EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-024 LHCb-PAPER-2015-059 11 October 2016

Constraints on the unitarity triangle angle $\gamma$ from Dalitz plot analysis
of ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays

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

The first study is presented of $C\\!P$ violation with an amplitude analysis
of the Dalitz plot of ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays,
with ${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$, ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$. The analysis is based on a data sample corresponding
to $3.0\mbox{\,fb}^{-1}$ of $pp$ collisions collected with the LHCb detector.
No significant $C\\!P$ violation effect is seen, and constraints are placed on
the angle $\gamma$ of the unitarity triangle formed from elements of the
Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated
with the ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$ decay are determined for
the first time. These measurements can be used to improve the sensitivity to
$\gamma$ of existing and future studies of the ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ decay.

Submitted to Phys. Rev. D.

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

##  1 Introduction

One of the most important challenges of physics today is to understand the
origin of the matter-antimatter asymmetry of the Universe. Within the Standard
Model (SM) of particle physics, the $C\\!P$ symmetry between particles and
antiparticles is broken only by the complex phase in the Cabibbo-Kobayashi-
Maskawa (CKM) quark mixing matrix [1, 2]. An important parameter in the CKM
description of the SM flavour structure is
$\gamma\equiv\arg\left[-V_{ud}V_{ub}^{*}/(V_{cd}V_{cb}^{*})\right]$, one of
the three angles of the unitarity triangle formed from CKM matrix elements [3,
4, 5]. Since the SM cannot account for the baryon asymmetry of the Universe
[6] new sources of $C\\!P$ violation, that would show up as deviations from
the SM, are expected. The precise determination of $\gamma$ is necessary in
order to be able to search for such small deviations.

The value of $\gamma$ can be determined from the $C\\!P$-violating
interference between the two amplitudes in, for example,
${{{B}^{+}}}\rightarrow D{{K}^{+}}$ and charge-conjugate decays [7, 8, 9, 10].
Here $D$ denotes a neutral charm meson reconstructed in a final state
accessible to both ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ and
${D}^{0}$ decays, that is therefore a superposition of the ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ and ${D}^{0}$ states produced
through ${b}\rightarrow{c}W$ and ${b}\rightarrow{u}W$ transitions (hereafter
referred to as $V_{cb}$ and $V_{ub}$ amplitudes). This approach has negligible
theoretical uncertainty in the SM [11] but limited data samples are available
experimentally.

A similar method based on ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays
has been proposed [12, 13] to help improve the precision. By studying the
Dalitz plot (DP) [14] distributions of ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${B}^{0}$ decays,
interference between different contributions, such as ${{B}^{0}}\rightarrow
D_{2}^{*}(2460)^{-}{{K}^{+}}$ and ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$
(Feynman diagrams shown in Fig. 1), can be exploited to obtain additional
sensitivity compared to the “quasi-two-body” analysis in which only the region
of the DP dominated by the ${{K}^{*}}(892)^{0}$ resonance is selected [15, 16,
17]. The method is illustrated in Fig. 2, where the relative amplitudes of the
different channels are sketched in the complex plane. The
${{B}^{0}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{*0}}$ ($V_{cb}$) amplitude
is determined, relative to that for ${{B}^{0}}\rightarrow D_{2}^{*-}{{K}^{+}}$
decays, from analysis of the Dalitz plot with the neutral $D$ meson
reconstructed in a favoured decay mode such as ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$.
The $V_{ub}$ amplitude can then be obtained from the difference in this
relative amplitude compared to the $V_{cb}$ only case when the neutral $D$
meson is reconstructed as a $C\\!P$ eigenstate. A non-zero value of $\gamma$
causes different relative amplitudes for ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays, and hence $C\\!P$
violation. The method allows the determination of $\gamma$ and the hadronic
parameters $r_{B}$ and $\delta_{B}$, which are the relative magnitude and
strong (i.e. $C\\!P$-conserving) phase of the $V_{ub}$ and $V_{cb}$ amplitudes
for the ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decay, with only $C\\!P$-even $D$
decays required to be reconstructed in addition to the favoured decays. This
feature, which is in constrast to the method of Refs. [7, 8] that requires
samples of both $C\\!P$-even and $C\\!P$-odd $D$ decays, is important for
analysis of data collected at a hadron collider where reconstruction of $D$
meson decays to $C\\!P$-odd final states such as
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{0}}$ is challenging. The
Dalitz analysis method also has only a single ambiguity
($\gamma\longleftrightarrow\gamma+\pi$,
$\delta_{B}\longleftrightarrow\delta_{B}+\pi$), whereas the method of Refs.
[7, 8] has an eight-fold ambiguity in the determination of $\gamma$.

Figure 1:  Feynman diagrams for the contributions to ${{B}^{0}}\rightarrow
D{{K}^{+}}{{\pi}^{-}}$ from (a) ${{B}^{0}}\rightarrow
D_{2}^{*}(2460)^{-}{{K}^{+}}$, (b) ${{B}^{0}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{*}}(892)^{0}$ and (c)
${{B}^{0}}\rightarrow{{D}^{0}}{{K}^{*}}(892)^{0}$ decays.

Figure 2:  Illustration of the method to determine $\gamma$ from Dalitz plot
analysis of ${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ decays [12, 13]:
(left) the $V_{cb}$ amplitude for ${{B}^{0}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{*0}}$ compared to that for
${{B}^{0}}\rightarrow D_{2}^{*-}{{K}^{+}}$ decay; (right) the effect of the
$V_{ub}$ amplitude that contributes to ${{B}^{0}}\rightarrow
D_{{C\\!P}}{{K}^{*0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow D_{{C\\!P}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ decays provides sensitivity
to $\gamma$. The notation $D_{{C\\!P}}$ represents a neutral $D$ meson
reconstructed in a $C\\!P$ eigenstate, while $D^{*-}_{2\,{C\\!P}}$ denotes the
decay chain $D_{2}^{*-}\rightarrow{D}_{{C\\!P}}{{\pi}^{-}}$, where the charge
of the pion tags the flavour of the neutral $D$ meson, independently of the
mode in which it is reconstructed, so there is no contribution from the
$V_{ub}$ amplitude.

This paper describes the first study of $C\\!P$ violation with a DP analysis
of ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays, with a sample
corresponding to $3.0\mbox{\,fb}^{-1}$ of $pp$ collision data collected with
the LHCb detector at centre-of-mass energies of $7$ and
$8\mathrm{\,Te\kern-1.00006ptV}$. The inclusion of charge conjugate processes
is implied throughout the paper except where discussing asymmetries.

##  2 Detector and simulation

The LHCb detector [18, 19] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter, is measured
with a resolution of $(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$,
where $p_{\mathrm{T}}$ is the component of the momentum transverse to the
beam, in ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged
hadrons are distinguished using information from two ring-imaging Cherenkov
detectors. Photons, electrons and hadrons are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers. The online event selection is performed by a trigger, which consists
of a hardware stage, based on information from the calorimeter and muon
systems, followed by a software stage, in which all charged particles with
$\mbox{$p_{\mathrm{T}}$}>500(300){\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ are
reconstructed for 2011 (2012) data. A detailed description of the trigger
conditions is available in Ref. [20].

Simulated data samples are used to study the response of the detector and to
investigate certain categories of background. In the simulation, $pp$
collisions are generated using Pythia [21, *Sjostrand:2006za] with a specific
LHCb configuration [23]. Decays of hadronic particles are described by EvtGen
[24], in which final-state radiation is generated using Photos [25]. The
interaction of the generated particles with the detector, and its response,
are implemented using the Geant4 toolkit [26, *Agostinelli:2002hh] as
described in Ref. [28].

##  3 Selection

Candidate ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays are selected
with the $D$ meson decaying into the ${{K}^{+}}{{\pi}^{-}}$,
${{K}^{+}}{{K}^{-}}$ or ${{\pi}^{+}}{{\pi}^{-}}$ final state. The selection
requirements are similar to those used for the DP analyses of
${{B}^{0}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{+}}{{\pi}^{-}}$ [29] and
${{B}^{0}_{s}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{-}}{{\pi}^{+}}$ [30, 31]
decays, where in both cases only the ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$
mode was used.

The more copious ${{B}^{0}}\rightarrow{D}{{\pi}^{+}}{{\pi}^{-}}$ modes, with
neutral $D$ meson decays to one of the three final states under study, are
used as control channels to optimise the selection requirements. Loose initial
requirements on the final state tracks and the $D$ and $B$ candidates are used
to obtain a visible peak of ${{B}^{0}}\rightarrow{D}{{\pi}^{+}}{{\pi}^{-}}$
decays. The neutral $D$ meson candidate must satisfy criteria on its invariant
mass, vertex quality and flight distance from any PV and from the $B$
candidate vertex. Requirements on the outputs of boosted decision tree
algorithms that identify neutral $D$ meson decays, in each of the decay chains
of interest, originating from $b$ hadron decays [32, 33] are also applied.
These requirements are sufficient to reduce to negligible levels potential
background from charmless $B$ meson decays that have identical final states
but without an intermediate $D$ meson. Vetoes are applied to remove
backgrounds from ${{B}^{0}}\rightarrow{{D}^{*}}(2010)^{-}{{K}^{+}}$,
${{B}^{0}}\rightarrow{{D}^{\mp}}{{\pi}^{\pm}}$,
${{B}^{0}_{s}}\rightarrow{{D}^{-}_{s}}{{\pi}^{+}}$ and
${{B}^{0}_{({s})}}\rightarrow{{D}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ decays, and candidates
consistent with originating from ${{B}^{0}_{({s})}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{\pm}}{{\pi}^{\mp}}$
decays, where the ${{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ has
been reconstructed from the wrong pair of tracks.

Separate neural network (NN) classifiers [34] for each $D$ decay mode are used
to distinguish signal decays from combinatorial background. The sPlot
technique [35], with the ${{B}^{0}}\rightarrow{D}{{\pi}^{+}}{{\pi}^{-}}$
candidate mass as the discriminating variable, is used to obtain signal and
background weights, which are then used to train the networks. The networks
are based on input variables that describe the topology of each decay channel,
and that depend only weakly on the ${B}$ candidate mass and on the position of
the candidate in the ${B}$ decay Dalitz plot. Loose requirements are made on
the NN outputs in order to retain large samples for the DP analysis.

##  4 Determination of signal and background yields

The yields of signal and of several different backgrounds are determined from
an extended maximum likelihood fit, in each mode, to the distributions of
candidates in $B$ candidate mass and NN output. Unbinned information on the
$B$ candidate mass is used, while each sample is divided into five bins of the
NN output that contain a similar number of signal, and varying numbers of
background, decays [36, 37].

In addition to ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays, components
are included in the fit to account for ${{B}^{0}_{s}}$ decays to the same
final state, partially reconstructed
${{B}^{0}_{({s})}}\rightarrow{{D}^{(*)}}{{K}^{\pm}}{{\pi}^{\mp}}$ backgrounds,
misidentified ${{B}^{0}}\rightarrow{{D}^{(*)}}{{\pi}^{+}}{{\pi}^{-}}$,
${{B}^{0}_{({s})}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$, ${{\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}\rightarrow{{D}^{(*)}}{\overline{p}}{{\pi}^{+}}$ and
${{\kern 1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}\rightarrow{{D}^{(*)}}{\overline{p}}{{K}^{+}}$ decays
as well as combinatorial background. The modelling of the signal and
background distributions in $B$ candidate mass is similar to that described in
Ref. [29]. The sum of two Crystal Ball functions [38] is used for each of the
correctly reconstructed $B$ decays, where the peak position and core width
(i.e. the narrower of the two widths) are free parameters of the fit, while
the ${B}^{0}_{s}$–${B}^{0}$ mass difference is fixed to its known value [39].
The fraction of the signal function contained in the core and the relative
width of the two components are constrained within uncertainties to, and all
other parameters are fixed to, their expected values obtained from simulated
data, separately for each of the three $D$ samples. An exponential function is
used to describe combinatorial background, with the shape parameter allowed to
vary. Due to the loose NN output requirement it is necessary, in the
$D\rightarrow{{K}^{+}}{{\pi}^{-}}$ sample, to account explicitly for partially
combinatorial background where the final state $D{{K}^{+}}$ pair originates
from a $B$ decay but is combined with a random pion; this is modelled with a
non-parametric function. Non-parametric functions obtained from simulation
based on known DP distributions [40, 41, 42, 43, 44, 45, 46] are used to model
the partially reconstructed and misidentified $B$ decays.

The fraction of signal decays in each NN output bin is allowed to vary freely
in the fit; the correctly reconstructed ${B}^{0}_{s}$ decays and misidentified
backgrounds are taken to have the same NN output distribution as signal. The
fractions of combinatorial and partially reconstructed backgrounds in each NN
output bin are each allowed to vary freely. All yields are free parameters of
the fit, except those for misidentified backgrounds which are constrained
within expectation relative to the signal yield, since the relative branching
fractions [39] and misidentification probabilities [47] are well known.

The results of the fits are shown in Fig. 3, in which the NN output bins have
been combined by weighting both the data and fit results by ${\cal S}/({\cal
S}+{\cal B})$, where ${\cal S}$ (${\cal B}$) is the signal (background) yield
in the signal window, defined as $\pm 2.5\,\sigma({\rm core})$ around the
${B}^{0}$ peak in each sample, where $\sigma({\rm core})$ is the core width of
the signal shape. The yields of each category in these regions, which
correspond to $5246.6$–$5309.9{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
$5246.9$–$5310.5{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$5243.1$–$5312.3{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ in the
${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$, ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ samples, are given in Tables 1, 2 and 3. In total,
there are $2840\pm 70$ signal decays within the signal window in the
$D\rightarrow{{K}^{+}}{{\pi}^{-}}$ sample, whilst the corresponding values for
the $D\rightarrow{{K}^{+}}{{K}^{-}}$ and $D\rightarrow{{\pi}^{+}}{{\pi}^{-}}$
samples are $339\pm 22$ and $168\pm 19$. The $\chi^{2}/\rm{ndf}$ values for
the projections of the fits to the ${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$,
${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and ${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$
datasets are $171.5/223$, $188.2/223$ and $169.1/222$, respectively, giving a
total $\chi^{2}/\rm{ndf}=528.8/668$. Note that there are some bins with low
numbers of entries which may result in this value not following exactly the
expected $\chi^{2}$ distribution.

Table 1: Yields in the signal window of the fit components in the five NN output bins for the ${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$ sample. The last column indicates whether or not each component is explicitly modelled in the Dalitz plot fit.  Component | Yield | Included?
---|---|---
| bin 1 | bin 2 | bin 3 | bin 4 | bin 5 |
${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 597 | 546 | 585 | 571 | 540 | Yes
${{B}^{0}_{s}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 1 | 1 | 1 | 1 | 1 | No
comb. bkgd. | 540 | 58 | 16 | 6 | 1 | Yes
${{{B}^{+}}}\rightarrow{{D}^{(*)}}{{K}^{+}}+X^{-}$ | 305 | 33 | 9 | 3 | 1 | Yes
${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{+}}{{\pi}^{-}}$ | 1 | 1 | 1 | 1 | 1 | No
${{B}^{0}}\rightarrow{{D}^{(*)}}{{\pi}^{+}}{{\pi}^{-}}$ | 20 | 18 | 20 | 19 | 18 | Yes
${{\kern 1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}}\rightarrow{{D}^{(*)}}{{K}^{+}}{\overline{p}}$ | 21 | 19 | 21 | 20 | 19 | Yes
${{B}^{0}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 8 | 7 | 8 | 7 | 7 | No
${{B}^{0}_{s}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 10 | 9 | 10 | 10 | 9 | No
Table 2: Yields in the signal window of the fit components in the five NN output bins for the ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ sample. The last column indicates whether or not each component is explicitly modelled in the Dalitz plot fit.  Component | Yield | Included?
---|---|---
| bin 1 | bin 2 | bin 3 | bin 4 | bin 5 |
${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 70 | 63 | 68 | 73 | 65 | Yes
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 5 | 5 | 5 | 6 | 5 | Yes
comb. bkgd. | 173 | 19 | 9 | 3 | 0 | Yes
${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{+}}{{\pi}^{-}}$ | 0 | 1 | 1 | 1 | 0 | No
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{+}}{{\pi}^{-}}$ | 19 | 28 | 34 | 28 | 20 | Yes
${{B}^{0}}\rightarrow{{D}^{(*)}}{{\pi}^{+}}{{\pi}^{-}}$ | 4 | 3 | 4 | 4 | 3 | Yes
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{D}^{(*)}}{p}{{\pi}^{-}}$ | 11 | 10 | 10 | 11 | 10 | Yes
${{\kern 1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}}\rightarrow{{D}^{(*)}}{{K}^{+}}{\overline{p}}$ | 2 | 1 | 2 | 2 | 2 | No
${{B}^{0}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 2 | 1 | 2 | 2 | 1 | No
${{B}^{0}_{s}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 1 | 1 | 1 | 2 | 1 | No
Table 3: Yields in the signal window of the fit components in the five NN output bins for the ${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ sample. The last column indicates whether or not each component is explicitly modelled in the Dalitz plot fit.  Component | Yield | Included?
---|---|---
| bin 1 | bin 2 | bin 3 | bin 4 | bin 5 |
${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 36 | 31 | 38 | 32 | 31 | Yes
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ | 3 | 2 | 3 | 3 | 2 | Yes
comb. bkgd. | 119 | 17 | 4 | 3 | 2 | Yes
${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{+}}{{\pi}^{-}}$ | 0 | 0 | 0 | 0 | 0 | No
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{+}}{{\pi}^{-}}$ | 9 | 16 | 15 | 12 | 10 | Yes
${{B}^{0}}\rightarrow{{D}^{(*)}}{{\pi}^{+}}{{\pi}^{-}}$ | 2 | 2 | 2 | 2 | 2 | Yes
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{D}^{(*)}}{p}{{\pi}^{-}}$ | 6 | 5 | 6 | 5 | 5 | Yes
${{\kern 1.00006pt\overline{\kern-1.00006pt\mathchar 28931\relax}}{}^{0}_{b}}\rightarrow{{D}^{(*)}}{{K}^{+}}{\overline{p}}$ | 1 | 1 | 1 | 1 | 1 | No
${{B}^{0}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 1 | 1 | 1 | 1 | 1 | No
${{B}^{0}_{s}}\rightarrow{{D}^{(*)}}{{K}^{+}}{{K}^{-}}$ | 1 | 1 | 1 | 1 | 1 | No

Projections of the fits separated by NN output bin in each sample are shown in
Figs. 4, 5 and 6. The fitted parameters obtained from all three data samples
are reported in Table 4. The parameters $\mu(B)$, $N({\rm core})/N({\rm
total})$, $\sigma({\rm wide})/\sigma({\rm core})$ are, respectively, the peak
position, the fraction of the signal function contained in the core and the
relative width of the two components of the ${B}^{0}$ signal shape. Quantities
denoted $N$ are total yields of each fit component, while those denoted
$f^{i}_{\rm signal}$ are fractions of the signal in NN output bin $i$ (with
similar notation for the fractions of the partially reconstructed and
combinatorial backgrounds). The NN output bin labels 1–5 range from the bin
with the lowest to highest value of ${\cal S}/{\cal B}$.

Figure 3: Results of fits to $D{{K}^{+}}{{\pi}^{-}}$ candidates in the (a,b)
$D\rightarrow{{K}^{+}}{{\pi}^{-}}$, (c,d) $D\rightarrow{{K}^{+}}{{K}^{-}}$ and
(e,f) $D\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ samples. The data and the fit
results in each NN output bin have been weighted according to ${\cal S}/({\cal
S}+{\cal B})$ as described in the text. The left and right plots are identical
but with (left) linear and (right) logarithmic $y$-axis scales. The components
are as described in the legend.

Figure 4: Results of the fit to ${D}{{K}^{+}}{{\pi}^{-}}$,
${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$ candidates shown separately in the five
bins of the neural network output variable. The bins are shown, from (a)–(e),
in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in
the legend. The vertical dotted lines in (a) show the signal window used for
the fit to the Dalitz plot.

Figure 5: Results of the fit to ${D}{{K}^{+}}{{\pi}^{-}}$,
${D}\rightarrow{{K}^{+}}{{K}^{-}}$ candidates shown separately in the five
bins of the neural network output variable. The bins are shown, from (a)–(e),
in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in
the legend. The vertical dotted lines in (a) show the signal window used for
the fit to the Dalitz plot.

Figure 6: Results of the fit to ${D}{{K}^{+}}{{\pi}^{-}}$, ${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ candidates shown separately in the five bins of the neural network output variable. The bins are shown, from (a)–(e), in order of increasing ${\cal S}/{\cal B}$. The components are as indicated in the legend. The vertical dotted lines in (a) show the signal window used for the fit to the Dalitz plot. Table 4: Results for the unconstrained parameters obtained from the fits to the three data samples. Entries where no number is given are fixed to zero. Fractions marked * are not varied in the fit, and give the difference between unity and the sum of the other fractions.  | ${D}\rightarrow{{K}^{+}}{{\pi}^{-}}$ | ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ | ${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$
---|---|---|---
Parameter | Value
$\mu(B)\ ({\mathrm{Me\kern-1.00006ptV\\!/}c^{2}})$ |  $5278.3$$\,\pm\,$ | $0.4$ |  $5278.7$$\,\pm\,$ | $0.5$ |  $5277.7$$\,\pm\,$ | $1.0$
$\sigma({\rm core})\ ({\mathrm{Me\kern-1.00006ptV\\!/}c^{2}})$ |  $12.7$$\,\pm\,$ | $0.4$ |  $12.7$$\,\pm\,$ | $0.5$ |  $13.9$$\,\pm\,$ | $0.8$
$N({\rm core})/N({\rm total})$ |  $0.787$$\,\pm\,$ | $0.017$ |  $0.798$$\,\pm\,$ | $0.018$ |  $0.797$$\,\pm\,$ | $0.018$
$\sigma({\rm wide})/\sigma({\rm core})$ |  $1.80$$\,\pm\,$ | $0.05$ |  $1.75$$\,\pm\,$ | $0.05$ |  $1.76$$\,\pm\,$ | $0.05$
Exp. slope $(c^{2}/\mathrm{Ge\kern-1.00006ptV})$ |  $-1.84$$\,\pm\,$ | $0.13$ |  $-1.05$$\,\pm\,$ | $0.19$ |  $-1.35$$\,\pm\,$ | $0.26$
$N({{B}^{0}}\rightarrow{D}K\pi)$ |  $3125$$\,\pm\,$ | $79$ |  $418$$\,\pm\,$ | $27$ |  $185$$\,\pm\,$ | $21$
$N({{B}^{0}_{s}}\rightarrow{D}K\pi)$ |  $146$$\,\pm\,$ | $27$ |  $1014$$\,\pm\,$ | $41$ |  $429$$\,\pm\,$ | $28$
$N({\rm comb.~{}bkgd.})$ |  $5694$$\,\pm\,$ | $529$ |  $2092$$\,\pm\,$ | $95$ |  $1288$$\,\pm\,$ | $86$
$N({B}\rightarrow{{D}^{(*)}}K+X)$ |  $2648$$\,\pm\,$ | $454$ | — | —
$N({{B}^{0}}\rightarrow{{D}^{*}}K\pi)$ |  $3028$$\,\pm\,$ | $115$ |  $543$$\,\pm\,$ | $48$ |  $183$$\,\pm\,$ | $33$
$N({{B}^{0}_{s}}\rightarrow{{D}^{*}}K\pi)$ | — |  $1493$$\,\pm\,$ | $77$ |  $639$$\,\pm\,$ | $52$
$N({{B}^{0}}\rightarrow{{D}^{(*)}}\pi\pi)$ |  $783$$\,\pm\,$ | $67$ |  $146$$\,\pm\,$ | $17$ |  $72$$\,\pm\,$ | $11$
$N({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{D}^{(*)}}p\pi)$ | — |  $241$$\,\pm\,$ | $47$ |  $118$$\,\pm\,$ | $26$
$N({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{D}^{(*)}}pK)$ |  $416$$\,\pm\,$ | $64$ |  $34$$\,\pm\,$ | $9$ |  $17$$\,\pm\,$ | $5$
$N({{B}^{0}}\rightarrow{{D}^{(*)}}KK)$ |  $371$$\,\pm\,$ | $51$ |  $64$$\,\pm\,$ | $15$ |  $33$$\,\pm\,$ | $8$
$N({{B}^{0}_{s}}\rightarrow{{D}^{(*)}}KK)$ |  $171$$\,\pm\,$ | $47$ |  $25$$\,\pm\,$ | $11$ |  $14$$\,\pm\,$ | $6$
$f^{1}_{\rm signal}$ |  $0.210$$\,\pm\,$ | $0.012$ |  $0.187$$\,\pm\,$ | $0.017$ |  $0.214$$\,\pm\,$ | $0.029$
$f^{2}_{\rm signal}$ |  $0.192$$\,\pm\,$ | $0.008$ |  $0.186$$\,\pm\,$ | $0.011$ |  $0.184$$\,\pm\,$ | $0.019$
$f^{3}_{\rm signal}$ |  $0.206$$\,\pm\,$ | $0.008$ |  $0.201$$\,\pm\,$ | $0.012$ |  $0.225$$\,\pm\,$ | $0.019$
$f^{4}_{\rm signal}$ |  $0.201$$\,\pm\,$ | $0.007$ |  $0.215$$\,\pm\,$ | $0.012$ |  $0.193$$\,\pm\,$ | $0.018$
$f^{5}_{\rm signal}$* |  $0.190$$\,\pm\,$ | $0.007$ |  $0.211$$\,\pm\,$ | $0.011$ |  $0.184$$\,\pm\,$ | $0.017$
$f^{1}_{\rm part.~{}rec.~{}bkgd.}$ |  $0.214$$\,\pm\,$ | $0.023$ |  $0.145$$\,\pm\,$ | $0.020$ |  $0.152$$\,\pm\,$ | $0.042$
$f^{2}_{\rm part.~{}rec.~{}bkgd.}$ |  $0.214$$\,\pm\,$ | $0.010$ |  $0.217$$\,\pm\,$ | $0.011$ |  $0.254$$\,\pm\,$ | $0.021$
$f^{3}_{\rm part.~{}rec.~{}bkgd.}$ |  $0.215$$\,\pm\,$ | $0.011$ |  $0.267$$\,\pm\,$ | $0.013$ |  $0.237$$\,\pm\,$ | $0.021$
$f^{4}_{\rm part.~{}rec.~{}bkgd.}$ |  $0.193$$\,\pm\,$ | $0.010$ |  $0.215$$\,\pm\,$ | $0.012$ |  $0.189$$\,\pm\,$ | $0.019$
$f^{5}_{\rm part.~{}rec.~{}bkgd.}$* |  $0.164$$\,\pm\,$ | $0.009$ |  $0.156$$\,\pm\,$ | $0.010$ |  $0.169$$\,\pm\,$ | $0.018$
$f^{1}_{\rm comb.~{}bkgd.}$ |  $0.870$$\,\pm\,$ | $0.013$ |  $0.849$$\,\pm\,$ | $0.012$ |  $0.828$$\,\pm\,$ | $0.018$
$f^{2}_{\rm comb.~{}bkgd.}$ |  $0.094$$\,\pm\,$ | $0.008$ |  $0.092$$\,\pm\,$ | $0.009$ |  $0.116$$\,\pm\,$ | $0.014$
$f^{3}_{\rm comb.~{}bkgd.}$ |  $0.025$$\,\pm\,$ | $0.004$ |  $0.043$$\,\pm\,$ | $0.007$ |  $0.027$$\,\pm\,$ | $0.008$
$f^{4}_{\rm comb.~{}bkgd.}$ |  $0.009$$\,\pm\,$ | $0.003$ |  $0.017$$\,\pm\,$ | $0.005$ |  $0.019$$\,\pm\,$ | $0.007$
$f^{5}_{\rm comb.~{}bkgd.}$* |  $0.002$$\,\pm\,$ | $0.002$ |  $0.000$$\,\pm\,$ | $0.000$ |  $0.010$$\,\pm\,$ | $0.006$

##  5 Dalitz plot analysis

Candidates within the signal region are used in the DP analysis. A
simultaneous fit is performed to the samples with different $D$ decays by
using the Jfit method [48] as implemented in the Laura++ package [49]. The
likelihood function contains signal and background terms, with yields in each
NN output bin fixed according to the results obtained previously. The NN
output bin with the lowest ${\cal S}/{\cal B}$ value in the
$D\rightarrow{{K}^{+}}{{\pi}^{-}}$ sample only is found not to contribute
significantly to the sensitivity and is susceptible to mismodelling of the
combinatorial background; it is therefore excluded from the subsequent
analysis.

The signal probability function is derived from the isobar model obtained in
Ref. [29], with amplitude

${\cal
A}\left(m^{2}(D{{\pi}^{-}}),m^{2}({{K}^{+}}{{\pi}^{-}})\right)=\sum_{j=1}^{N}c_{j}F_{j}\left(m^{2}(D{{\pi}^{-}}),m^{2}({{K}^{+}}{{\pi}^{-}})\right)\,,$
(1)

where $c_{j}$ are complex coefficients describing the relative contribution
for each intermediate process, and the
$F_{j}\left(m^{2}(D{{\pi}^{-}}),m^{2}({{K}^{+}}{{\pi}^{-}})\right)$ terms
describe the resonant dynamics through the lineshape, angular distribution and
barrier factors. The sum is over amplitudes from the $D_{0}^{*}(2400)^{-}$,
$D_{2}^{*}(2460)^{-}$, ${{K}^{*}}(892)^{0}$, ${{K}^{*}}(1410)^{0}$ and
$K_{2}^{*}(1430)^{0}$ resonances as well as a ${{K}^{+}}{{\pi}^{-}}$ S-wave
component and both S-wave and P-wave nonresonant $D{{\pi}^{-}}$ amplitudes
[29]. The masses and widths of ${{K}^{+}}{{\pi}^{-}}$ resonances are fixed,
and those of $D{{\pi}^{-}}$ resonances are constrained within uncertainties to
known values [39, 42, 50, 29]. The values of the $c_{j}$ coefficients are
allowed to vary in the fit, as are the shape parameters of the nonresonant
amplitudes.

For the $D\rightarrow{{K}^{+}}{{\pi}^{-}}$ sample, the contribution from the
$V_{ub}$ amplitude followed by doubly-Cabibbo-suppressed $D$ decay is
negligible. This sample can therefore be treated as if only the $V_{cb}$
amplitude contributes, and the signal probability function is given by Eq.
(1). For the samples with $D\rightarrow{{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ decays, the $c_{j}$ terms are modified,

$c_{j}\longrightarrow\left\\{\begin{array}[]{cl}c_{j}&{\rm for\ a}\
{D}{{\pi}^{-}}\ {\rm resonance}\,,\\\
c_{j}\left[1+x_{\pm,\,j}+iy_{\pm,\,j}\right]&{\rm for\ a}\
{{K}^{+}}{{\pi}^{-}}\ {\rm resonance}\,,\end{array}\right.$ (2)

with $x_{\pm,\,j}=r_{B,\,j}\cos\left(\delta_{B,\,j}\pm\gamma\right)$ and
$y_{\pm,\,j}=r_{B,\,j}\sin\left(\delta_{B,\,j}\pm\gamma\right)$, where the $+$
and $-$ signs correspond to ${{B}^{0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ DPs, respectively. Here
$r_{B,\,j}$ and $\delta_{B,\,j}$ are the relative magnitude and strong phase
of the $V_{ub}$ and $V_{cb}$ amplitudes for each ${{K}^{+}}{{\pi}^{-}}$
resonance $j$. In this analysis the $x_{\pm,\,j}$ and $y_{\pm,\,j}$ parameters
are measured only for the ${{K}^{*}}(892)^{0}$ resonance, which has a large
enough yield and a sufficiently well-understood lineshape to allow reliable
determinations of these parameters; therefore the $j$ subscript is omitted
hereafter. In addition, a component corresponding to the ${{B}^{0}}\rightarrow
D_{s1}^{*}(2700)^{+}{{\pi}^{-}}$ decay, which is mediated by the $V_{ub}$
amplitude alone, is included in the fit with mass and width parameters fixed
to their known values [39, 51] and magnitude constrained according to
expectation based on the ${{B}^{0}}\rightarrow D_{s1}^{*}(2700)^{+}{{D}^{-}}$
decay rate [51].

The signal efficiency and backgrounds are modelled in the likelihood function,
separately for each of the samples, following Refs. [29, 40, 41]. The DP
distribution of combinatorial background is obtained from a sideband in $B$
candidate mass, defined as $5400\
(5450)<m(D{{K}^{+}}{{\pi}^{-}})<5900{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
for the samples with $D\rightarrow{{K}^{+}}{{\pi}^{-}}$
($D\rightarrow{{K}^{+}}{{K}^{-}}$ or ${{\pi}^{+}}{{\pi}^{-}}$). The shapes of
partially reconstructed and misidentified backgrounds are obtained from
simulated samples based on known DP distributions [40, 41, 42, 43, 44, 45,
46]. Combinatorial background is the largest component in the NN output bins
with the lowest ${\cal S}/{\cal B}$ values, while in the purest bins in the
$D\rightarrow{{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ samples the
${{B}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{-}}{{\pi}^{+}}$ background makes an
important contribution. Background sources with yields below $2\,\%$ relative
to the signal in all NN bins are neglected, as indicated in Tables 1, 2 and 3.

The fit procedure is validated with ensembles of pseudoexperiments. In
addition, samples of ${{B}^{0}_{s}}\rightarrow D{{K}^{-}}{{\pi}^{+}}$ decays
are selected for each of the $D$ decays. These are used to test the fit with a
model based on that of Refs. [40, 41] and where $D{{K}^{-}}$ resonances have
contributions only from $V_{cb}$ amplitudes, while the coefficients for
${{K}^{-}}{{\pi}^{+}}$ resonances are parametrised by Eq. (2). The results are

$\begin{array}[]{c}x_{+}({{B}^{0}_{s}}\rightarrow D{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}}(892)^{0})=\phantom{-}0.05\pm
0.05\,,\qquad y_{+}({{B}^{0}_{s}}\rightarrow D{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}}(892)^{0})=-0.08\pm 0.11\,,\\\
x_{-}({{B}^{0}_{s}}\rightarrow D{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}}(892)^{0})=\phantom{-}0.01\pm
0.05\,,\qquad y_{-}({{B}^{0}_{s}}\rightarrow D{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*}}(892)^{0})=-0.08\pm
0.12\,,\end{array}$

where the uncertainties are statistical only. No significant $C\\!P$ violation
effect is observed, consistent with the expectation that $V_{ub}$ amplitudes
are highly suppressed in this control channel.

##  6 Systematic uncertainties

Sources of systematic uncertainty on the $x_{\pm}$ and $y_{\pm}$ parameters
can be divided into two categories: experimental and model uncertainties.
These are summarised in Tables 5 and 6. The former category includes effects
due to knowledge of the signal and background yields in the signal region
(denoted “${\cal S}/{\cal B}$” in Table 5), the variation of the efficiency
($\epsilon$) across the Dalitz plot, the background Dalitz plot distributions
(${\cal B}$ DP) and fit bias, all of which are evaluated in similar ways to
those described in Ref. [29]. Additionally, effects that may induce fake
asymmetries, including asymmetry between ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${B}^{0}$ candidates in the
background yields (${\cal B}$ asym.) as well as asymmetries in the background
Dalitz plot distributions (${\cal B}$ DP asym.) and in the efficiency
variation ($\epsilon$ asym.) are accounted for. The largest source of
uncertainty in this category arises from lack of knowledge of the DP
distribution for the ${{B}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{-}}{{\pi}^{+}}$
background.

Model uncertainties arise due to fixing parameters in the amplitude model
(denoted “fixed pars.” in Table 6), the addition or removal of marginal
components, namely the ${{K}^{*}}(1410)^{0}$, ${{K}^{*}}(1680)^{0}$,
$D_{1}^{*}(2760)^{-}$, $D_{3}^{*}(2760)^{-}$ and $D_{s2}^{*}(2573)^{+}$
resonances, in the Dalitz plot fit (add/rem.), and the use of alternative
models for the ${{K}^{+}}{{\pi}^{-}}$ S-wave and $D{{\pi}^{-}}$ nonresonant
amplitudes (alt. mod.); all of these are evaluated as in Ref. [29]. The
possibilities of $C\\!P$ violation associated to the $D_{s1}^{*}(2700)^{+}$
amplitude ($D_{s}^{**}$ ${C\\!P}$V), and of independent $C\\!P$ violation
parameters in the two components of the ${{K}^{+}}{{\pi}^{-}}$ S-wave
amplitude [52] ($K\pi_{\rm S-wave}$ ${C\\!P}$V), are also accounted for. The
largest source of uncertainty in this category arises from changing the
description of the ${{K}^{+}}{{\pi}^{-}}$ S-wave. Other possible sources of
systematic uncertainty, such as production asymmetry [53] or $C\\!P$ violation
in the $D\rightarrow{{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ decays
[54, 55, 56], are found to be negligible.

The total uncertainties are obtained by combining all sources in quadrature.
The leading sources of systematic uncertainty are expected to be reducible
with larger data samples.

Table 5: Experimental systematic uncertainties. Parameter | Uncertainty
---|---
| ${\cal S}/{\cal B}$ | $\epsilon$ |  ${\cal B}$ DP | fit bias |  ${\cal B}$ asym. |  ${\cal B}$ DP asym. |  $\epsilon$ asym. | total
$x_{+}$ | 0.010 | 0.035 | 0.046 | 0.021 | 0.007 | 0.049 | 0.000 | 0.079
$x_{-}$ | 0.026 | 0.028 | 0.063 | 0.019 | 0.010 | 0.045 | 0.001 | 0.089
$y_{+}$ | 0.019 | 0.042 | 0.122 | 0.066 | 0.017 | 0.027 | 0.000 | 0.149
$y_{-}$ | 0.024 | 0.022 | 0.054 | 0.035 | 0.018 | 0.071 | 0.000 | 0.103
Table 6: Model uncertainties. Parameter | Uncertainty
---|---
| fixed pars. | add/rem. | alt. mod. |  $D_{s}^{**}$ ${C\\!P}$V |  $K\pi_{\rm S-wave}$ ${C\\!P}$V | total
$x_{+}$ | 0.027 | 0.028 | 0.068 | 0.008 | 0.003 | 0.079
$x_{-}$ | 0.030 | 0.034 | 0.076 | 0.056 | 0.022 | 0.107
$y_{+}$ | 0.075 | 0.061 | 0.131 | 0.012 | 0.047 | 0.170
$y_{-}$ | 0.040 | 0.066 | 0.255 | 0.286 | 0.064 | 0.396

##  7 Results and summary

The DPs for candidates in the $B$ candidate mass signal region in the
${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ samples are
shown separately for ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
and ${B}^{0}$ candidates in Fig. 7. Projections of the fit results onto
$m(D\pi)$, $m(K\pi)$ and $m(DK)$ for the $D\rightarrow{{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ samples are shown separately for ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ and ${{B}^{0}}$ candidates in
Fig. 8. No significant $C\\!P$ violation effect is seen.

Figure 7: Dalitz plots for candidates in the $B$ candidate mass signal region
in the ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ samples
for (a) ${\kern 1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ and (b)
${B}^{0}$ candidates. Only candidates in the three purest NN bins are
included. Background has not been subtracted, and therefore some contribution
from ${{\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*0}}{{K}^{+}}{{\pi}^{-}}$
decays is expected at low $m(D{{K}^{+}})$ (i.e. along the top right diagonal).

Figure 8: Projections of the $D\rightarrow{{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ samples and the fit result onto (a,b)
$m({D}{{\pi}^{\mp}})$, (c,d) $m({{K}^{\pm}}{{\pi}^{\mp}})$ and (e,f)
$m({D}{{K}^{\pm}})$ for (a,c,e) ${\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}$ and (b,d,f) ${B}^{0}$
candidates. The data and the fit results in each NN output bin have been
weighted according to ${\cal S}/({\cal S}+{\cal B})$ and combined. The
components are described in the legend.

The results, with statistical uncertainties only, for the complex coefficients
$c_{j}$ are given in Table 7. Due to the changes in the selection
requirements, the overlap between the $D\rightarrow{{K}^{+}}{{\pi}^{-}}$
sample and the dataset used in Ref. [29] is only around $60\,\%$, and the
results are found to be consistent.

Table 7: Results for the complex coefficients $c_{j}$ from the fit to data. Uncertainties are statistical only. All reported quantities are unconstrained in the fit, except that the $D^{*}_{2}(2460)^{-}$ component is fixed as a reference amplitude, and the magnitude of the $D^{*}_{s1}(2700)^{+}$ component is constrained. The ${{K}^{+}}{{\pi}^{-}}$ S-wave is the coherent sum of the ${{K}^{*}_{0}}(1430)^{0}$ and the nonresonant $K\pi$ S-wave component [52].  Resonance | Real part | Imaginary part
---|---|---
${{K}^{*}}(892)^{0}$ | $-0.07\pm 0.10$ | $-1.19\pm 0.04$
${{K}^{*}}(1410)^{0}$ | $\phantom{-}0.16\pm 0.04$ | $\phantom{-}0.21\pm 0.06$
${{K}^{*}_{0}}(1430)^{0}$ | $\phantom{-}0.40\pm 0.08$ | $\phantom{-}0.67\pm 0.06$
Nonresonant $K\pi$ S-wave | $\phantom{-}0.37\pm 0.07$ | $\phantom{-}0.69\pm 0.07$
${{K}^{*}_{2}}(1430)^{0}$ | $-0.01\pm 0.06$ | $-0.48\pm 0.04$
$D^{*}_{0}(2400)^{-}$ | $-1.10\pm 0.05$ | $-0.18\pm 0.07$
$D^{*}_{2}(2460)^{-}$ | $\phantom{-}1.00$ | $\phantom{-}0.00$
Nonresonant $D\pi$ S-wave | $-0.44\pm 0.06$ | $\phantom{-}0.02\pm 0.07$
Nonresonant $D\pi$ P-wave | $-0.61\pm 0.05$ | $-0.08\pm 0.06$
$D^{*}_{s1}(2700)^{+}$ | $\phantom{-}0.57\pm 0.05$ | $-0.09\pm 0.19$

The results for the $C\\!P$ violation parameters associated with the
${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$ decay are

$\begin{array}[]{c}x_{+}=\phantom{-}0.04\pm 0.16\pm 0.11\,,\qquad
y_{+}=-0.47\pm 0.28\pm 0.22\,,\\\ x_{-}=-0.02\pm 0.13\pm 0.14\,,\qquad
y_{-}=-0.35\pm 0.26\pm 0.41\,,\end{array}$

where the uncertainties are statistical and systematic. The statistical and
systematic correlation matrices are given in Table 8. The results for
$(x_{+},y_{+})$ and $(x_{-},y_{-})$ are shown as contours in Fig. 9.

Table 8: Correlation matrices associated to the (left) statistical and (right)
systematic uncertainties of the $C\\!P$ violation parameters associated with
the ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$ decay.

| $x_{-}$ | $y_{-}$ | $x_{+}$ | $y_{+}$
---|---|---|---|---
$x_{-}$ | 1.00 |  |  |
$y_{-}$ | 0.34 | 1.00 |  |
$x_{+}$ | 0.10 | 0.05 | 1.00 |
$y_{+}$ | 0.13 | 0.15 | 0.50 | 1.00

| $x_{-}$ | $y_{-}$ | $x_{+}$ | $y_{+}$
---|---|---|---|---
$x_{-}$ | 1.00 |  |  |
$y_{-}$ | 0.87 | 1.00 |  |
$x_{+}$ | 0.25 | 0.29 | 1.00 |
$y_{+}$ | 0.37 | 0.41 | 0.73 | 1.00

Figure 9: Contours at $68\,\%$ CL for the (blue) $(x_{+},y_{+})$ and (red)
$(x_{-},y_{-})$ parameters associated with the ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ decay, with statistical uncertainties only. The central
values are marked by a circle and a cross, respectively.

The GammaCombo package [57] is used to evaluate constraints from these results
on $\gamma$ and the hadronic parameters $r_{B}$ and $\delta_{B}$ associated
with the ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$ decay. A frequentist
treatment referred to as the “plug-in” method, described in Refs. [58, 59, 60,
61], is used. Figure 10 shows the results of likelihood scans for $\gamma$,
$r_{B}$ and $\delta_{B}$. Figure 11 shows the two-dimensional $68\,\%$
confidence level for each pair of observables from $\gamma$, $r_{B}$ and
$\delta_{B}$. No value of $\gamma$ is excluded at 95 % confidence level (CL);
the world-average value for $\gamma$ [62, 63] has a CL of 0.85.

(a)(b)(c) Figure 10: Results of likelihood scans for (a) $\gamma$, (b) $r_{B}$
and (c) $\delta_{B}$.  (a)(b)(c) Figure 11: Confidence level contours for (a)
$\gamma$ and $r_{B}$, (b) $\gamma$ and $\delta_{B}$ and (c) $r_{B}$ and
$\delta_{B}$. The shaded regions are allowed at $68\,\%$ CL.

The ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$ decay can also be used to
determine parameters sensitive to $\gamma$ with a quasi-two-body approach, as
has been done with $D\rightarrow{{K}^{+}}{{K}^{-}}$, ${{\pi}^{+}}{{\pi}^{-}}$
[64], ${{K}^{\pm}}{{\pi}^{\mp}}$, ${{K}^{\pm}}{{\pi}^{\mp}}{{\pi}^{0}}$,
${{K}^{\pm}}{{\pi}^{\mp}}{{\pi}^{+}}{{\pi}^{-}}$ [64, 65, 66] and
$D\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$
decays [67, 68, 69, 70]. In the quasi-two-body analysis, the results depend on
the effective hadronic parameters $\kappa$, $\bar{r}_{B}$ and
$\bar{\delta}_{B}$, which are, respectively, the coherence factor and the
relative magnitude and strong phase of the $V_{ub}$ and $V_{cb}$ amplitudes
averaged over the selected region of phase space [17]. Precise definitions are
given in the Appendix. These parameters are calculated from the models for
$V_{cb}$ and $V_{ub}$ amplitudes obtained from the fit for the
${{K}^{*}}(892)^{0}$ selection region
$\left|m({{K}^{+}}{{\pi}^{-}})-m_{{{K}^{*}}(892)^{0}}\right|<50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
and $\left|\cos\theta_{{{K}^{*0}}}\right|>0.4$, where $m_{{{K}^{*}}(892)^{0}}$
is the known value of the ${{K}^{*}}(892)^{0}$ mass [39] and
$\theta_{{{K}^{*0}}}$ is the ${K}^{*0}$ helicity angle, i.e. the angle between
the ${K}^{+}$ and $D$ directions in the ${{K}^{+}}{{\pi}^{-}}$ rest frame. To
reduce correlations with the values for $r_{B}$ and $\delta_{B}$ determined
from the DP analysis, the quantities $\bar{R}_{B}=\bar{r}_{B}/r_{B}$ and
$\Delta\bar{\delta}_{B}=\bar{\delta}_{B}-\delta_{B}$ are calculated. The
results are

$\kappa=0.958\,^{+0.005}_{-0.010}\,{}^{+0.002}_{-0.045}\,,\quad\bar{R}_{B}=1.02\,^{+0.03}_{-0.01}\pm
0.06\,,\quad\Delta\bar{\delta}_{B}=0.02\,^{+0.03}_{-0.02}\pm 0.11\,,$

where the uncertainties are statistical and systematic and are evaluated as
described in the Appendix.

In summary, a data sample corresponding to $3.0\mbox{\,fb}^{-1}$ of $pp$
collisions collected with the LHCb detector has been used to measure, for the
first time, parameters sensitive to the angle $\gamma$ from a Dalitz plot
analysis of ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays. No
significant $C\\!P$ violation effect is seen. The results are consistent with,
and supersede, the results for ${\cal A}_{d}^{KK,\pi\pi}$ and ${\cal
R}_{d}^{KK,\pi\pi}$ from Ref. [64]. Parameters that are needed to determine
$\gamma$ from quasi-two-body analyses of ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ decays are measured. These results can be combined with
current and future measurements with the ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ channel to obtain stronger constraints on $\gamma$.

## 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 and MPG (Germany); 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). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex
LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (USA). We are indebted to the communities behind the multiple
open source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany), EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), The Royal Society, Royal
Commission for the Exhibition of 1851 and the Leverhulme Trust (United
Kingdom).

## Appendix: Quasi-two-body parameters

In the quasi-two-body analyses of ${{B}^{0}}\rightarrow D{{K}^{*}}(892)^{0}$
decays, the following parameters are defined [17]:

$\displaystyle\kappa$ $\displaystyle=$
$\displaystyle\left|\frac{\int\left|A_{cb}(p)A_{ub}(p)\right|\exp\left[i\delta(p)\right]{\rm
d}p}{\sqrt{\int\left|A_{cb}(p)\right|^{2}{\rm
d}p\int\left|A_{ub}(p)\right|^{2}{\rm d}p}}\right|\,,$ (3)
$\displaystyle\bar{r}_{B}$ $\displaystyle=$
$\displaystyle\sqrt{\frac{\int\left|A_{ub}(p)\right|^{2}{\rm
d}p}{\int\left|A_{cb}(p)\right|^{2}{\rm d}p}}\,,$ (4)
$\displaystyle\bar{\delta}_{B}$ $\displaystyle=$
$\displaystyle\arg\left(\frac{\int\left|A_{cb}(p)A_{ub}(p)\right|\exp\left[i\delta(p)\right]{\rm
d}p}{\sqrt{\int\left|A_{cb}(p)\right|^{2}{\rm
d}p\int\left|A_{ub}(p)\right|^{2}{\rm d}p}}\right)\,,$ (5)

where all the integrations are over the part of the phase space $p$ inside the
used ${{K}^{*}}(892)^{0}$ selection window. In these equations,
$\left|A_{cb}(p)\right|$ and $\left|A_{ub}(p)\right|$ refer to the magnitudes
of the total $V_{cb}$ and $V_{ub}$ amplitudes, and $\delta(p)$ is their
relative strong phase. In terms of the parameters used in this analysis,

$\displaystyle\left|A_{cb}(p)\right|$ $\displaystyle=$
$\displaystyle\left|\sum_{j}c_{j}F_{j}(p)\right|\,,$ (6)
$\displaystyle\left|A_{ub}(p)\right|$ $\displaystyle=$
$\displaystyle\left|\sum_{j}c_{j}r_{B,j}\exp\left[i\delta_{B,j}\right]F_{j}(p)\right|\,,$
(7) $\displaystyle\delta(p)$ $\displaystyle=$
$\displaystyle\arg\left(\frac{\sum_{j}c_{j}r_{B,j}\exp\left[i\delta_{B,j}\right]F_{j}(p)}{\sum_{j}c_{j}F_{j}(p)}\right)\,,$
(8)

where the $r_{B,j}$, $\delta_{B,j}$ values are allowed to differ for each
${{K}^{+}}{{\pi}^{-}}$ resonance, and $r_{B,j}=0$ for $D{{\pi}^{-}}$
resonances. (The $r_{B}$, $\delta_{B}$ notation without the $j$ subscript is
retained for the parameters associated with the ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ decay.) In the limit that there is no amplitude (either
resonant or nonresonant) contributing within the ${{K}^{*}}(892)^{0}$
selection window other than those associated with the ${{B}^{0}}\rightarrow
D{{K}^{*}}(892)^{0}$ decay, one finds $\left|A_{ub}(p)\right|\longrightarrow
r_{B}\left|A_{cb}(p)\right|$ and $\delta(p)\longrightarrow\delta_{B}$, and
hence $\kappa\longrightarrow 1$, $\bar{r}_{B}\longrightarrow r_{B}$ and
$\bar{\delta}_{B}\longrightarrow\delta_{B}$. In order to reduce correlations
between $\bar{r}_{B}$ and $r_{B}$ and between $\bar{\delta}_{B}$ and
$\delta_{B}$, it is convenient to introduce the parameters

$\displaystyle\bar{R}_{B}$ $\displaystyle=$
$\displaystyle\frac{\bar{r}_{B}}{r_{B}}\,,$ (9)
$\displaystyle\Delta\bar{\delta}_{B}$ $\displaystyle=$
$\displaystyle\bar{\delta}_{B}-\delta_{B}\,,$ (10)

which are obtained by replacing all $r_{B,j}$ by $r_{B,j}/r_{B}$ and all
$\delta_{B,j}$ by $\delta_{B,j}-\delta_{B}$ in Eqs. (6)–(8).

These quantities are determined from the results of the Dalitz plot analysis.
An alternative fit is performed with $x_{\pm,\,j}+iy_{\pm,\,j}$, defined in
Eq. (2), replaced by
$r_{B,\,j}\exp\left[i\left(\delta_{B,\,j}\pm\gamma\right)\right]$. The results
of this fit are consistent with the values for $\gamma$, $r_{B}$ and
$\delta_{B}$ obtained from the fitted $x_{\pm}$ and $y_{\pm}$, and are used to
evaluate $\left|A_{cb}(p)\right|$, $\left|A_{ub}(p)\right|$ and $\delta(p)$ at
many points inside the selection window and thereby to determine $\kappa$,
$\bar{R}_{B}$ and $\Delta\bar{\delta}_{B}$. The procedure is repeated many
times with both $V_{cb}$ and $V_{ub}$ amplitude model parameters varied within
their statistical uncertainties from the fit, leading to the distributions
shown in Fig. 12. Since the transformations from the fitted model parameters
to the quasi-two-body parameters are highly non-linear, the reported central
values correspond to the peak positions of these distributions, while positive
and negative uncertainties are obtained by incrementally including the most
probable values until $68\,\%$ of all entries are covered.

Sources of systematic uncertainty are accounted for by evaluating their
effects on the quasi-two-body parameters. The dominant sources are from the
use of an alternative description of the ${{K}^{+}}{{\pi}^{-}}$ S-wave, and
from changing the treatment of $C\\!P$ violation in the $D_{s1}^{*}(2700)^{+}$
component and the ${{K}^{+}}{{\pi}^{-}}$ S-wave. Most systematic uncertainties
are symmetrised for consistency with the rest of the analysis, but asymmetric
systematic uncertainties are reported on $\kappa$ since this quantity is $\leq
1$ by definition.

Figure 12: Distributions of (a) $\kappa$, (b) $\bar{R}_{B}$ and (c)
$\Delta\bar{\delta}_{B}$, obtained as described in the text.

## References

  * [1] N. Cabibbo, _Unitary symmetry and leptonic decays_ , Phys. Rev. Lett. 10 (1963) 531
  * [2] M. Kobayashi and T. Maskawa, _$C\\!P$ violation in the renormalizable theory of weak interaction_, Prog. Theor. Phys. 49 (1973) 652
  * [3] L. Wolfenstein, _Parametrization of the Kobayashi-Maskawa Matrix_ , Phys. Rev. Lett. 51 (1983) 1945
  * [4] C. Jarlskog, _Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal $C\\!P$ violation_, Phys. Rev. Lett. 55 (1985) 1039
  * [5] A. J. Buras, M. E. Lautenbacher, and G. Ostermaier, _Waiting for the top quark mass, ${{K}^{+}}\rightarrow{{\pi}^{+}}\nu\bar{\nu}$, ${{B}^{0}_{s}}$–${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ mixing and $C\\!P$ asymmetries in $B$ decays_, Phys. Rev. D50 (1994) 3433, arXiv:hep-ph/9403384
  * [6] A. Riotto and M. Trodden, _Recent progress in baryogenesis_ , Ann. Rev. Nucl. Part. Sci. 49 (1999) 35, arXiv:hep-ph/9901362
  * [7] M. Gronau and D. London, _How to determine all the angles of the unitarity triangle from ${{B}^{0}}\rightarrow D{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$ and ${{B}^{0}_{s}}\rightarrow D\phi$_, Phys. Lett. B253 (1991) 483
  * [8] M. Gronau and D. Wyler, _On determining a weak phase from charged $B$ decay asymmetries_, Phys. Lett. B265 (1991) 172
  * [9] D. Atwood, I. Dunietz, and A. Soni, _Enhanced $C\\!P$ violation with ${B}\rightarrow K{{D}^{0}}({{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})$ modes and extraction of the Cabibbo-Kobayashi-Maskawa angle $\gamma$_, Phys. Rev. Lett. 78 (1997) 3257, arXiv:hep-ph/9612433
  * [10] D. Atwood, I. Dunietz, and A. Soni, _Improved methods for observing $C\\!P$ violation in ${{B}^{\pm}}\rightarrow{{K}^{\pm}}D$ and measuring the CKM phase $\gamma$_, Phys. Rev. D63 (2001) 036005, arXiv:hep-ph/0008090
  * [11] J. Brod and J. Zupan, _The ultimate theoretical error on $\gamma$ from $B\rightarrow DK$ decays_, JHEP 01 (2014) 051, arXiv:1308.5663
  * [12] T. Gershon, _On the measurement of the unitarity triangle angle $\gamma$ from ${{B}^{0}}\rightarrow D{{K}^{*0}}$ decays_, Phys. Rev. D79 (2009) 051301, arXiv:0810.2706
  * [13] T. Gershon and M. Williams, _Prospects for the measurement of the unitarity triangle angle $\gamma$ from ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays_, Phys. Rev. D80 (2009) 092002, arXiv:0909.1495
  * [14] R. H. Dalitz, _On the analysis of $\tau$-meson data and the nature of the $\tau$-meson_, Phil. Mag. 44 (1953) 1068
  * [15] I. I. Bigi and A. I. Sanda, _On direct $C\\!P$ violation in ${B}\rightarrow\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptD$}{}^{0}K\pi$’s versus ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptD$}{}^{0}{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}\pi$’s decays_, Phys. Lett. B211 (1988) 213
  * [16] I. Dunietz, _$C\\!P$ violation with self-tagging ${B}^{0}$ modes_, Phys. Lett. B270 (1991) 75
  * [17] M. Gronau, _Improving bounds on $\gamma$ in ${{B}^{\pm}}\rightarrow D{{K}^{\pm}}$ and $B^{\pm,0}\rightarrow DX_{s}^{\pm,0}$_, Phys. Lett. B557 (2003) 198, arXiv:hep-ph/0211282
  * [18] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [19] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [20] A. Puig, _The LHCb trigger in 2011 and 2012_ , LHCb-PUB-2014-046
  * [21] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [22] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [23] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [24] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [25] 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
  * [26] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [27] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [28] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [29] LHCb collaboration, R. Aaij et al., _Amplitude analysis of $B^{0}\rightarrow\overline{D}^{0}K^{+}\pi^{-}$ decays_, Phys. Rev. D92 (2015) 012012, arXiv:1505.01505
  * [30] LHCb collaboration, R. Aaij et al., _Observation of the decay $B^{0}_{s}\rightarrow\overline{D}^{0}\phi$_, Phys. Lett. B727 (2013) 403, arXiv:1308.4583
  * [31] LHCb collaboration, R. Aaij et al., _Observation of $B^{0}_{s}$–$\overline{B}^{0}_{s}$ mixing and measurement of mixing frequencies using semileptonic $B$ decays_, Eur. Phys. J. C73 (2013) 2655, arXiv:1308.1302
  * [32] LHCb collaboration, R. Aaij et al., _First evidence for the annihilation decay mode $B^{+}\rightarrow D_{s}^{+}\phi$_, JHEP 02 (2013) 043, arXiv:1210.1089
  * [33] LHCb collaboration, R. Aaij et al., _First observations of $\overline{B}^{0}_{s}\rightarrow D^{+}D^{-}$, $D_{s}^{+}D^{-}$ and $D^{0}\overline{D}^{0}$ decays_, Phys. Rev. D87 (2013) 092007, arXiv:1302.5854
  * [34] M. Feindt and U. Kerzel, _The NeuroBayes neural network package_ , Nucl. Instrum. Meth. A 559 (2006) 190
  * [35] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [36] LHCb collaboration, R. Aaij et al., _Search for the decay $B^{0}_{s}\rightarrow\overline{D}^{0}f_{0}(980)$_, JHEP 08 (2015) 005, arXiv:1505.01654
  * [37] LHCb collaboration, R. Aaij et al., _First observation of the rare $B^{+}\rightarrow D^{+}K^{+}\pi^{-}$ decay_, Phys. Rev. D93 (2016) 051101(R), Erratum ibid. D93 (2016) 119902, arXiv:1512.02494
  * [38] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [39] Particle Data Group, K. A. Olive et al., _Review of particle physics_ , Chin. Phys. C38 (2014) 090001, and 2015 update
  * [40] LHCb collaboration, R. Aaij et al., _Observation of overlapping spin- $1$ and spin-$3$ $\overline{D}^{0}K^{-}$ resonances at mass $2.86$ GeV/$c^{2}$_, Phys. Rev. Lett. 113 (2014) 162001, arXiv:1407.7574
  * [41] LHCb collaboration, R. Aaij et al., _Dalitz plot analysis of $B^{0}_{s}\rightarrow\overline{D}^{0}K^{-}\pi^{+}$ decays_, Phys. Rev. D90 (2014) 072003, arXiv:1407.7712
  * [42] LHCb collaboration, R. Aaij et al., _Dalitz plot analysis of $B^{0}\rightarrow\overline{D}^{0}\pi^{+}\pi^{-}$ decays_, Phys. Rev. D92 (2015) 032002, arXiv:1505.01710
  * [43] Belle collaboration, A. Kuzmin et al., _Study of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{{D}^{0}}{{\pi}^{+}}{{\pi}^{-}}$ decays_, Phys. Rev. D76 (2007) 012006, arXiv:hep-ex/0611054
  * [44] Belle collaboration, K. Abe et al., _Study of $B^{0}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{(*)0}}{{\pi}^{+}}{{\pi}^{-}}$ decays_, arXiv:hep-ex/0412072
  * [45] LHCb collaboration, R. Aaij et al., _Observation of $B^{0}\rightarrow\overline{D}^{0}K^{+}K^{-}$ and evidence for $B^{0}_{s}\rightarrow\overline{D}^{0}K^{+}K^{-}$_, Phys. Rev. Lett. 109 (2012) 131801, arXiv:1207.5991
  * [46] LHCb collaboration, R. Aaij et al., _Study of beauty baryon decays to $D^{0}ph^{-}$ and $\Lambda_{c}^{+}h^{-}$ final states_, Phys. Rev. D89 (2014) 032001, arXiv:1311.4823
  * [47] M. Adinolfi et al., _Performance of the LHCb RICH detector at the LHC_, Eur. Phys. J. C73 (2013) 2431, arXiv:1211.6759
  * [48] E. Ben-Haim, R. Brun, B. Echenard, and T. E. Latham, _JFIT: A framework to obtain combined experimental results through joint fits_ , arXiv:1409.5080
  * [49] Laura++ Dalitz plot fitting package, http://laura.hepforge.org/, University of Warwick
  * [50] LHCb collaboration, R. Aaij et al., _Study of $D_{J}$ meson decays to $D^{+}\pi^{-}$, $D^{0}\pi^{+}$ and $D^{*+}\pi^{-}$ final states in $pp$ collisions_, JHEP 09 (2013) 145, arXiv:1307.4556
  * [51] BaBar collaboration, J. P. Lees et al., _Dalitz plot analyses of ${{B}^{0}}\rightarrow{{D}^{-}}{{D}^{0}}{{K}^{+}}$ and ${{{B}^{+}}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{D}^{0}}{{K}^{+}}$ decays_, Phys. Rev. D91 (2015) 052002, arXiv:1412.6751
  * [52] LASS collaboration, D. Aston et al., _A study of $K^{-}\pi^{+}$ scattering in the reaction $K^{-}p\rightarrow K^{-}\pi^{+}n$ at $11\,Ge\kern-1.00006ptV\\!/c$_, Nucl. Phys. B296 (1988) 493
  * [53] LHCb collaboration, R. Aaij et al., _Measurement of the $\overline{B}^{0}$–$B^{0}$ and $\overline{B}^{0}_{s}$–$B^{0}_{s}$ production asymmetries in $pp$ collisions at $\sqrt{s}=7$ TeV_, Phys. Lett. B739 (2014) 218, arXiv:1408.0275
  * [54] Heavy Flavor Averaging Group, Y. Amhis et al., _Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014_, arXiv:1412.7515, updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/
  * [55] LHCb collaboration, R. Aaij et al., _Measurement of indirect $C\\!P$ asymmetries in $D^{0}\rightarrow K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$ decays_, JHEP 04 (2015) 043, arXiv:1501.06777
  * [56] LHCb collaboration, R. Aaij et al., _Measurement of the difference of time-integrated $C\\!P$ asymmetries in $D^{0}\rightarrow K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$ decays_, Phys. Rev. Lett. 116 (2016) 191601, arXiv:1602.03160
  * [57] GammaCombo framework for combinations of measurements and computation of confidence intervals, http://gammacombo.hepforge.org/, CERN
  * [58] LHCb collaboration, R. Aaij et al., _A measurement of the CKM angle $\gamma$ from a combination of $B^{\pm}\rightarrow Dh^{\pm}$ analyses_, Phys. Lett. B726 (2013) 151, arXiv:1305.2050
  * [59] LHCb collaboration, _Improved constraints on $\gamma$: CKM2014 update_, LHCb-CONF-2014-004
  * [60] LHCb collaboration, _LHCb $\gamma$ combination update from $B\rightarrow DKX$ decays_, LHCb-CONF-2016-001
  * [61] B. Sen, M. Walker, and M. Woodroofe, _On the unified method with nuisance parameters_ , Statist. Sinica 19 (2009) 301
  * [62] CKMfitter group, J. Charles et al., _CP violation and the CKM matrix: Assessing the impact of the asymmetric $B$ factories_, Eur. Phys. J. C41 (2005) 1, arXiv:hep-ph/0406184
  * [63] UTfit collaboration, M. Bona et al., _The 2004 UTfit collaboration report on the status of the unitarity triangle in the standard model_ , JHEP 07 (2005) 028, arXiv:hep-ph/0501199
  * [64] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ violation parameters in $B^{0}\rightarrow DK^{*0}$ decays_, Phys. Rev. D90 (2014) 112002, arXiv:1407.8136
  * [65] BaBar collaboration, B. Aubert et al., _Search for $b\rightarrow u$ transitions in ${{B}^{0}}\rightarrow{{D}^{0}}{{K}^{*0}}$ decays_, Phys. Rev. D80 (2009) 031102, arXiv:0904.2112
  * [66] Belle collaboration, K. Negishi et al., _Search for the decay $B^{0}\rightarrow DK^{*0}$ followed by $D\rightarrow K^{-}\pi^{+}$_, Phys. Rev. D86 (2012) 011101, arXiv:1205.0422
  * [67] BaBar collaboration, B. Aubert et al., _Constraints on the CKM angle $\gamma$ in ${{B}^{0}}\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{*0}}$ and ${{B}^{0}}\rightarrow{{D}^{0}}{{K}^{*0}}$ from a Dalitz analysis of ${{D}^{0}}$ and ${{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ decays to ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$_, Phys. Rev. D79 (2009) 072003, arXiv:0805.2001
  * [68] Belle collaboration, K. Negishi et al., _First model-independent Dalitz analysis of ${{B}^{0}}\rightarrow D{{K}^{*0}}$, $D\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$ decay_, PTEP (2016) 043C01, arXiv:1509.01098
  * [69] LHCb collaboration, R. Aaij et al., _Model-independent measurement of the CKM angle $\gamma$ using $B^{0}\rightarrow DK^{*0}$ decays with $D\rightarrow K_{S}^{0}\pi^{+}\pi^{-}$ and $K_{S}^{0}K^{+}K^{-}$_, arXiv:1604.01525, to appear in JHEP
  * [70] LHCb collaboration, R. Aaij et al., _Measurement of the CKM angle $\gamma$ using $B^{0}\rightarrow DK^{*0}$ with $D\rightarrow K^{0}_{S}\pi^{+}\pi^{-}$ decays_, arXiv:1605.01082, to appear in JHEP

LHCb collaboration

R. Aaij39, C. Abellán Beteta41, B. Adeva38, M. Adinolfi47, A. Affolder53, Z.
Ajaltouni5, S. Akar6, J. Albrecht10, F. Alessio39, M. Alexander52, S. Ali42,
G. Alkhazov31, P. Alvarez Cartelle54, A.A. Alves Jr58, S. Amato2, S. Amerio23,
Y. Amhis7, L. An3,40, L. Anderlini18, G. Andreassi40, M. Andreotti17,g, J.E.
Andrews59, R.B. Appleby55, O. Aquines Gutierrez11, F. Archilli39, P.
d’Argent12, A. Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,n, M.
Baalouch5, S. Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, W.
Baldini17,39, R.J. Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V.
Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F.
Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,k, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A.
Berezhnoy33, R. Bernet41, A. Bertolin23, F. Betti15, M.-O. Bettler39, M. van
Beuzekom42, S. Bifani46, P. Billoir8, T. Bird55, A. Birnkraut10, A.
Bizzeti18,i, T. Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, A.
Bondar35, N. Bondar31,39, W. Bonivento16, A. Borgheresi21,k, S. Borghi55, M.
Borisyak67, M. Borsato38, T.J.V. Bowcock53, E. Bowen41, C. Bozzi17,39, S.
Braun12, M. Britsch12, T. Britton60, J. Brodzicka55, N.H. Brook47, E.
Buchanan47, C. Burr55, A. Bursche2, J. Buytaert39, S. Cadeddu16, R.
Calabrese17,g, M. Calvi21,k, M. Calvo Gomez37,p, P. Campana19, D. Campora
Perez39, L. Capriotti55, A. Carbone15,e, G. Carboni25,l, R. Cardinale20,j, A.
Cardini16, P. Carniti21,k, L. Carson51, K. Carvalho Akiba2, G. Casse53, L.
Cassina21,k, L. Castillo Garcia40, M. Cattaneo39, Ch. Cauet10, G. Cavallero20,
R. Cenci24,t, M. Charles8, Ph. Charpentier39, M. Chefdeville4, S. Chen55,
S.-F. Cheung56, N. Chiapolini41, M. Chrzaszcz41,27, X. Cid Vidal39, G.
Ciezarek42, P.E.L. Clarke51, M. Clemencic39, H.V. Cliff48, J. Closier39, V.
Coco39, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30, G.
Collazuol23,r, P. Collins39, A. Comerma-Montells12, A. Contu39, A. Cook47, M.
Coombes47, S. Coquereau8, G. Corti39, M. Corvo17,g, B. Couturier39, G.A.
Cowan51, D.C. Craik51, A. Crocombe49, M. Cruz Torres61, S. Cunliffe54, R.
Currie54, C. D’Ambrosio39, E. Dall’Occo42, J. Dalseno47, P.N.Y. David42, A.
Davis58, O. De Aguiar Francisco2, K. De Bruyn6, S. De Capua55, M. De Cian12,
J.M. De Miranda1, L. De Paula2, P. De Simone19, C.-T. Dean52, D. Decamp4, M.
Deckenhoff10, L. Del Buono8, N. Déléage4, M. Demmer10, D. Derkach67, O.
Deschamps5, F. Dettori39, B. Dey22, A. Di Canto39, F. Di Ruscio25, H.
Dijkstra39, S. Donleavy53, F. Dordei39, M. Dorigo40, A. Dosil Suárez38, A.
Dovbnya44, K. Dreimanis53, L. Dufour42, G. Dujany55, K. Dungs39, P. Durante39,
R. Dzhelyadin36, A. Dziurda27, A. Dzyuba31, S. Easo50,39, U. Egede54, V.
Egorychev32, S. Eidelman35, S. Eisenhardt51, U. Eitschberger10, R. Ekelhof10,
L. Eklund52, I. El Rifai5, Ch. Elsasser41, S. Ely60, S. Esen12, H.M. Evans48,
T. Evans56, A. Falabella15, C. Färber39, N. Farley46, S. Farry53, R. Fay53, D.
Fazzini21,k, D. Ferguson51, V. Fernandez Albor38, F. Ferrari15, F. Ferreira
Rodrigues1, M. Ferro-Luzzi39, S. Filippov34, M. Fiore17,39,g, M. Fiorini17,g,
M. Firlej28, C. Fitzpatrick40, T. Fiutowski28, F. Fleuret7,b, K. Fohl39, M.
Fontana16, F. Fontanelli20,j, D. C. Forshaw60, R. Forty39, M. Frank39, C.
Frei39, M. Frosini18, J. Fu22, E. Furfaro25,l, A. Gallas Torreira38, D.
Galli15,e, S. Gallorini23, S. Gambetta51, M. Gandelman2, P. Gandini56, Y.
Gao3, J. García Pardiñas38, J. Garra Tico48, L. Garrido37, D. Gascon37, C.
Gaspar39, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M.
Gersabeck55, T. Gershon49, Ph. Ghez4, S. Gianì40, V. Gibson48, O.G. Girard40,
L. Giubega30, V.V. Gligorov39, C. Göbel61, D. Golubkov32, A. Golutvin54,39, A.
Gomes1,a, C. Gotti21,k, M. Grabalosa Gándara5, R. Graciani Diaz37, L.A.
Granado Cardoso39, E. Graugés37, E. Graverini41, G. Graziani18, A. Grecu30, P.
Griffith46, L. Grillo12, O. Grünberg65, B. Gui60, E. Gushchin34, Yu. Guz36,39,
T. Gys39, T. Hadavizadeh56, C. Hadjivasiliou60, G. Haefeli40, C. Haen39, S.C.
Haines48, S. Hall54, B. Hamilton59, X. Han12, S. Hansmann-Menzemer12, N.
Harnew56, S.T. Harnew47, J. Harrison55, J. He39, T. Head40, V. Heijne42, A.
Heister9, K. Hennessy53, P. Henrard5, L. Henry8, J.A. Hernando Morata38, E.
van Herwijnen39, M. Heß65, A. Hicheur2, D. Hill56, M. Hoballah5, C. Hombach55,
L. Hongming40, W. Hulsbergen42, T. Humair54, M. Hushchyn67, N. Hussain56, D.
Hutchcroft53, M. Idzik28, P. Ilten57, R. Jacobsson39, A. Jaeger12, J.
Jalocha56, E. Jans42, A. Jawahery59, M. John56, D. Johnson39, C.R. Jones48, C.
Joram39, B. Jost39, N. Jurik60, S. Kandybei44, W. Kanso6, M. Karacson39, T.M.
Karbach39,†, S. Karodia52, M. Kecke12, M. Kelsey60, I.R. Kenyon46, M.
Kenzie39, T. Ketel43, E. Khairullin67, B. Khanji21,39,k, C. Khurewathanakul40,
T. Kirn9, S. Klaver55, K. Klimaszewski29, O. Kochebina7, M. Kolpin12, I.
Komarov40, R.F. Koopman43, P. Koppenburg42,39, M. Kozeiha5, L. Kravchuk34, K.
Kreplin12, M. Kreps49, P. Krokovny35, F. Kruse10, W. Krzemien29, W.
Kucewicz27,o, M. Kucharczyk27, V. Kudryavtsev35, A. K. Kuonen40, K. Kurek29,
T. Kvaratskheliya32, D. Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51,
G. Lanfranchi19, C. Langenbruch49, B. Langhans39, T. Latham49, C. Lazzeroni46,
R. Le Gac6, J. van Leerdam42, J.-P. Lees4, R. Lefèvre5, A. Leflat33,39, J.
Lefrançois7, E. Lemos Cid38, O. Leroy6, T. Lesiak27, B. Leverington12, Y. Li7,
T. Likhomanenko67,66, M. Liles53, R. Lindner39, C. Linn39, F. Lionetto41, B.
Liu16, X. Liu3, D. Loh49, I. Longstaff52, J.H. Lopes2, D. Lucchesi23,r, M.
Lucio Martinez38, H. Luo51, A. Lupato23, E. Luppi17,g, O. Lupton56, A.
Lusiani24, F. Machefert7, F. Maciuc30, O. Maev31, K. Maguire55, S. Malde56, A.
Malinin66, G. Manca7, G. Mancinelli6, P. Manning60, A. Mapelli39, J. Maratas5,
J.F. Marchand4, U. Marconi15, C. Marin Benito37, P. Marino24,39,t, J. Marks12,
G. Martellotti26, M. Martin6, M. Martinelli40, D. Martinez Santos38, F.
Martinez Vidal68, D. Martins Tostes2, L.M. Massacrier7, A. Massafferri1, R.
Matev39, A. Mathad49, Z. Mathe39, C. Matteuzzi21, A. Mauri41, B. Maurin40, A.
Mazurov46, M. McCann54, J. McCarthy46, A. McNab55, R. McNulty13, B. Meadows58,
F. Meier10, M. Meissner12, D. Melnychuk29, M. Merk42, A Merli22,u, E
Michielin23, D.A. Milanes64, M.-N. Minard4, D.S. Mitzel12, J. Molina
Rodriguez61, I.A. Monroy64, S. Monteil5, M. Morandin23, P. Morawski28, A.
Mordà6, M.J. Morello24,t, J. Moron28, A.B. Morris51, R. Mountain60, F.
Muheim51, D. Müller55, J. Müller10, K. Müller41, V. Müller10, M. Mussini15, B.
Muster40, P. Naik47, T. Nakada40, R. Nandakumar50, A. Nandi56, I. Nasteva2, M.
Needham51, N. Neri22, S. Neubert12, N. Neufeld39, M. Neuner12, A.D. Nguyen40,
C. Nguyen-Mau40,q, V. Niess5, S. Nieswand9, R. Niet10, N. Nikitin33, T.
Nikodem12, A. Novoselov36, D.P. O’Hanlon49, A. Oblakowska-Mucha28, V.
Obraztsov36, S. Ogilvy52, O. Okhrimenko45, R. Oldeman16,48,f, C.J.G.
Onderwater69, B. Osorio Rodrigues1, J.M. Otalora Goicochea2, A. Otto39, P.
Owen54, A. Oyanguren68, A. Palano14,d, F. Palombo22,u, M. Palutan19, J.
Panman39, A. Papanestis50, M. Pappagallo52, L.L. Pappalardo17,g, C.
Pappenheimer58, W. Parker59, C. Parkes55, G. Passaleva18, G.D. Patel53, M.
Patel54, C. Patrignani20,j, A. Pearce55,50, A. Pellegrino42, G. Penso26,m, M.
Pepe Altarelli39, S. Perazzini15,e, P. Perret5, L. Pescatore46, K. Petridis47,
A. Petrolini20,j, M. Petruzzo22, E. Picatoste Olloqui37, B. Pietrzyk4, M.
Pikies27, D. Pinci26, A. Pistone20, A. Piucci12, S. Playfer51, M. Plo
Casasus38, T. Poikela39, F. Polci8, A. Poluektov49,35, I. Polyakov32, E.
Polycarpo2, A. Popov36, D. Popov11,39, B. Popovici30, C. Potterat2, E.
Price47, J.D. Price53, J. Prisciandaro38, A. Pritchard53, C. Prouve47, V.
Pugatch45, A. Puig Navarro40, G. Punzi24,s, W. Qian56, R. Quagliani7,47, B.
Rachwal27, J.H. Rademacker47, M. Rama24, M. Ramos Pernas38, M.S. Rangel2, I.
Raniuk44, G. Raven43, F. Redi54, S. Reichert55, A.C. dos Reis1, V. Renaudin7,
S. Ricciardi50, S. Richards47, M. Rihl39, K. Rinnert53,39, V. Rives Molina37,
P. Robbe7,39, A.B. Rodrigues1, E. Rodrigues55, J.A. Rodriguez Lopez64, P.
Rodriguez Perez55, A. Rogozhnikov67, S. Roiser39, V. Romanovsky36, A. Romero
Vidal38, J. W. Ronayne13, M. Rotondo23, T. Ruf39, P. Ruiz Valls68, J.J.
Saborido Silva38, N. Sagidova31, B. Saitta16,f, V. Salustino Guimaraes2, C.
Sanchez Mayordomo68, B. Sanmartin Sedes38, R. Santacesaria26, C. Santamarina
Rios38, M. Santimaria19, E. Santovetti25,l, A. Sarti19,m, C. Satriano26,n, A.
Satta25, D.M. Saunders47, D. Savrina32,33, S. Schael9, M. Schiller39, H.
Schindler39, M. Schlupp10, M. Schmelling11, T. Schmelzer10, B. Schmidt39, O.
Schneider40, A. Schopper39, M. Schubiger40, M.-H. Schune7, R. Schwemmer39, B.
Sciascia19, A. Sciubba26,m, A. Semennikov32, A. Sergi46, N. Serra41, J.
Serrano6, L. Sestini23, P. Seyfert21, M. Shapkin36, I. Shapoval17,44,g, Y.
Shcheglov31, T. Shears53, L. Shekhtman35, V. Shevchenko66, A. Shires10, B.G.
Siddi17, R. Silva Coutinho41, L. Silva de Oliveira2, G. Simi23,s, M.
Sirendi48, N. Skidmore47, T. Skwarnicki60, E. Smith54, I.T. Smith51, J.
Smith48, M. Smith55, H. Snoek42, M.D. Sokoloff58,39, F.J.P. Soler52, F.
Soomro40, D. Souza47, B. Souza De Paula2, B. Spaan10, P. Spradlin52, S.
Sridharan39, F. Stagni39, M. Stahl12, S. Stahl39, S. Stefkova54, O.
Steinkamp41, O. Stenyakin36, S. Stevenson56, S. Stoica30, S. Stone60, B.
Storaci41, S. Stracka24,t, M. Straticiuc30, U. Straumann41, L. Sun58, W.
Sutcliffe54, K. Swientek28, S. Swientek10, V. Syropoulos43, M. Szczekowski29,
T. Szumlak28, S. T’Jampens4, A. Tayduganov6, T. Tekampe10, G. Tellarini17,g,
F. Teubert39, C. Thomas56, E. Thomas39, J. van Tilburg42, V. Tisserand4, M.
Tobin40, J. Todd58, S. Tolk43, L. Tomassetti17,g, D. Tonelli39, S. Topp-
Joergensen56, E. Tournefier4, S. Tourneur40, K. Trabelsi40, M. Traill52, M.T.
Tran40, M. Tresch41, A. Trisovic39, A. Tsaregorodtsev6, P. Tsopelas42, N.
Tuning42,39, A. Ukleja29, A. Ustyuzhanin67,66, U. Uwer12, C. Vacca16,39,f, V.
Vagnoni15, G. Valenti15, A. Vallier7, R. Vazquez Gomez19, P. Vazquez
Regueiro38, C. Vázquez Sierra38, S. Vecchi17, M. van Veghel43, J.J.
Velthuis47, M. Veltri18,h, G. Veneziano40, M. Vesterinen12, B. Viaud7, D.
Vieira2, M. Vieites Diaz38, X. Vilasis-Cardona37,p, V. Volkov33, A.
Vollhardt41, D. Voong47, A. Vorobyev31, V. Vorobyev35, C. Voß65, J.A. de
Vries42, R. Waldi65, C. Wallace49, R. Wallace13, J. Walsh24, J. Wang60, D.R.
Ward48, N.K. Watson46, D. Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49,
G. Wilkinson56,39, M. Wilkinson60, M. Williams39, M.P. Williams46, M.
Williams57, T. Williams46, F.F. Wilson50, J. Wimberley59, J. Wishahi10, W.
Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48,
K. Wyllie39, Y. Xie63, Z. Xu40, Z. Yang3, H. Yin63, J. Yu63, X. Yuan35, O.
Yushchenko36, M. Zangoli15, M. Zavertyaev11,c, L. Zhang3, Y. Zhang3, A.
Zhelezov12, Y. Zheng62, A. Zhokhov32, L. Zhong3, V. Zhukov9, S. Zucchelli15.

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

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 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
†Deceased