta\Gamma$ | $0.0007$ | $0.0007$
decay-time resolution | $0.0012$ | $0.0008$
assumption on $C$ | $0.0006$ | $0.0006$
total | 0.0111 | 0.0073
statistical uncertainty | 0.0198 | 0.0199

##  8 Interpretation of the ${C\\!P}$ asymmetries

The values of $S_{f}$ and $S_{\bar{f}}$ are interpreted in terms of the angle
$2\beta+\gamma$, the ratio of amplitudes $r_{D\pi}$, and the strong phase
$\delta$, using the statistical method described in Ref. [7].

By taking external measurements of $r_{D\pi}$, confidence intervals for
$|\sin(2\beta+\gamma)|$ and $\delta$ are derived. The ratio $r_{D\pi}$ is
calculated from the branching fraction of
${{B}^{0}}\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$ decays, assuming SU(3)
symmetry, following the same relation used in Refs. [5, 4]:

$r_{D\pi}=\tan\theta_{c}\frac{f_{D^{+}}}{f_{D_{s}}}\sqrt{\frac{\mathcal{B}({{B}^{0}}\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})}{\mathcal{B}({{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}})}},$
(14)

where $\tan\theta_{c}=0.23101\pm 0.00032$ is the tangent of the Cabibbo angle
from Ref. [42], $f_{D_{s}}/f_{D^{+}}=1.173\pm 0.003$ is the ratio of decay
constants [43, 44, 45], and
$\mathcal{B}({{B}^{0}}\rightarrow{{D}^{+}_{s}}{{\pi}^{-}})=(2.16\pm
0.26)\times 10^{-5}$ and
$\mathcal{B}({{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}})=(2.52\pm 0.13)\times
10^{-3}$ are branching fractions taken from Ref. [25]. We determine
$r_{D\pi}=0.0182\pm 0.0012\pm 0.0036$, where the second uncertainty accounts
for possible nonfactorizable SU(3)-breaking effects, considered to be 20% of
the value of $r_{D\pi}$ as suggested in Ref. [46]. In addition, using the
known value of $\beta=(22.2\pm 0.7)^{\circ}$ [6], confidence intervals for
$\gamma$ are determined.

The confidence intervals are

$\displaystyle|\sin(2\beta+\gamma)|\in\mbox{$[0.77,1.0]$}\,,$
$\displaystyle\gamma\in\mbox{$\mbox{$[5,86]$}^{\circ}\cup\mbox{$[185,266]$}^{\circ}$}\,,$
$\displaystyle\delta\in\mbox{$\mbox{$[-41,41]$}^{\circ}\cup\mbox{$[140,220]$}^{\circ}$}\,,$

all at the 68% confidence level (CL). The uncertainties on $r_{D\pi}$ and
$\beta$ have a negligible impact on these values. The intervals are
illustrated in Figs. 5 and 6.

Figure 5: 1–CL as a function of $|\sin(2\beta+\gamma)|$.

Figure 6: (Left) 1–CL as a function of $\gamma$ and (right) confidence regions
for $\gamma$ and $\delta$. The confidence regions hold the $39\%$ and $87\%$
CL. Points denote the preferred values.

##  9 Conclusion

A measurement of the ${C\\!P}$ asymmetries $S_{f}$ and $S_{\bar{f}}$ in the
decay ${{B}^{0}}\rightarrow{D}^{\mp}\pi^{\pm}$ is reported. The decay
candidates are reconstructed in a data set collected with the LHCb experiment
at centre-of-mass energies of $7$ and $8\mathrm{\,Te\kern-1.00006ptV}$,
corresponding to an integrated luminosity of $3.0\mbox{\,fb}^{-1}$. We measure

$S_{f}$
$\displaystyle=\mbox{$0.058$}\pm\mbox{$0.020$}\mathrm{\,(stat)}\pm\mbox{$0.011$}\mathrm{\,(syst)},$
$S_{\bar{f}}$
$\displaystyle=\mbox{$0.038$}\pm\mbox{$0.020$}\mathrm{\,(stat)}\pm\mbox{$0.007$}\mathrm{\,(syst)},$

with a correlation of $60\%$ ($-41\%$) between the statistical (systematic)
uncertainties. These values are in agreement with, and more precise than,
measurements from the Belle and BaBar collaborations [9, 10]. This
measurement, in combination with the external inputs of $r_{D\pi}$ and
$\beta$, constrains the CKM angle $\gamma$ to be in the interval
$\mbox{$[5,86]$}^{\circ}\cup\mbox{$[185,266]$}^{\circ}$ at the 68% confidence
level.

## 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 (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing
resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany),
INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),
RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF
(Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities
behind the multiple open-source software packages on which we depend.
Individual groups or members have received support from AvH Foundation
(Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
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] I. Dunietz and R. G. Sachs, _Asymmetry between inclusive charmed and anticharmed modes in ${B}^{0}$, $\bar{B}^{0}$ decay as a measure of CP violation_, Phys. Rev. D37 (1988) 3186, Erratum ibid. D39 (1989) 3515
  * [2] R. Aleksan, I. Dunietz, and B. Kayser, _Determining the CP violating phase $\gamma$_, Z. Phys. C54 (1992) 653
  * [3] R. Fleischer, _New strategies to obtain insights into CP violation through $B_{(s)}\rightarrow D_{(s)}^{\pm}K^{\mp}$, $D_{(s)}^{*\pm}K^{\mp}$, … and $B_{(d)}\rightarrow D^{\pm}\pi^{\mp}$, $D^{*\pm}\pi^{\mp}$, … decays_, Nucl. Phys. B671 (2003) 459, arXiv:hep-ph/0304027
  * [4] BaBar collaboration, B. Aubert et al., _Measurement of the branching fractions of the rare decays $B^{0}\rightarrow D_{s}^{(*)+}\pi^{-}$, $B^{0}\rightarrow D_{s}^{(*)+}\rho^{-}$, and $B^{0}\rightarrow D_{s}^{(*)-}K^{(*)+}$_, Phys. Rev. D78 (2008) 032005, arXiv:0803.4296
  * [5] Belle collaboration, A. Das et al., _Measurements of branching fractions for $B^{0}\rightarrow D_{s}^{+}\pi^{-}$ and ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow D_{s}^{+}K^{-}$_, Phys. Rev. D82 (2010) 051103, arXiv:1007.4619
  * [6] Heavy Flavor Averaging Group, Y. Amhis et al., _Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016_, Eur. Phys. J. C77 (2017) 895, arXiv:1612.07233, updated results and plots available at https://hflav.web.cern.ch
  * [7] LHCb collaboration, R. Aaij et al., _Measurement of the CKM angle $\gamma$ from a combination of LHCb results_, JHEP 12 (2016) 087, arXiv:1611.03076
  * [8] BaBar collaboration, B. Aubert et al., _Measurement of time-dependent CP-violating asymmetries and constraints on $sin(2\beta+\gamma)$ with partial reconstruction of $B\rightarrow D^{*\mp}\pi^{\pm}$ decays_, Phys. Rev. D71 (2005) 112003, arXiv:hep-ex/0504035
  * [9] BaBar collaboration, B. Aubert et al., _Measurement of time-dependent CP asymmetries in $B^{0}\rightarrow D^{(*)\pm}\pi^{\mp}$ and $B^{0}\rightarrow D^{\pm}\rho^{\mp}$ decays_, Phys. Rev. D73 (2006) 111101, arXiv:hep-ex/0602049
  * [10] Belle collaboration, F. J. Ronga et al., _Measurement of CP violation in ${B}^{0}\rightarrow D^{*-}\pi^{+}$ and ${B}^{0}\rightarrow D^{-}\pi^{+}$ decays_, Phys. Rev. D73 (2006) 092003, arXiv:hep-ex/0604013
  * [11] Belle collaboration, S. Bahinipati et al., _Measurements of time-dependent CP asymmetries in $B\rightarrow D^{*\mp}\pi^{\pm}$ decays using a partial reconstruction technique_, Phys. Rev. D84 (2011) 021101, arXiv:1102.0888
  * [12] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [13] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [14] R. Aaij et al., _Performance of the LHCb Vertex Locator_ , JINST 9 (2014) P09007, arXiv:1405.7808
  * [15] R. Arink et al., _Performance of the LHCb Outer Tracker_ , JINST 9 (2014) P01002, arXiv:1311.3893
  * [16] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [17] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [18] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [19] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [20] 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
  * [21] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [22] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [23] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [24] V. V. Gligorov and M. Williams, _Efficient, reliable and fast high-level triggering using a bonsai boosted decision tree_ , JINST 8 (2013) P02013, arXiv:1210.6861
  * [25] Particle Data Group, C. Patrignani et al., _Review of particle physics_ , Chin. Phys. C40 (2016) 100001, and 2017 update
  * [26] W. D. Hulsbergen, _Decay chain fitting with a Kalman filter_ , Nucl. Instrum. Meth. A552 (2005) 566, arXiv:physics/0503191
  * [27] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
  * [28] Y. Freund and R. E. Schapire, _A decision-theoretic generalization of on-line learning and an application to boosting_ , J. Comput. Syst. Sci. 55 (1997) 119
  * [29] D. Martínez Santos and F. Dupertuis, _Mass distributions marginalized over per-event errors_ , Nucl. Instrum. Meth. A764 (2014) 150, arXiv:1312.5000
  * [30] N. L. Johnson, _Systems of frequency curves generated by methods of translation_ , Biometrika 36 (1949) 149
  * [31] L. Anderlini et al., _The PIDCalib package_ , LHCb-PUB-2016-021
  * [32] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [33] LHCb collaboration, R. Aaij et al., _Opposite-side flavour tagging of ${B}$ mesons at the LHCb experiment_, Eur. Phys. J. C72 (2012) 2022, arXiv:1202.4979
  * [34] LHCb collaboration, R. Aaij et al., _${B}$ flavour tagging using charm decays at the LHCb experiment_, JINST 10 (2015) P10005, arXiv:1507.07892
  * [35] LHCb collaboration, R. Aaij et al., _New algorithms for identifying the flavour of ${{B}^{0}}$ mesons using pions and protons_, Eur. Phys. J. C77 (2017) 238, arXiv:1610.06019
  * [36] A. Agresti, Categorical data analysis, Wiley Series in Probability and Statistics, 2013
  * [37] T. Hastie, R. Tibshirani, and J. Friedman, The elements of statistical learning, Springer Series in Statistics, 2001
  * [38] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ asymmetry in $B^{0}_{s}\rightarrow D_{s}^{\mp}K^{\pm}$ decays_, arXiv:1712.07428, submitted to JHEP
  * [39] LHCb collaboration, R. Aaij et al., _Measurement of ${B}^{0}$, ${B}^{0}_{s}$, ${{B}^{+}}$ and ${\mathchar 28931\relax}^{0}_{b}$ production asymmetries in $7$ and $8~{}\rm TeV$ $pp$ collisions_, Phys. Lett. B774 (2017) 139, arXiv:1703.08464
  * [40] C. de Boor, A practical guide to splines (revised edition), Springer, New York, NY, USA, 2001
  * [41] LHCb collaboration, R. Aaij et al., _A precise measurement of the ${{B}^{0}}$ meson oscillation frequency_, Eur. Phys. J. C76 (2016) 412, arXiv:1604.03475
  * [42] CKMfitter group, J. Charles et al., _$C\\!P$ violation and the CKM matrix: Assessing the impact of the asymmetric $B$ factories_, Eur. Phys. J. C41 (2005) 1, arXiv:hep-ph/0406184, updated results and plots available at http://ckmfitter.in2p3.fr/
  * [43] S. Aoki et al., _Review of lattice results concerning low-energy particle physics_ , Eur. Phys. J. C77 (2017), no. 2 112, arXiv:1607.00299
  * [44] Fermilab Lattice, MILC, A. Bazavov et al., _Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks_ , Phys. Rev. D90 (2014) 074509, arXiv:1407.3772
  * [45] N. Carrasco et al., _Leptonic decay constants $f_{K},f_{D},$ and $f_{{D}_{s}}$ with $N_{f}=2+1+1$ twisted-mass lattice QCD_, Phys. Rev. D91 (2015) 054507, arXiv:1411.7908
  * [46] K. De Bruyn et al., _Exploring $B_{s}\rightarrow D_{s}^{(*)\pm}K^{\mp}$ decays in the presence of a sizable width difference $\Delta\Gamma_{s}$_, Nucl. Phys. B868 (2013) 351, arXiv:1208.6463

LHCb collaboration

R. Aaij43, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, P.
Albicocco18, J. Albrecht10, F. Alessio40, M. Alexander53, A. Alfonso Albero38,
S. Ali43, G. Alkhazov31, P. Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S.
Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G. Andreassi41, M. Andreotti16,g,
J.E. Andrews60, R.B. Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6,
A. Artamonov37, M. Artuso61, E. Aslanides6, M. Atzeni42, G. Auriemma26, S.
Bachmann12, J.J. Back50, S. Baker55, V. Balagura7,b, W. Baldini16, A.
Baranov35, R.J. Barlow56, S. Barsuk7, W. Barter56, F. Baryshnikov32, V.
Batozskaya29, V. Battista41, A. Bay41, J. Beddow53, F. Bedeschi24, I.
Bediaga1, A. Beiter61, L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli20,i, K.
Belous37, I. Belyaev32,40, E. Ben-Haim8, G. Bencivenni18, S. Benson43, S.
Beranek9, A. Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A.
Bertolin23, C. Betancourt42, F. Betti15,40, M.O. Bettler49, M. van Beuzekom43,
Ia. Bezshyiko42, S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bizzeti17,u, M.
Bjørn57, T. Blake50, F. Blanc41, S. Blusk61, V. Bocci26, O. Boente Garcia39,
T. Boettcher58, A. Bondar36,w, N. Bondar31, S. Borghi56,40, M. Borisyak35, M.
Borsato39,40, F. Bossu7, M. Boubdir9, T.J.V. Bowcock54, E. Bowen42, C.
Bozzi16,40, S. Braun12, M. Brodski40, J. Brodzicka27, D. Brundu22, E.
Buchanan48, C. Burr56, A. Bursche22, J. Buytaert40, W. Byczynski40, S.
Cadeddu22, H. Cai64, R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo
Gomez38,m, A. Camboni38,m, P. Campana18, D.H. Campora Perez40, 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. Cattaneo40, G.
Cavallero19,h, R. Cenci24,p, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen22, S.-G.
Chitic40, V. Chobanova39, M. Chrzaszcz40, A. Chubykin31, P. Ciambrone18, X.
Cid Vidal39, G. Ciezarek40, P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J.
Closier40, V. Coco40, J. Cogan6, E. Cogneras5, V. Cogoni22,f, L. Cojocariu30,
P. Collins40, T. Colombo40, A. Comerma-Montells12, A. Contu22, G. Coombs40, S.
Coquereau38, G. Corti40, M. Corvo16,g, C.M. Costa Sobral50, B. Couturier40,
G.A. Cowan52, D.C. Craik58, A. Crocombe50, M. Cruz Torres1, R. Currie52, C.
D’Ambrosio40, F. Da Cunha Marinho2, C.L. Da Silva73, E. Dall’Occo43, J.
Dalseno48, A. Danilina32, A. Davis3, O. De Aguiar Francisco40, K. De Bruyn40,
S. De Capua56, M. De Cian41, 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. Dendek28, D. Derkach35, O. Deschamps5, F.
Dettori54, B. Dey65, A. Di Canto40, P. Di Nezza18, S. Didenko69, H.
Dijkstra40, F. Dordei40, M. Dorigo40, A. Dosil Suárez39, L. Douglas53, A.
Dovbnya45, K. Dreimanis54, L. Dufour43, G. Dujany8, P. Durante40, J.M.
Durham73, D. Dutta56, R. Dzhelyadin37, M. Dziewiecki12, A. Dziurda40, A.
Dzyuba31, S. Easo51, U. Egede55, V. Egorychev32, S. Eidelman36,w, S.
Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53, S. Ely61, A.
Ene30, S. Escher9, S. Esen43, H.M. Evans49, T. Evans57, A. Falabella15, N.
Farley47, S. Farry54, D. Fazzini20,40,i, L. Federici25, G. Fernandez38, P.
Fernandez Declara40, A. Fernandez Prieto39, F. Ferrari15, L. Ferreira Lopes41,
F. Ferreira Rodrigues2, M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M.
Fiorini16,g, M. Firlej28, C. Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, M.
Fontana22,40, F. Fontanelli19,h, R. Forty40, V. Franco Lima54, M. Frank40, C.
Frei40, J. Fu21,q, W. Funk40, C. Färber40, E. Gabriel52, A. Gallas Torreira39,
D. Galli15,e, S. Gallorini23, S. Gambetta52, M. Gandelman2, P. Gandini21, Y.
Gao3, L.M. Garcia Martin71, B. Garcia Plana39, J. García Pardiñas42, J. Garra
Tico49, L. Garrido38, D. Gascon38, C. Gaspar40, L. Gavardi10, G. Gazzoni5, D.
Gerick12, E. Gersabeck56, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41,
V. Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V. Gligorov8, D.
Golubkov32, A. Golutvin55,69, A. Gomes1,a, I.V. Gorelov33, C. Gotti20,i, E.
Govorkova43, J.P. Grabowski12, R. Graciani Diaz38, L.A. Granado Cardoso40, E.
Graugés38, E. Graverini42, G. Graziani17, A. Grecu30, R. Greim43, P.
Griffith22, L. Grillo56, L. Gruber40, B.R. Gruberg Cazon57, O. Grünberg67, E.
Gushchin34, Yu. Guz37,40, T. Gys40, C. Göbel62, T. Hadavizadeh57, C.
Hadjivasiliou5, G. Haefeli41, C. Haen40, S.C. Haines49, B. Hamilton60, X.
Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57, S.T. Harnew48, C.
Hasse40, M. Hatch40, J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K.
Hennessy54, L. Henry71, E. van Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57,
P.H. Hopchev41, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen43, T.
Humair55, M. Hushchyn35, D. Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten47,
K. Ivshin31, R. Jacobsson40, J. Jalocha57, E. Jans43, A. Jawahery60, F.
Jiang3, M. John57, D. Johnson40, C.R. Jones49, C. Joram40, B. Jost40, N.
Jurik57, S. Kandybei45, M. Karacson40, J.M. Kariuki48, S. Karodia53, N.
Kazeev35, M. Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel44, E.
Khairullin35, B. Khanji12, C. Khurewathanakul41, K.E. Kim61, T. Kirn9, S.
Klaver18, K. Klimaszewski29, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R.
Kopecna12, P. Koppenburg43, S. Kotriakhova31, M. Kozeiha5, L. Kravchuk34, M.
Kreps50, F. Kress55, P. Krokovny36,w, W. Krupa28, W. Krzemien29, W.
Kucewicz27,l, M. Kucharczyk27, V. Kudryavtsev36,w, A.K. Kuonen41, T.
Kvaratskheliya32,40, D. Lacarrere40, G. Lafferty56, A. Lai22, G. Lanfranchi18,
C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A. Leflat33,40, J.
Lefrançois7, R. Lefèvre5, F. Lemaitre40, O. Leroy6, T. Lesiak27, B.
Leverington12, P.-R. Li63, T. Li3, Z. Li61, X. Liang61, T. Likhomanenko68, R.
Lindner40, F. Lionetto42, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi22, I.
Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39, A. Lupato23,
E. Luppi16,g, O. Lupton40, A. Lusiani24, X. Lyu63, F. Machefert7, F. Maciuc30,
V. Macko41, P. Mackowiak10, S. Maddrell-Mander48, O. Maev31,40, K. Maguire56,
D. Maisuzenko31, M.W. Majewski28, S. Malde57, B. Malecki27, A. Malinin68, T.
Maltsev36,w, G. Manca22,f, G. Mancinelli6, D. Marangotto21,q, J. Maratas5,v,
J.F. Marchand4, U. Marconi15, C. Marin Benito38, M. Marinangeli41, P.
Marino41, J. Marks12, G. Martellotti26, M. Martin6, M. Martinelli41, D.
Martinez Santos39, F. Martinez Vidal71, A. Massafferri1, R. Matev40, A.
Mathad50, Z. Mathe40, C. Matteuzzi20, A. Mauri42, E. Maurice7,b, B. Maurin41,
A. Mazurov47, M. McCann55,40, A. McNab56, R. McNulty13, J.V. Mead54, B.
Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D. Melnychuk29, M. Merk43, A.
Merli21,q, E. Michielin23, D.A. Milanes66, E. Millard50, M.-N. Minard4, L.
Minzoni16,g, D.S. Mitzel12, A. Mogini8, J. Molina Rodriguez1,y, T.
Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, G. Morello18, M.J.
Morello24,t, O. Morgunova68, J. Moron28, A.B. Morris6, R. Mountain61, F.
Muheim52, M. Mulder43, D. Müller40, J. Müller10, K. Müller42, V. Müller10, P.
Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57, I. Nasteva2, M. Needham52,
N. Neri21, S. Neubert12, N. Neufeld40, M. Neuner12, T.D. Nguyen41, C. Nguyen-
Mau41,n, S. Nieswand9, R. Niet10, N. Nikitin33, A. Nogay68, D.P. O’Hanlon15,
A. Oblakowska-Mucha28, V. Obraztsov37, S. Ogilvy18, R. Oldeman22,f, C.J.G.
Onderwater72, A. Ossowska27, J.M. Otalora Goicochea2, P. Owen42, A.
Oyanguren71, P.R. Pais41, A. Palano14, M. Palutan18,40, G. Panshin70, A.
Papanestis51, M. Pappagallo52, L.L. Pappalardo16,g, W. Parker60, C. Parkes56,
G. Passaleva17,40, A. Pastore14, M. Patel55, C. Patrignani15,e, A. Pearce40,
A. Pellegrino43, G. Penso26, M. Pepe Altarelli40, S. Perazzini40, D.
Pereima32, P. Perret5, L. Pescatore41, K. Petridis48, A. Petrolini19,h, A.
Petrov68, M. Petruzzo21,q, B. Pietrzyk4, G. Pietrzyk41, M. Pikies27, D.
Pinci26, F. Pisani40, A. Pistone19,h, A. Piucci12, V. Placinta30, S.
Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener18, A. Poluektov50, N.
Polukhina69,c, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce40, A.
Popov37, D. Popov11,40, S. Poslavskii37, C. Potterat2, E. Price48, J.
Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig Navarro42, H. Pullen57, G.
Punzi24,p, W. Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal28,
J.H. Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, F.
Ratnikov35,x, G. Raven44, M. Ravonel Salzgeber40, M. Reboud4, F. Redi41, S.
Reichert10, A.C. dos Reis1, C. Remon Alepuz71, V. Renaudin7, S. Ricciardi51,
S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B. Rodrigues41, E.
Rodrigues59, J.A. Rodriguez Lopez66, A. Rogozhnikov35, S. Roiser40, A.
Rollings57, V. Romanovskiy37, A. Romero Vidal39,40, M. Rotondo18, T. Ruf40, J.
Ruiz Vidal71, J.J. Saborido Silva39, N. Sagidova31, B. Saitta22,f, V.
Salustino Guimaraes62, C. Sanchez Mayordomo71, B. Sanmartin Sedes39, R.
Santacesaria26, C. Santamarina Rios39, M. Santimaria18, E. Santovetti25,j, G.
Sarpis56, A. Sarti18,k, C. Satriano26,s, A. Satta25, D. Savrina32,33, S.
Schael9, M. Schellenberg10, M. Schiller53, H. Schindler40, M. Schmelling11, T.
Schmelzer10, B. Schmidt40, O. Schneider41, A. Schopper40, H.F. Schreiner59, M.
Schubiger41, M.H. Schune7, R. Schwemmer40, B. Sciascia18, A. Sciubba26,k, A.
Semennikov32, E.S. Sepulveda8, A. Sergi47,40, N. Serra42, J. Serrano6, L.
Sestini23, P. Seyfert40, M. Shapkin37, Y. Shcheglov31,†, T. Shears54, L.
Shekhtman36,w, V. Shevchenko68, B.G. Siddi16, R. Silva Coutinho42, L. Silva de
Oliveira2, G. Simi23,o, S. Simone14,d, N. Skidmore12, T. Skwarnicki61, I.T.
Smith52, M. Smith55, l. Soares Lavra1, M.D. Sokoloff59, F.J.P. Soler53, B.
Souza De Paula2, B. Spaan10, P. Spradlin53, F. Stagni40, M. Stahl12, S.
Stahl40, P. Stefko41, S. Stefkova55, O. Steinkamp42, S. Stemmle12, O.
Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B. Storaci42, S.
Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U. Straumann42, S. Strokov70,
J. Sun3, L. Sun64, K. Swientek28, V. Syropoulos44, T. Szumlak28, M.
Szymanski63, S. T’Jampens4, Z. Tang3, A. Tayduganov6, T. Tekampe10, G.
Tellarini16, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J. Tilley55, V.
Tisserand5, M. Tobin41, S. Tolk40, L. Tomassetti16,g, D. Tonelli24, R.
Tourinho Jadallah Aoude1, E. Tournefier4, M. Traill53, M.T. Tran41, M.
Tresch42, A. Trisovic49, A. Tsaregorodtsev6, A. Tully49, N. Tuning43,40, A.
Ukleja29, A. Usachov7, A. Ustyuzhanin35, U. Uwer12, C. Vacca22,f, A. Vagner70,
V. Vagnoni15, A. Valassi40, S. Valat40, G. Valenti15, R. Vazquez Gomez40, P.
Vazquez Regueiro39, S. Vecchi16, M. van Veghel43, J.J. Velthuis48, M.
Veltri17,r, G. Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M.
Vesterinen57, J.V. Viana Barbosa40, D. Vieira63, M. Vieites Diaz39, H.
Viemann67, X. Vilasis-Cardona38,m, A. Vitkovskiy43, M. Vitti49, V. Volkov33,
A. Vollhardt42, B. Voneki40, A. Vorobyev31, V. Vorobyev36,w, C. Voß9, J.A. de
Vries43, C. Vázquez Sierra43, R. Waldi67, J. Walsh24, J. Wang61, M. Wang3, Y.
Wang65, Z. Wang42, D.R. Ward49, H.M. Wark54, N.K. Watson47, D. Websdale55, A.
Weiden42, C. Weisser58, M. Whitehead9, J. Wicht50, G. Wilkinson57, M.
Wilkinson61, M.R.J. Williams56, M. Williams58, T. Williams47, F.F.
Wilson51,40, J. Wimberley60, M. Winn7, J. Wishahi10, W. Wislicki29, M.
Witek27, G. Wormser7, S.A. Wotton49, K. Wyllie40, D. Xiao65, Y. Xie65, A. Xu3,
M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z. Yang3, Z. Yang60, Y. Yao61, H. Yin65, J.
Yu65,aa, X. Yuan61, O. Yushchenko37, K.A. Zarebski47, M. Zavertyaev11,c, L.
Zhang3, W.C. Zhang3,z, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V.
Zhukov9,33, 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, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
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
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National University of Science and Technology ”MISIS”, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los 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
yEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
zSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
aaPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased