EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-182 LHCb-PAPER-2014-028 2 December 2014

Measurement of $C\\!P$ violation parameters in
${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decays

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

An analysis of ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decays is presented, where
$D$ represents an admixture of ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons reconstructed in four
separate final states: ${{K}^{-}}{{\pi}^{+}}$, ${{\pi}^{-}}{{K}^{+}}$,
${{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$. The data sample corresponds
to 3.0$\mbox{\,fb}^{-1}$ of proton-proton collision, collected by the LHCb
experiment. Measurements of several observables are performed, including
$C\\!P$ asymmetries. The most precise determination is presented of
$r_{{B}}({D}{{K}^{*0}})$, the magnitude of the ratio of the amplitudes of the
decay ${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ with a ${b}\rightarrow{u}$
or a ${b}\rightarrow{c}$ transition, in a $K\pi$ mass region of $\pm
50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the $K^{*}(892)$ mass and
for an absolute value of the cosine of the ${K}^{*0}$ helicity angle larger
than 0.4.

Published in Phys. Rev. D90 (2014) 112002

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

##  1 Introduction

Direct $C\\!P$ violation can arise in ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$
decays from the interference between the two colour-suppressed
${b}\rightarrow{u}$ and ${b}\rightarrow{c}$ transitions shown in the Feynman
diagrams of Fig. 1, when the ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons decay to a common final
state. Here and in the following, $D$ represents a neutral meson that is an
admixture of ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons and ${K}^{*0}$
represents the $K^{*}(892)^{0}$ meson. Inclusion of charge conjugate processes
is implied unless specified otherwise.

Figure 1: Feynman diagrams of (left) ${{B}^{0}}\rightarrow{{D}^{0}}{{K}^{*0}}$
and (right) ${{B}^{0}}\rightarrow{{\kern
1.79997pt\overline{\kern-1.79997ptD}{}}{}^{0}}{{K}^{*0}}$.

The amount of $C\\!P$ violation is related to the value of the weak phase

$\gamma\equiv\arg\left(-\frac{V_{ud}V_{ub}^{*}}{V_{cd}V_{cb}^{*}}\right),$ (1)

the least-well determined angle of the unitarity triangle, where $V_{ij}$ are
elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix [1, *Kobayashi:1973fv].
The current experimental measurements are
$\gamma=\left(72.0_{-15.6}^{+14.7}\right)^{\circ}$ by the LHCb collaboration
[3], $\gamma=\left(69_{-16}^{+17}\right)^{\circ}$ by the BaBar [4]
collaboration and $\gamma=\left(68_{-14}^{+15}\right)^{\circ}$ by the Belle
collaboration [5]. This angle can be measured with extremely small theoretical
uncertainties [6], using decay modes proceeding through amplitudes involving
only the exchange of a $W$ boson. Such methods to determine $\gamma$ from
hadronic $B$-decay rates were originally proposed in Refs. [7, *bib:GL,
*Atwood:1996ci, 10] for ${B}\rightarrow{D}{K}$ decays and can be applied to
the ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decay [11]. In this decay, the charge
of the kaon from the ${{K}^{*0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$ decay
unambiguously identifies the flavour of the decaying $B$ meson. Hence, no
flavour tagging is needed.

The use of these specific neutral $B$ meson decays is interesting since the
interfering amplitudes are of comparable size, as opposed to the charged
${{{B}^{+}}}\rightarrow{D}{{K}^{+}}$ decay that involves both colour-
suppressed and colour-allowed amplitudes; hence the system could exhibit
larger $C\\!P$-violating effects. Contributions from ${B}^{0}$ decays to the
${D}{{K}^{+}}{{\pi}^{-}}$ final state through non-${{K}^{*0}}$ intermediate
resonances can pollute the ${D}{{K}^{*0}}$ reconstructed signal candidates
because of the large natural width of the ${{K}^{*0}}$. They are treated
following Ref. [12], with the use of a coherence factor, $\kappa$, in addition
to the hadronic parameters $r_{B}$ and $\delta_{B}$, defined as

$\displaystyle\kappa$
$\displaystyle\equiv\left|\frac{\int\left|A_{cb}(p)A_{ub}(p)\right|e^{i\delta(p)}{\rm
d}p}{\sqrt{\int\left|A_{ub}(p)\right|^{2}{\rm
d}p\int\left|A_{cb}(p)\right|^{2}{\rm d}p}}\right|,$ (2)
$\displaystyle\delta_{B}$
$\displaystyle\equiv\arg\left(\frac{\int\left|A_{cb}(p)A_{ub}(p)\right|e^{i\delta(p)}{\rm
d}p}{\sqrt{\int\left|A_{ub}(p)\right|^{2}{\rm
d}p\int\left|A_{cb}(p)\right|^{2}{\rm d}p}}\right),$ (3) $\displaystyle r_{B}$
$\displaystyle\equiv\sqrt{\frac{\int\left|A_{ub}(p)\right|^{2}{\rm
d}p}{\int\left|A_{cb}(p)\right|^{2}{\rm d}p}},$ (4)

where $A_{ub}(p)$ and $A_{cb}(p)$ are the amplitudes of the
${b}\rightarrow{u}$ and ${b}\rightarrow{c}$ transitions, respectively, to the
${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ decays, $\delta(p)$ is the
strong-phase difference between the two amplitudes and $p$ is a point in the
three-body phase space of the ${B}^{0}$ meson. The integrals are defined over
the phase space considered here, namely in a ${{K}^{+}}{{\pi}^{-}}$ mass range
of $\pm 50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the nominal
${{K}^{*0}}$ mass [13] and for an absolute value of the cosine of the helicity
angle $\theta^{*}$ greater than 0.4, where $\theta^{*}$ is defined as the
angle between the $K$ momentum and the opposite of the $B$ momentum in the
${K}^{*0}$ rest frame. The formalism of (2)-(4) applies to the generic three-
body decay ${{B}^{0}}\rightarrow D{{K}^{+}}{{\pi}^{-}}$ with any number of
intermediate resonances included. The integration range is restricted here to
the ${K}^{*0}$ resonance in order to obtain a large value of the coherence
factor.

This paper presents two measurements of the ratio, ${\cal R}_{{C\\!P}+}$, of
flavour-averaged partial widths of the ${B}^{0}$ $\rightarrow$ $D$ ${K}^{*0}$
decay with the $D$ decaying to a $C\\!P$-even eigenstate,

${\cal R}_{{C\\!P}+}\equiv 2\times\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}_{{C\\!P}+}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}_{{C\\!P}+}{{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{{D}^{0}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{*0}})}.$ (5)

The relation above is approximated using specific final states of the $D$
meson as ${\cal R}_{{C\\!P}+}\approx{\cal R}_{d}^{hh}$, neglecting corrections
from doubly Cabibbo-suppressed ${{D}^{0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$
decays, with

${\cal R}_{d}^{hh}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}(h^{+}h^{-}){{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}})}\times\frac{{\cal
B}({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}})}{{\cal B}({{D}^{0}}\rightarrow
h^{+}h^{-})},$ (6)

where $h$ represents either a $\pi$ or a $K$ meson. This quantity is related
to the $\gamma$ angle and the hadronic parameters by [14]

${\cal
R}_{d}^{hh}=\frac{1+r_{B}^{2}+2r_{B}\kappa\cos\delta_{B}\cos\gamma}{1+r_{B}^{2}r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}-\delta_{D})\cos\gamma},$
(7)

where $r_{D}$ and $\delta_{D}$ are the magnitude of the ratio and the phase
difference, respectively, between the amplitudes of the
${{D}^{0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$ and
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays. Charm mixing and $C\\!P$
violation in the decays of $D$ mesons have an effect on the determination of
$\gamma$ [10, 15] but are neglected here because of the large expected value
of $r_{B}$.

Measurements of the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$-${B}^{0}$ partial decay-rate
asymmetry, ${\cal A}_{d}^{hh}$, using ${D}\rightarrow h^{+}h^{-}$ final states
are also presented,

${\cal A}_{d}^{hh}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})-\Gamma({{B}^{0}}\rightarrow{D}(h^{+}h^{-}){{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow D(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}(h^{+}h^{-}){{K}^{*0}})}=\frac{2r_{B}\kappa\sin\delta_{B}\sin\gamma}{1+r_{B}^{2}+2r_{B}\kappa\cos\delta_{B}\cos\gamma}.$
(8)

The ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$-${B}^{0}$
asymmetry, ${\cal A}_{d}^{K\pi}$, obtained from the Cabibbo-favoured decay
${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ with $D$ $\rightarrow$ ${K}^{+}$
${\pi}^{-}$, where the two kaons from the $D$ and the ${K}^{*0}$ decay have
the same sign, is

${\cal A}_{d}^{K\pi}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})-\Gamma({{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}})}\\\
=\frac{2r_{B}r_{D}\kappa\sin(\delta_{B}-\delta_{D})\sin\gamma}{1+r_{B}^{2}r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}-\delta_{D})\cos\gamma}.$
(9)

The Cabibbo-suppressed decay ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ with
${D}\rightarrow{{\pi}^{+}}{{K}^{-}}$, where the two kaons have opposite
charge, is studied for the first time by LHCb. The ratios of suppressed
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ to favoured
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ partial widths are
measured separately for ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$, and defined as ${\cal
R}_{d}^{+}$ and ${\cal R}_{d}^{-}$, respectively,

$\displaystyle{\cal{R}}^{+}_{d}\equiv$
$\displaystyle\frac{\Gamma({{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}})}{\Gamma({{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}})}=\frac{r_{B}^{2}+r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}+\delta_{D}+\gamma)}{1+r_{B}^{2}r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}-\delta_{D}+\gamma)},$
(10) $\displaystyle{\cal{R}}^{-}_{d}\equiv$ $\displaystyle\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}=\frac{r_{B}^{2}+r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}+\delta_{D}-\gamma)}{1+r_{B}^{2}r_{D}^{2}+2r_{B}r_{D}\kappa\cos(\delta_{B}-\delta_{D}-\gamma)}.$
(11)

In $pp$ collisions, ${B}^{0}_{s}$ mesons are produced and can decay to the
same final state, ${{B}^{0}_{s}}\rightarrow{D}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ [16]. Similar asymmetry
observables to those defined above for ${B}^{0}$ mesons are measured with
${B}^{0}_{s}$ mesons. These are the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$-${B}^{0}_{s}$ asymmetry,
${\cal A}_{s}^{hh}$, obtained from the ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ final states of the $D$ meson,

${\cal A}^{hh}_{s}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}(h^{+}h^{-}){{K}^{*0}})-\Gamma({{B}^{0}_{s}}\rightarrow{D}(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}(h^{+}h^{-}){{K}^{*0}})+\Gamma({{B}^{0}_{s}}\rightarrow{D}(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})},$ (12)

and the asymmetry, ${\cal A}_{s}^{\pi K}$, from the Cabibbo-favoured decay
${{B}^{0}_{s}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$, where the two kaons have
opposite charge,

${\cal A}^{\pi K}_{s}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}})-\Gamma({{B}^{0}_{s}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}})+\Gamma({{B}^{0}_{s}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}.$ (13)

The ${{B}^{0}_{s}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ decay, where the two kaons
have the same charge, is highly suppressed and therefore unobserved with the
current data sample. Finally, the ratios of the flavour-averaged partial
widths of the ${B}^{0}$ and ${{B}^{0}_{s}}$ decays, when the $D$ meson is
reconstructed as ${D}\rightarrow h^{+}h^{-}$, ${\cal{R}}^{hh}_{ds}$, are also
considered,

${\cal{R}}^{hh}_{ds}\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow D(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow
D(h^{+}h^{-}){{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D(h^{+}h^{-}){{K}^{*0}})+\Gamma({{B}^{0}_{s}}\rightarrow D(h^{+}h^{-}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})}.$ (14)

The observables related to ${B}^{0}_{s}$ decays could in principle also be
used to determine the value of $\gamma$. However, the observables pertaining
to ${B}^{0}$ mesons are far more sensitive, owing to the fact that the ratio
of interfering amplitudes is closer to unity. Those related to ${B}^{0}_{s}$
mesons are measured and reported in this paper but are not yet precise enough
to provide any constraint on $\gamma$.

##  2 The LHCb detector, data set and event selection

The study reported here is based on a data sample of $pp$ collisions obtained
from 3.0$\mbox{\,fb}^{-1}$ of integrated luminosity with the LHCb detector
[17]. The centre-of-mass energy was $7\,{\rm TeV}$ during the year 2011, when
approximately $1/3$ of the data were collected, and $8\,{\rm TeV}$ during the
year 2012.

The LHCb detector [17] 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 [18], a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\rm\,Tm}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, with
a relative uncertainty that varies from 0.4% at low momentum to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum distance of a track to
a primary vertex, the impact parameter, is measured with a resolution of
$(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is the component
of $p$ 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 [19]. Photon, electron and hadron
candidates are identified by a calorimeter system consisting of scintillating-
pad and preshower detectors, an electromagnetic calorimeter and a hadronic
calorimeter. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers. The trigger [20] consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

The analysis uses events triggered at the hardware level either when one of
the charged tracks of the signal decay gives a large enough energy deposit in
the calorimeter system (hadron trigger), or when one of the particles in the
event, not reconstructed as forming the signal candidate, fulfills any trigger
requirement (i.e. mainly events triggered by one high $p_{\rm T}$ muon,
hadron, photon or electron coming from the decay of the other $B$ meson in the
event). The software trigger requires a two-, three- or four-track secondary
vertex with a large sum of the $p_{\rm T}$ of the charged particles and a
significant displacement from the primary $pp$ interaction vertices (PVs). At
least one charged particle should have $\mbox{$p_{\rm
T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $\chi^{2}_{\rm IP}$ with
respect to any PV greater than 16, where $\chi^{2}_{\rm IP}$ is defined as the
difference in $\chi^{2}$ of a given PV reconstructed with and without the
considered particle. A multivariate algorithm [21] is used for the
identification of secondary vertices consistent with the decay of a $b$
hadron.

Approximately 1 million simulated events are used to describe the signal
shapes and to compute the efficiencies when data-driven methods are not
available. In the simulation, $pp$ collisions are generated using Pythia [22,
23] with a specific LHCb configuration [24]. Decays of hadronic particles are
described by EvtGen [25], in which final state radiation is generated using
Photos [26]. The interaction of the generated particles with the detector and
its response are implemented using the Geant4 toolkit [27,
*Agostinelli:2002hh] as described in Ref. [29].

Candidate ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decays are reconstructed in
events fulfilling these trigger conditions combining $D$ mesons reconstructed
in the ${{K}^{\pm}}{{\pi}^{\mp}}$, ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ decays and ${{K}^{*0}}$ mesons reconstructed in the
${{K}^{+}}{{\pi}^{-}}$ final state. The invariant masses of the $D$ and
${K}^{*0}$ mesons are required to be within
20${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
50${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of their known masses [13],
respectively. The $B$ candidate momentum is refit constraining the mass of the
$D$ meson to its known value. It is required that
$\left|\cos\theta^{*}\right|>0.4$.

A boosted decision tree (BDT) [30] is used with the algorithm described in
Ref. [31] to separate signal from combinatorial background. Separate BDTs are
optimised for ${{K}^{\pm}}{{\pi}^{\mp}}$, ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ final states of the $D$ meson. In all cases the
samples used to train the BDT are fully simulated events for the signal and
candidates from the upper sideband of the $B$ mass distribution in data for
the background. This upper sideband is defined as events with a
${D}{{K}^{*0}}$ invariant mass between
5.8${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ and
7${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, lying outside the region used for
the fit described in Sect. 3. The variables used by the BDT to differentiate
signal and background are: the $p_{\rm T}$ of each particle in the final
state; the fit quality of the $D$ and ${B}^{0}$ vertices; the ${K}^{*0}$, $D$
and ${B}^{0}$ $\chi^{2}_{\rm IP}$; the angle between the ${B}^{0}$ momentum
and the vector from the PV to the ${B}^{0}$ decay vertex; the significance of
the displacement of the four final-state tracks from the PV.

Thresholds on the BDT classifier are optimised with respect to the signal
significance of the ${B}^{0}$ decay modes for the three final states
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$,
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ and
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$, where the
significance is defined as $S/\sqrt{S+B}$ with $S$ and $B$ the expected number
of signal and background candidates. The efficiencies of the selection based
on the BDT output classifier are equal to 69%, 71% and 75% for the
${D}\rightarrow{{K}^{\pm}}{{\pi}^{\mp}}$, ${D}\rightarrow{{K}^{+}}{{K}^{-}}$
and ${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decay channels, respectively.

To improve the purity of the data sample, further selection requirements are
made in addition to the BDT. Particle identification (PID) criteria are
applied and only well identified pions and kaons are retained. The kaon
identification efficiency of the PID criteria is equal to $87\%$ with a pion
misidentification rate of 5%. Possible contamination from ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}ph^{-}$ decays is reduced by
keeping only kaon candidates incompatible with being a proton.

A potentially significant background is due to events where the $K$ from
${D}\rightarrow{{K}^{\pm}}{{\pi}^{\mp}}$ decays is misidentified as a $\pi$
and the $\pi$ is simultaneously mis-identified as a $K$. This causes cross-
feed from the favoured
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decay into the
suppressed ${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ decay. A
veto is applied on the $D$ invariant mass computed with a pion mass assignment
for the kaon and a kaon mass assignment for the pion. Only candidates for
which this invariant mass differs by more than
7${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ from the known ${D}^{0}$ mass [13]
are kept, reducing this background to a negligible level while keeping $97\%$
of the signal candidates.

Another potential background is due to charmless decays $B^{0}\rightarrow
h^{\pm}h^{\prime\mp}{{K}^{+}}{{\pi}^{-}}$, where $h^{\prime}$ is also $\pi$ or
$K$. It is removed by requiring the $D$ flight distance with respect to the
$B$ vertex to exceed three times its uncertainty. Specific peaking backgrounds
from $B_{(s)}^{0}\rightarrow D_{(s)}^{\mp}h^{\pm}$ decays are eliminated by
applying a veto on candidates for which the invariant mass of three of the
four charged mesons is compatible within $\pm
15{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${D}^{+}$ or
${D}^{+}_{s}$ masses.

After all selections are applied, $0.9\%$ of the events contain more than one
signal candidate. Only the candidate with the largest $B$ flight distance with
respect to the PV, divided by its uncertainty, is retained. In case several
PVs are reconstructed, the PV with respect to which the $B$ candidate has the
smallest displacement is used.

Figure 2 shows the background-subtracted ${{K}^{+}}{{\pi}^{-}}$ invariant mass
of the ${K}^{*0}$ candidates used to reconstruct
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decays, obtained
with the sPlot technique [32]. All selections described above have been
applied except the requirement on the ${K}^{*0}$ candidate mass. This
distribution is fitted with a relativistic Breit-Wigner function to describe
the ${K}^{*0}$ signal and a first-order polynomial for the non-${K}^{*0}$
contribution. From the fit result, it is estimated that $(8.4\pm 3.4)\%$ of
the signal ${B}^{0}$ candidates are formed with a ${{K}^{+}}{{\pi}^{-}}$ pair
that does not originate from a ${K}^{*0}$ decay, in the ${{K}^{+}}{{\pi}^{-}}$
mass region considered for the analysis.

Figure 2: Background-subtracted ${{K}^{*0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$
invariant mass for ${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$
signal candidates. The data (points) and the fit described in the text (solid
line) are shown. The dashed line represents the ${{K}^{*0}}$ signal and the
filled area the non-${K}^{*0}$ contribution to the
${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ signal. The vertical dotted lines indicate
the invariant mass region used in the analysis.

##  3 Invariant mass fit

The numbers of reconstructed signal ${B}^{0}$ and ${B}^{0}_{s}$ candidates are
determined from an unbinned maximum-likelihood fit to the $D{{K}^{*0}}$
invariant mass distributions. Candidates are split into eight categories,
which are fitted simultaneously: ${D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$,
${D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$,
${D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$, ${D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$,
${D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$, ${D}({{K}^{+}}{{K}^{-}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$,
${D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ and
${D}({{\pi}^{+}}{{\pi}^{-}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ candidates. The mass
distribution of each category is fitted with a sum of probability density
functions (PDFs) modelling the various contributing components:

  1. 1.

The ${B}^{0}$ and ${B}^{0}_{s}$ signals are both described by a sum of two
Gaussian functions with a common mean;

  2. 2.

The combinatorial background is described by an exponential function;

  3. 3.

The cross-feed from ${{B}^{0}}\rightarrow{D}\rho^{0}$ decays, where one $\pi$
from the $\rho^{0}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decay is misidentified as
a $K$, is described by a non-parametric PDF [33] determined from simulation;

  4. 4.

The partially reconstructed ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ and
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
decays, where ${D}^{*}$ stands for ${D}^{*0}$ or ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*0}$ with the ${\pi}^{0}$ or
$\gamma$ from the ${{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}}$ or
${{D}^{*0}}\rightarrow{{D}^{0}}\gamma$ decay not reconstructed, are each
modelled by non-parametric PDFs determined from simulation.

A separate fit to ${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}})\rho^{0}$
candidates in the same data sample is performed, reconstructing $\rho^{0}$ in
the ${{\pi}^{+}}{{\pi}^{-}}$ final state within a $\pm
50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ mass range around the known
${\rho}^{0}$ mass. The observed number of
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}})\rho^{0}$ candidates is used,
along with the efficiency to reconstruct
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}})\rho^{0}$ candidates as
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ from simulation, to
constrain the number of cross-feed events in the
${D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ category. The numbers of cross-feed
candidates in the other categories are derived from the
${D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ category using the relative $D$
branching fractions from Ref. [13] and selection efficiencies from simulation.
As a negligible $C\\!P$ asymmetry is expected for the
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}})\rho^{0}$ background, the
numbers of cross-feed events in the ${D}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ categories are constrained to
be identical to those of the corresponding ${D}{{K}^{*0}}$ categories.

The partially reconstructed background accumulates at masses lower than the
known ${B}^{0}$ mass. Its shape depends on the unknown fraction of
longitudinal polarisation in the ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ and
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
decays, i.e. the probability that the ${{D}^{*}}$ in these decays is produced
with helicity equal to 0. In order to model the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
contribution, a PDF is built from a linear combination of two non-parametric
functions corresponding to the three orthogonal helicity amplitudes. Two of
the orthogonal helicity amplitudes result in the same distribution in
invariant mass because of parity conservation in the
${{D}^{*0}}\rightarrow{{D}^{0}}{\gamma}$ decay, hence simplifying the model.
Each function, modelled from simulated events, corresponds to the weighted sum
of the ${{D}^{*0}}\rightarrow{{D}^{0}}\gamma$ and
${{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}}$ contributions for a defined
helicity eigenstate, where the weights take into account the relative
${D}^{*0}$ decay branching fractions from Ref. [13] and the corresponding
efficiencies from simulation. The ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$
background is modelled in a similar way, shifting the shape obtained for the
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
decay by the known difference between the ${B}^{0}$ and ${B}^{0}_{s}$ masses
[13]. The coefficients of the two functions in the linear combinations are
different for the ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
decays but are common to the 8 categories and are free parameters in the fit.

The yields of the ${B}^{0}_{s}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ partially reconstructed
backgrounds in the ${D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ categories are fixed
to zero since the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
decay modes have negligible total branching fractions when the kaons from the
$D$ and ${K}^{*0}$ have the same charge sign. The yields of the
${{B}^{0}_{s}}\rightarrow{{D}^{*}}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
backgrounds in the ${D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ categories are
constrained to be the same because $C\\!P$ violation is expected to be
negligible for this background. Additional constraints on the normalisations
of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
backgrounds in the ${D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ and
${D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ categories, relative to the
${D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ categories, are imposed using the
relevant $D$ decay branching fractions from Ref. [13] and selection
efficiencies obtained from simulation.

There are 35 free parameters in the fit: the ${B}^{0}$ peak position; the core
Gaussian resolution for the ${B}^{0}$ and the ${B}^{0}_{s}$ signal shapes; the
slope of the combinatorial background, which is different for each $D$ meson
final state (one parameter for ${D}\rightarrow{{K}^{\pm}}{{\pi}^{\mp}}$, one
for ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and one for
${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$); the fractions of longitudinal
polarisation in the ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{*}}{{K}^{*0}}$
backgrounds and the yields for each fit component within each category.
$C\\!P$ violation in ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ decays is
allowed by floating the yields of this background in the ${D}{{K}^{*0}}$ and
${D}{{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ categories
separately. The difference between the central value of the ${B}^{0}_{s}$ and
${B}^{0}$ mass is fixed to its known value from Ref. [13] and the ratio
between the signal Gaussian resolutions is fixed from the simulation.

The non-parametric functions used to model all the specific backgrounds are
smeared to take into account the different mass resolutions observed in data
and simulation. The invariant mass distributions together with the function
resulting from the fit are shown in Figs. 3 and 4. The numbers of signal
events in each category are summarised in Table 1.

Figure 3: Distributions of (top left) ${D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$, (top right)
${D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$, (bottom left)
${D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$ and (bottom right)
${D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ invariant mass. The data (black points)
and the fitted invariant mass model (thick solid line) are shown. The PDFs
corresponding to the different species are indicated in the legend: the
${{B}^{0}}$ signal, the ${{B}^{0}_{s}}$ signal, combinatorial background,
${{B}^{0}}\rightarrow{D}\rho^{0}$ background, partially reconstructed
${{B}^{0}_{s}}\rightarrow{{D}^{*}}{{\kern
1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$ and
${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ backgrounds.

Figure 4: Distributions of (top left) ${D}({{K}^{+}}{{K}^{-}}){{\kern 1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$, (top right) ${D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$, (bottom left) ${D}({{\pi}^{+}}{{\pi}^{-}}){{\kern 1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$ and (bottom right) ${D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ invariant mass. The data (black points) and the fitted invariant mass model (thick solid line) are shown. The PDFs corresponding to the different species are indicated in the legend: the ${{B}^{0}}$ signal, the ${{B}^{0}_{s}}$ signal, combinatorial background, ${{B}^{0}}\rightarrow{D}\rho^{0}$ background and partially reconstructed ${{B}^{0}_{s}}\rightarrow{{D}^{*}}{{\kern 1.79997pt\overline{\kern-1.79997ptK}{}}{}^{*0}}$ and ${{B}^{0}}\rightarrow{{D}^{*}}{{K}^{*0}}$ backgrounds. Table 1: Yields of signal candidates with their statistical uncertainties. Channel | Signal yield | Channel | Signal yield
---|---|---|---
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $\phantom{1}24\pm 12$ | ${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ | $\phantom{1}26\pm 12$
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $370\pm 22$ | ${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ | $405\pm 23$
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $\phantom{1}36\pm 9$ | ${{B}^{0}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ | $\phantom{1}53\pm 10$
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $\phantom{1}18\pm 6$ | ${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ | $\phantom{1}21\pm 7$
${{B}^{0}_{s}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $933\pm 33$ | ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ | $993\pm 34$
${{B}^{0}_{s}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $115\pm 12$ | ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ | $125\pm 13$
${{B}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ | $\phantom{1}39\pm 7$ | ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ | $\phantom{1}35\pm 7$

##  4 Systematic uncertainties

The signal yields determined from the invariant mass fit are corrected in
order to evaluate the asymmetries and ratios described in (5)-(13). These
corrections account for selection efficiency and detection asymmetry, ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}}$-${B}$ production asymmetry and its
dilution due to mixing, misidentification of $D$ meson decays, ${D}^{0}$ decay
branching fractions, hadronisation fractions and biases introduced by the fit
model. The uncertainties in these corrections cause systematic uncertainties
in the results. Systematic uncertainties are also introduced by the
uncertainties in the various constraints on the invariant mass model. The
systematic uncertainties incurred from all sources are obtained combining in
quadrature the individual uncertainties and are summarised in Table 2.

###  4.1 Efficiencies

Separate corrections are applied to account for differing trigger and PID
efficiencies. These efficiencies are obtained from real data by means of low-
background calibration samples of kaons and pions from
${{D}^{*\pm}}\rightarrow{D}({{K}^{\mp}}{{\pi}^{\pm}}){{\pi}^{\pm}}$ decays
[34]. They are evaluated separately for ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}$ and $B$ modes to account for
detection asymmetries. The relative trigger and PID efficiencies differ from
unity by 1% and 5%, respectively, and their uncertainties result in the
systematic uncertainties given in Table 2.

Another correction is applied to account for the differences in the kinematic
selection requirements of the different decay modes. The efficiencies are
evaluated from simulated data and they are assumed to be equal for the
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ and
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ decays. They differ
between decay modes by 8% at maximum. The uncertainties on these efficiencies
affect the measured observables as shown in Table 2. It is noted that the
${\cal R}_{d}^{\pm}$ observables have no systematic uncertainty from selection
efficiency. This is because they are separated by $B$ meson flavour and have
the same $D$ meson final state; therefore all efficiencies are assumed to
cancel.

Because of the different ${B}^{0}$ and ${B}^{0}_{s}$ lifetimes, the ratio of
efficiencies for ${{B}^{0}}\rightarrow{D}(h^{+}h^{\prime-}){{K}^{*0}}$ to
${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}(h^{\prime+}h^{-}){{K}^{*0}}$
is different from one. This ratio is assumed to be equal between all the $D$
meson final states and is calculated using the
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$
decay modes, assuming that the lifetime difference effects factorise from the
other selection effects. The difference in ${B}^{0}$ and ${B}^{0}_{s}$
selection efficiencies arises from the use of variables sensitive to the decay
topology in the BDT and is equal to 3%. The systematic uncertainty from this
source is labelled “Lifetime difference” in Table 2. The only observables
affected by the systematic uncertainty due to lifetime difference are the
${\cal R}_{ds}^{hh}$ observables, since only these involve both ${B}^{0}$ and
${B}^{0}_{s}$ partial widths.

###  4.2 Production asymmetry

The difference between ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$, or ${B}^{0}_{s}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$, production rates in $pp$
collisions is accounted for by applying a correction factor $a_{P}=(1-\alpha
A_{P})/(1+\alpha A_{P})$ to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ signal yields, where

$A_{P}\equiv\frac{\sigma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}})-\sigma({B})}{\sigma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}})+\sigma({B})}$ (15)

is the raw production asymmetry of the ${B}^{0}$ or ${B}^{0}_{s}$ mesons in
question. In the case of ${B}^{0}$ mesons, $A_{P}$ has been measured, using
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{*0}}$
decays, to be $A_{P}=0.010\pm 0.013$ [35]. The effect of the raw production
asymmetry on the number of observed ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ or ${B}^{0}$ decays becomes
less pronounced for larger decay times due to mixing. It is also affected by
the selection efficiency as a function of the decay time,
$\epsilon({{B}^{0}}\rightarrow{D}{{K}^{*0}},t)$. A factor, $\alpha$, accounts
for this dilution and is given for ${B}^{0}$ mesons by

$\alpha=\frac{\int_{0}^{+\infty}e^{-t/{\tau_{{B}^{0}}}}\cos(\Delta
m_{d}t)\epsilon({{B}^{0}}\rightarrow{D}{{K}^{*0}},t)\,{\rm
d}t}{\int_{0}^{+\infty}e^{-t/{\tau_{{B}^{0}}}}\epsilon({{B}^{0}}\rightarrow{D}{{K}^{*0}},t)\,{\rm
d}t},$ (16)

where $\Delta m_{d}$ is the ${B}^{0}$-${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ oscillation frequency and
$\tau_{{B}^{0}}$ is the ${B}^{0}$ lifetime.

The factor $\alpha$ is evaluated separately for each
${{B}^{0}}\rightarrow{D}({{K}^{\pm}}{{\pi}^{\mp}}){{K}^{*0}}$,
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ and
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decays since it is
dependent on the separately optimised selection requirements. The resulting
values of $\alpha$ are $0.362\pm 0.014$, $0.391\pm 0.014$ and $0.398\pm
0.014$, respectively. These figures are computed using fully simulated events
and data-driven PID efficiencies from calibration samples. The uncertainty on
$a_{P}$ is propagated to the measured observables to estimate the systematic
uncertainty from the production asymmetry and mixing. Owing to the large
${B}^{0}_{s}$ oscillation frequency, a potential production asymmetry of
${B}^{0}_{s}$ mesons does not significantly affect the measurements presented
here and is neglected.

###  4.3 Misidentification of $D$ meson decays

Favoured ${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decays are
misidentified as suppressed
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ decays at a small
but non-negligible rate. The fraction of signal
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decays reconstructed
as signal ${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ decays is
estimated from the simulation to be less than 1% after applying the veto
described in Sect. 2. However, the best-fit values of the numbers of
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$ decays are corrected
to take this into account. The uncertainty in this correction causes a
systematic uncertainty in the ${\cal R}_{d}^{\pm}$ observables given in Table
2 as misID.

###  4.4 Other corrections

Two ratios of ${D}^{0}$ meson decay branching fractions (BF) are needed to
compute the final results because of the approximation made between ${\cal
R}_{{C\\!P}+}$ and ${\cal R}_{d}^{hh}$ in Eq. (6). These are taken from Ref.
[13], the results of which imply that the ratio of ${\cal
B}\left({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}\right)$ to ${\cal
B}\left({{D}^{0}}\rightarrow{{K}^{+}}{{K}^{-}}\right)$ is $9.80\pm 0.24$ and
the ratio of ${\cal B}\left({{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}\right)$
to ${\cal B}\left({{D}^{0}}\rightarrow{{\pi}^{+}}{{\pi}^{-}}\right)$ is
$27.7\pm 0.6$.

The fraction of $b$ quarks that hadronize into ${{B}^{0}}$ and ${{B}^{0}_{s}}$
mesons in $pp$ collisions, $f_{d}$ and $f_{s}$, respectively, has an effect on
the number of ${{B}^{0}}$ and ${{B}^{0}_{s}}$ mesons produced in LHCb. Since
the ${\cal R}_{ds}^{hh}$ observables are ratios of ${{B}^{0}}$ and
${{B}^{0}_{s}}$ decay partial widths, they are corrected with the
hadronisation fraction ratio $f_{s}/f_{d}=0.267\pm 0.021$ [36]. The ${\cal
R}_{ds}^{hh}$ observables also contain a factor of
$\tau_{{{B}^{0}_{s}}}/\tau_{{{B}^{0}}}$, which arises because of the
lifetimes, $\tau$, of the ${B}^{0}$ and ${B}^{0}_{s}$ mesons. This is taken
from Ref. [13], the results of which imply that
$\tau_{{{B}^{0}_{s}}}/\tau_{{{B}^{0}}}=0.99\pm 0.01$.

Table 2: Uncertainties in the observables. All model-related systematic uncertainties are added in quadrature and the result is shown as one source of systematic uncertainty. The presence of ‘–’ indicates that the source of uncertainty does not affect the observable. Source | Observable
---|---
| ${\cal{A}}^{KK}_{d}$ | ${\cal{A}}^{\pi\pi}_{d}$ | ${\cal{R}}^{KK}_{d}$ | ${\cal{R}}^{\pi\pi}_{d}$ | ${\cal{R}}_{d}^{+}$ | ${\cal{R}}_{d}^{-}$ | ${\cal{R}}^{KK}_{ds}$ | ${\cal{R}}^{\pi\pi}_{ds}$ | ${\cal{A}}^{KK}_{s}$ | ${\cal{A}}^{\pi\pi}_{s}$ | ${\cal{A}}_{d}^{K\pi}$ | ${\cal{A}}^{\pi K}_{s}$
Trigger efficiency | 0.011 | 0.011 | 0.015 | 0.019 | – | – | 0.000 | 0.000 | 0.011 | 0.011 | 0.012 | 0.012
PID efficiency | 0.005 | 0.005 | 0.010 | 0.012 | – | – | 0.000 | 0.000 | 0.005 | 0.005 | 0.005 | 0.005
Selection efficiency | 0.014 | 0.014 | 0.029 | 0.037 | – | – | 0.000 | 0.000 | 0.015 | 0.014 | 0.014 | 0.014
Lifetime difference | – | – | – | – | – | – | 0.002 | 0.003 | – | – | – | –
Prod. asymmetry | 0.005 | 0.005 | 0.001 | 0.000 | – | – | 0.000 | 0.001 | – | – | 0.005 | –
${D}\rightarrow K\pi$ misID | – | – | – | – | 0.000 | 0.001 | – | – | – | – | – | –
$D^{0}$ decay BFs | – | – | 0.025 | 0.028 | – | – | – | – | – | – | – | –
$f_{s}/f_{d}$ | – | – | – | – | – | – | 0.008 | 0.012 | – | – | – | –
$\tau_{s}/\tau_{d}$ | – | – | – | – | – | – | 0.001 | 0.001 | – | – | – | –
Model-related | 0.004 | 0.001 | 0.011 | 0.012 | 0.010 | 0.011 | 0.002 | 0.001 | 0.004 | 0.002 | 0.001 | 0.000
Total systematic | 0.020 | 0.019 | 0.044 | 0.053 | 0.010 | 0.011 | 0.009 | 0.012 | 0.020 | 0.019 | 0.020 | 0.019
Statistical | 0.144 | 0.217 | 0.159 | 0.268 | 0.028 | 0.031 | 0.017 | 0.038 | 0.073 | 0.131 | 0.041 | 0.025

###  4.5 Model-related systematic uncertainty

The $B$ meson invariant mass model is validated with an ensemble of simulated
pseudoexperiments. The results of these pseudoexperiments show small biases,
of the order of 1% of the statistical uncertainty, in the best-fit values of
the signal yields, as determined by the invariant mass fit. The affected
signal yields are corrected for these biases before computing the observables.
The statistical uncertainty on the bias due to the limited number of
pseudoexperiments causes systematic uncertainty in the observables.

Systematic uncertainties due to the effects of the constraints made when
constructing the invariant mass fit model are also evaluated with
pseudoexperiments. The constraints considered are

  1. 1.

The values fixed from simulation of the core fraction and the ratio between
the widths of the two Gaussian functions used as signal PDF;

  2. 2.

The difference in mass of the ${B}^{0}$ and ${B}^{0}_{s}$ mesons from Ref.
[13];

  3. 3.

The branching ratios from Ref. [13] and selection efficiencies from simulation
used to constrain the relative normalisations of the background PDFs.

Each fixed parameter of the model has an associated uncertainty. To evaluate
this, the invariant mass model is altered such that a particular fixed
parameter is varied by its uncertainty and data sets generated with the
default model are fitted with this altered value. The variations in the best-
fit values of the signal yields observed when changing the model are used to
assign a systematic uncertainty on the signal yields. This process is repeated
for each fixed parameter and the systematic uncertainties in the signal yields
are propagated to the observables. All model-related systematic uncertainties
are added in quadrature and this figure is given in Table 2.

##  5 Results

The results are

${\cal{A}}^{KK}_{d}$ | $\,=\,\,$ |  $-0.20\,\pm 0.15\,\pm 0.02$, | ${\cal{A}}^{\pi\pi}_{d}$ | $\,=\,\,$ |  $-0.09\,\pm 0.22\,\pm 0.02$,
---|---|---|---|---|---
${\cal{R}}^{KK}_{d}$ | $\,=\,\,$ |  $\phantom{-}1.05\,^{+0.17}_{-0.15}\,\pm 0.04$, | ${\cal{R}}^{\pi\pi}_{d}$ | $\,=\,\,$ |  $\phantom{-}1.21\,^{+0.28}_{-0.25}\,\pm 0.05$,
${\cal{R}}^{+}_{d}$ | $\,=\,\,$ |  $\phantom{-}0.06\,\pm 0.03\,\pm 0.01$, | ${\cal{R}}^{-}_{d}$ | $\,=\,\,$ |  $\phantom{-}0.06\,\pm 0.03\,\pm 0.01$,
${\cal{R}}^{KK}_{ds}$ | $\,=\,\,$ |  $\phantom{-}0.10\,\pm 0.02\,\pm 0.01$, | ${\cal{R}}^{\pi\pi}_{ds}$ | $\,=\,\,$ |  $\phantom{-}0.15\,\pm 0.04\,\pm 0.01$,
${\cal{A}}^{KK}_{s}$ | $\,=\,\,$ |  $-0.04\pm 0.07\,\pm 0.02$, | ${\cal{A}}^{\pi\pi}_{s}$ | $\,=\,\,$ |  $\phantom{-}0.06\,\pm 0.13\,\pm 0.02$,
${\cal{A}}_{d}^{K\pi}$ | $\,=\,\,$ |  $-0.03\,\pm 0.04\,\pm 0.02$, | ${\cal{A}}^{\pi K}_{s}$ | $\,=\,\,$ |  $-0.01\,\pm 0.03\,\pm 0.02$,

where the first uncertainties are statistical and the second systematic [37].
The significances of the combined ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ signals for the
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}}$,
${{B}^{0}}\rightarrow{D}({{K}^{+}}{{K}^{-}}){{K}^{*0}}$ and
${{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{\pi}^{-}}){{K}^{*0}}$ decay modes are
$2.9\sigma$, $8.6\sigma$ and $5.8\sigma$, respectively, including systematic
uncertainties. The statistical significances, expressed in terms of number of
standard deviations ($\sigma$), are computed from $\sqrt{2\ln(L_{\rm
sig}/L_{0})}$ where $L_{\rm sig}$ and $L_{0}$ are the likelihoods from the
nominal mass fit described in Sect. 3 and from the same fit omitting the
signal component, respectively. The likelihoods are convolved with a Gaussian
function of width equal to the systematic uncertainties on the fit model in
order to compute the total significances. No significant $C\\!P$ violation
effect is observed.

The constraints from the measurements pertaining to ${B}^{0}$ mesons on the
angle $\gamma$ of the unitarity triangle and the hadronic parameters $r_{B}$
and $\delta_{B}$ are presented in Sect. 6. With more data, improved
measurements of the quantities related to ${{B}^{0}_{s}}\rightarrow{D}{{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}$ decays will also contribute
to the sensitivity but are not used here.

##  6 Implication on the value of $\boldsymbol{r_{B}}$

The sensitivity of these results to the CKM phase $\gamma$ is investigated by
employing a frequentist method described in Ref. [3] to scan the
$(\gamma,r_{B},\delta_{B})$ parameter space and calculate the $\chi^{2}$
probability at each point, given the measurements of the observables and using
(7)-(11). The statistical and systematic uncertainties are combined in
quadrature and their correlations are accounted for. In principle, the
coherence factor $\kappa$ can also be extracted together with $\gamma$,
$r_{B}$ and $\delta_{B}$ but the uncertainties of the measurements are too
large with the current data sample size to constrain all parameters together.
A value of $\kappa=0.95\pm 0.03$ is used instead. This value is determined
from a toy simulation study of a realistic model for the resonance content of
${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ decays, similar to the method
used in Ref. [38]. This model describes the decay amplitude in the analysis
phase space as a superposition of a non-resonant component and amplitudes
corresponding to the intermediate ${{K}^{*}}(892)^{0}$, ${{K}^{*}}(1410)^{0}$,
$K_{0}^{*}(1430)^{0}$, $K_{2}^{*}(1430)^{0}$, ${{K}^{*}}(1680)^{0}$,
$D_{0}^{*}(2410)^{-}$, $D_{2}^{*}(2460)^{-}$ and $D_{s2}(2573)^{+}$
resonances. The relative fractions and phases between these components are
generated randomly according to their known values and uncertainties [13] when
they have been observed or within conservatively large ranges when they have
not been measured. The analysis selection effects are taken into account, and
the main requirements affecting the value of $\kappa$ are the $K^{*}(892)^{0}$
mass selection of 50${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the
known mass and the selection on $|\cos\theta^{*}|$ being larger than 0.4. The
${{D}^{0}}\rightarrow{{K}^{\pm}}{{\pi}^{\mp}}$ amplitude ratio $r_{D}$ and
strong phase difference $\delta_{D}$ are taken from the Heavy Flavour
Averaging Group [39].

A one-dimensional projection of the $p$-value, or $1-{\rm CL}$, is given in
Fig. 5, which shows that $r_{B}$ is

$r_{B}=0.240\,^{+0.055}_{-0.048}$

at a confidence level of 68.3% and is different from 0 with a significance of
$2.7\sigma$. The $p$-value at each point of $r_{B}$ is computed with simulated
pseudoexperiments following a Feldman-Cousins method, where the nuisance
parameters are kept at their best-fit values obtained at each point of
$r_{B}$.

Two-dimensional projections of the $p$-value from the profile likelihood are
shown in Fig. 6. The LHCb average value for $\gamma$, extracted from a
combination of ${{B}^{\pm}}\rightarrow{D}{{K}^{\pm}}$ and
${{B}^{\pm}}\rightarrow{D}{{\pi}^{\pm}}$ analyses [3], is shown with its 68.3%
confidence level interval. The precision of the current results does not allow
a significant measurement of $\gamma$ from ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$
decays alone, but these measurements could nonetheless be used in a global
fit.

Figure 5: $p$-value as a function of $r_{{B}}$, for $\kappa=0.95\pm 0.03$. The
horizontal dashed lines represent the $1\sigma$ and $2\sigma$ confidence
levels and the vertical dotted line represents the obtained central value.

Figure 6: Two-dimensional projections of the $p$-value in
$(r_{B},\delta_{B},{\gamma})$ parameter space onto (left) $r_{{B}}$ and
$\gamma$ and (right) $\delta_{{B}}$ and $\gamma$, for $\kappa=0.95\pm 0.03$.
The contours are the $n\sigma$ profile likelihood contours, where
$\Delta\chi^{2}=n^{2}$ with $n=1$ (black), 2 (medium grey), and 3 (light
gray), corresponding to 39.4%, 86.5% and 98.9% confidence level, respectively.
The vertical line and hashed band represent the best-fit value of $\gamma$ and
the 68.3% confidence level interval by Ref. [3].

##  7 Conclusions

The parameters of the ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decay, which are
sensitive to the CKM angle $\gamma$, have been measured with a sample of
3.0$\mbox{\,fb}^{-1}$ of LHC $pp$ collision data collected by the LHCb
detector. The results include the first measurements of $C\\!P$ asymmetries in
${B}^{0}$ and ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ to
${D}{{K}^{*0}}$ decays with the neutral $D$ meson decaying into the
${{\pi}^{+}}{{\pi}^{-}}$ final state. The results related to the
${{K}^{+}}{{K}^{-}}$ final state of the $D$ meson, ${\cal A}_{d}^{KK}$ and
${\cal R}_{d}^{KK}$, are in agreement with and more precise than those from a
previous analysis of LHCb data [40], and supersede them. The measurements of
${\cal R}_{d}^{+}$ and ${\cal R}_{d}^{-}$ presented here are the first
obtained separately for ${B}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ mesons. They are consistent
with the measurement of the flavour-averaged ratio

$\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{\pi}^{-}}{{K}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}({{\pi}^{+}}{{K}^{-}}){{K}^{*0}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{D}({{K}^{-}}{{\pi}^{+}}){{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}})+\Gamma({{B}^{0}}\rightarrow{D}({{K}^{+}}{{\pi}^{-}}){{K}^{*0}})}$
(17)

by the Belle collaboration [41] using the same ${{K}^{*0}}$ invariant mass
range.

From the measurements presented in this article, we measure the value of
$r_{{B}}({D}{{K}^{*0}})$, the ratio of the amplitudes of the decay
${{B}^{0}}\rightarrow{D}{{K}^{+}}{{\pi}^{-}}$ with a ${b}\rightarrow{u}$ or a
${b}\rightarrow{c}$ transition, in a $K\pi$ mass region of $\pm
50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the $K^{*}(892)^{0}$ mass,
and for an absolute value of the cosine of the ${K}^{*0}$ helicity angle
larger than 0.4. It is found to be equal to $0.240_{-0.048}^{+0.055}$ at a
confidence level of 68.3%. This is the first measurement of this parameter
with LHCb data and is more accurate than the previous measurement made by the
BaBar collaboration [42], in a comparable region of phase space.

## Acknowledgements

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

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M. Plo Casasus37, F. Polci8, A. Poluektov48,34, E. Polycarpo2, A. Popov35, D.
Popov10, B. Popovici29, C. Potterat2, E. Price46, J. Prisciandaro39, A.
Pritchard52, C. Prouve46, V. Pugatch44, A. Puig Navarro39, G. Punzi23,s, W.
Qian4, B. Rachwal26, J.H. Rademacker46, B. Rakotomiaramanana39, M. Rama18,
M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G. Raven42, S. Reichert54, M.M.
Reid48, A.C. dos Reis1, S. Ricciardi49, S. Richards46, M. Rihl38, K.
Rinnert52, V. Rives Molina36, D.A. Roa Romero5, P. Robbe7, A.B. Rodrigues1, E.
Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V. Romanovsky35, A. Romero
Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, F. Ruffini23, H. Ruiz36, P.
Ruiz Valls64, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B. Saitta15,e,
V. Salustino Guimaraes2, C. Sanchez Mayordomo64, B. Sanmartin Sedes37, R.
Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A. Sarti18,m, C.
Satriano25,n, A. Satta24, D.M. Saunders46, M. Savrie16,f, D. Savrina31,32, M.
Schiller42, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O.
Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A.
Sciubba25, M. Seco37, A. Semennikov31, I. Sepp53, N. Serra40, J. Serrano6, L.
Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T.
Shears52, L. Shekhtman34, V. Shevchenko63, A. Shires9, R. Silva Coutinho48, G.
Simi22, M. Sirendi47, N. Skidmore46, T. Skwarnicki59, N.A. Smith52, E.
Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D. Sokoloff57,
F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B. Spaan9, A.
Sparkes50, P. Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl11,
O. Steinkamp40, O. Stenyakin35, S. Stevenson55, S. Stoica29, S. Stone59, B.
Storaci40, S. Stracka23,38, M. Straticiuc29, U. Straumann40, R. Stroili22,
V.K. Subbiah38, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, D. Szilard2, T. Szumlak27,
S. T’Jampens4, M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E.
Thomas38, J. van Tilburg41, V. Tisserand4, M. Tobin39, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, M.T. Tran39, M. Tresch40, A. Tsaregorodtsev6, P. Tsopelas41, N.
Tuning41, M. Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin63, U. Uwer11, V.
Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez
Regueiro37, C. Vázquez Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h,
G. Veneziano39, M. Vesterinen11, B. Viaud7, D. Vieira2, M. Vieites Diaz37, X.
Vilasis-Cardona36,p, A. Vollhardt40, D. Volyanskyy10, D. Voong46, A.
Vorobyev30, V. Vorobyev34, C. Voß62, H. Voss10, J.A. de Vries41, R. Waldi62,
C. Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59, D.R.
Ward47, N.K. Watson45, D. Websdale53, M. Whitehead48, J. Wicht38, D.
Wiedner11, G. Wilkinson55, M.P. Williams45, M. Williams56, F.F. Wilson49, J.
Wimberley58, J. Wishahi9, W. Wislicki28, M. Witek26, G. Wormser7, S.A.
Wotton47, S. Wright47, S. Wu3, K. Wyllie38, Y. Xie61, Z. Xing59, Z. Xu39, Z.
Yang3, X. Yuan3, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b, L. Zhang59,
W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3, A. Zvyagin38.

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

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