EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-313 LHCb-PAPER-2015-054 21 June 2016

First observation of the rare
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ decay

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

The ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ decay is observed in
a data sample corresponding to $3.0\mbox{\,fb}^{-1}$ of $pp$ collision data
recorded by the LHCb experiment during 2011 and 2012. The signal significance
is $8\,\sigma$ and the branching fraction is measured to be ${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)=(5.31\pm
0.90\pm 0.48\pm 0.35)\times 10^{-6}$, where the uncertainties are statistical,
systematic and due to the normalisation mode
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$, respectively. The
Dalitz plot appears to be dominated by broad structures. Angular distributions
are exploited to search for quasi-two-body contributions from
${{{B}^{+}}}\rightarrow D^{*}_{2}(2460)^{0}{{K}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$ decays. No significant signals
are observed and upper limits are set on their branching fractions.

Published in Phys. Rev. D. (R)

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

A key goal of flavour physics is to determine precisely the angle $\gamma$ of
the unitarity triangle constructed from pairs of elements of the Cabibbo-
Kobayashi-Maskawa (CKM) quark mixing matrix [1, 2]. The value of
$\gamma\equiv\arg\left[-V_{ud}V_{ub}^{*}/(V_{cd}V_{cb}^{*})\right]$ is
currently known to a precision of only about $10^{\circ}$ [3, 4, 5], which
limits the sensitivity of tests of the Standard Model through global fits to
the CKM matrix parameters.

Figure 1: Decay diagrams for (a) ${{{B}^{+}}}\\!\rightarrow{\kern
1.79997pt\overline{\kern-1.79997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}$, (b)
${{{B}^{+}}}\\!\rightarrow D^{*}_{2}(2460)^{0}K^{+}$ and (c)
${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$ channels.

A powerful method to determine $\gamma$, known as the GLW method [6, 7], is to
use ${{{B}^{+}}}\rightarrow D{{K}^{+}}$ decays with the neutral $D$ meson
decaying to $C\\!P$ eigenstates. The ${\overline{b}}\rightarrow{\overline{c}}$
and ${\overline{b}}\rightarrow{\overline{u}}$ amplitudes both contribute to
the decay, and the sensitivity to $\gamma$ comes from their interference. A
challenge with this method is that the ratio of magnitudes of the suppressed
and favoured amplitudes, $r_{B}$, is not known independently and must be
determined simultaneously with $\gamma$. This is usually addressed by using in
addition other decays of the ${D}$ meson that provide complementary
information on $r_{B}$ and $\gamma$ [8, 9].

In the case of ${{{B}^{+}}}\rightarrow D^{**}{{K}^{+}}$ decays, where $D^{**}$
represents an excited ${D}$ or ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}$ meson such as the $D_{2}^{*}(2460)$
state which can decay to both ${{D}^{\pm}}{{\pi}^{\mp}}$ and ${D}{{\pi}^{0}}$,
it is possible to obtain a clean determination of $r_{B}$ [10]. The relative
branching fractions of the ${\overline{b}}\rightarrow{\overline{u}}$ mediated
${{{B}^{+}}}\rightarrow
D^{**0}{{K}^{+}}\rightarrow{{D}^{+}}{{\pi}^{-}}{{K}^{+}}$ and the
${\overline{b}}\rightarrow{\overline{c}}$ mediated
${{{B}^{+}}}\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{**0}{{K}^{+}}\rightarrow{{D}^{-}}{{\pi}^{+}}{{K}^{+}}$
processes give the value of $r^{2}_{B}$, whilst the ${{{B}^{+}}}\rightarrow
D^{**}{{K}^{+}}\rightarrow D{{\pi}^{0}}{{K}^{+}}$ final state, where the $D$
meson is reconstructed using $C\\!P$ eigenstate decay modes, provides
sensitivity to $\gamma$. Decay diagrams for ${{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}$ and
${{{B}^{+}}}\\!\rightarrow D^{*}_{2}(2460)^{0}K^{+}$ decays are shown in Fig.
1(a) and (b).

Knowledge of the resonant structure of
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ decays is therefore
needed. The latter channel has recently been studied with a Dalitz plot
analysis [11]. Such a study would be difficult with the low yields expected
for ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ decays in the
available data samples, but an alternative approach exploiting the angular
decay information to separate different spin states is viable in the region of
the narrow $D_{2}^{*}(2460)^{0}$ resonance. The same method can also be used
to search for ${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$ decays, which
contribute to the ${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ final state and are of
interest since they are mediated by annihilation amplitudes, as shown in Fig.
1(c). A previous LHCb analysis of this mode set an upper limit ${\cal
B}({{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0})<1.8\times 10^{-6}$ at the 90
% credibility level [12].

In this paper, the ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$
channel is studied for the first time, and searches for
${{{B}^{+}}}\rightarrow D_{2}^{*}(2460)^{0}{{K}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$ decays are performed. The
${{D}^{+}}$ meson is reconstructed in the ${{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$
final state. (The inclusion of charge conjugate processes is implied.) The
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ decay [11] is used for
normalisation. The analysis is based on $3.0\mbox{\,fb}^{-1}$ of $pp$
collision data collected with the LHCb detector during 2011 and 2012. The LHCb
detector is a single-arm forward spectrometer covering the pseudorapidity
range $2<\eta<5$, described in detail in Refs. [13, 14]. Simulated events are
produced using the software described in Refs. [15, *Sjostrand:2006za, 17, 18,
19, *Allison:2006ve, 21, 22]. To reduce the risk of biasing results, all
analysis procedures were established before the data in the signal region were
examined.

Candidates consistent with the decay chains
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ with
${{D}^{\pm}}\rightarrow{{K}^{\mp}}{{\pi}^{\pm}}{{\pi}^{\pm}}$ are selected.
The criteria for ${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ candidates are
identical, except for charge requirements, and are very similar to those
described in Ref. [11]. A loose preselection is applied before two neural
network classifiers (NNs) [23] are used to separate signal decays from
background events. The first NN separates true
${{D}^{\pm}}\rightarrow{{K}^{\mp}}{{\pi}^{\pm}}{{\pi}^{\pm}}$ decays from
random combinations, and the second (NN2) identifies signal ${{{B}^{+}}}$
decays. Both NNs are trained with a sample of candidates from the
topologically similar ${{{B}^{+}}}\rightarrow{{D}^{-}}{{\pi}^{+}}{{\pi}^{+}}$
decay. Additional selection requirements are imposed to reject contributions
from specific decay modes. Only candidates with $DK$ mass, $m(DK)$, less than
$5140{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are kept, in order to remove
backgrounds from ${{B}^{0}}\rightarrow{{D}^{-}}{{K}^{+}}$ decays combined with
a random pion candidate. Similarly, potential
${{B}^{0}}\rightarrow{{D}^{-}}{{\pi}^{+}}$ background is eliminated by
requiring $m(D\pi)<4790{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.
Contributions from ${{{B}^{+}}}\rightarrow{{D}^{+}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ decays, with ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{+}}{{\pi}^{-}}$,
are removed by rejecting candidates within $\sim 3\,\sigma_{K\pi}$ of the
${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mass, where
$\sigma_{K\pi}$ is the ${{K}^{+}}{{\pi}^{-}}$ mass resolution, corresponding
to $1830<m(K\pi)<1890{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Although each
of these backgrounds affects only one of the final states, the vetoes are
applied to both to avoid biasing the relative efficiency.

Signal candidates with invariant mass in the range
$5100$–$5800{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are retained for further
analysis. Following all selection requirements, fewer than $1\,\%$ of events
contain more than one candidate; all are retained.

Extended maximum likelihood fits to the distributions of candidates in NN2
output and in $B$ candidate mass are used to determine the yields of
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ decays. Similar fitting
techniques have been used successfully in several previous LHCb analyses [24,
25, 26, 27]. A loose requirement is placed on the output of NN2 and the
remaining data in each sample are divided into six bins of the NN2 output
variable, each containing a similar number of signal decays. This binning
scheme enhances the sensitivity whilst giving stable fit performance.

The $B$ candidate mass shapes in the fit to
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ candidates are modelled
in the same way as described in Ref. [11]. The signal is described by the sum
of two Crystal Ball (CB) [28] functions, with a common mean. The tails on both
sides of the peak are described by parameters that are fixed to values found
in fits to simulated samples. Components are included for combinatorial
background, modelled with an exponential shape, and for partially
reconstructed backgrounds from
${{{B}^{+}}}\rightarrow{{D}^{*-}}{{K}^{+}}{{\pi}^{+}}$ decays and
misidentified ${{{B}^{+}}}\rightarrow D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}_{s}}{{K}^{+}}{{\pi}^{+}}$ decays, for which
non-parametric descriptions are determined from simulation. Data-driven
estimates of the misidentification probabilities, the phase-space
distributions of the ${{{B}^{+}}}\rightarrow D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$
decays [29, 30] and the relative branching fractions of the
${{{B}^{+}}}\rightarrow{{D}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{*-}}{{\pi}^{+}}{{\pi}^{+}}$ modes [29, 31], are
used to obtain these shapes. For signal and partially reconstructed and
combinatorial background components, the relative yields in each NN2 bin are
free parameters of the fit, while those of misidentified
${{{B}^{+}}}\rightarrow D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}_{s}}{{K}^{+}}{{\pi}^{+}}$ decays are taken to
be the same as for signal decays, since their NN2 responses are expected to be
very similar.

A total of 25 parameters are determined from the fit to the
${{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ sample. These include yields of
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ decays, the
combinatorial background, the partially reconstructed background, and the
${{{B}^{+}}}\rightarrow D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}_{s}}{{K}^{+}}{{\pi}^{+}}$ misidentified
backgrounds. For the signal category, and for combinatorial and partially
reconstructed backgrounds, the fractional yields $f_{i}$ of each component in
NN2 bins 1–5 are free parameters, with the fraction in bin 6 determined as
$f_{6}=1-\sum_{i=1}^{5}f_{i}$. In addition, the exponential slope parameter of
the combinatorial background and parameters of the signal invariant mass shape
(the peak position, the width of the core CB function, the relative
normalisation and ratio of the CB widths) are allowed to vary. Figure 2 shows
the combined ${{B}^{+}}$ candidate mass distribution of all NN2 bins weighted
by $S/(S+B)$, where $S$ and $B$ are the fitted signal and background yields
within $\pm 2.5\,\sigma_{\rm CB}$ of the signal peak position and $\sigma_{\rm
CB}$ is the width of the core CB function. The fit results are summarised in
Table 1.

The model for the fit to ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$
candidates is similar to that for the
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ case. The functional
forms for the mass shapes for signal and combinatorial background are
identical. The signal peak position, the width of the core CB function, and
the fractional yields in each NN2 bin are fixed to the values obtained from
the ${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ fit. A component is
included for partially reconstructed background, which is likely to be
dominated by ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$
decays; although this channel is unobserved, it is expected to be a sizable
source of background based on studies of similar decay modes [32, 33, 34]. As
the resonant structure of this mode is unknown, its mass shape is modelled
using a combination of simulated samples generated with various
${{D}^{+}}{{\pi}^{-}}$, ${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{K}^{+}}{{\pi}^{-}}$ resonances and nonresonant amplitudes. The unknown
structure of this background could cause some disagreement between data and
the fit result at low $m({{D}^{+}}{{K}^{+}}{{\pi}^{-}})$. The fractional
yields in each NN2 bin are fixed to be the same as those for partially
reconstructed backgrounds in the
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ fit. Potential partially
reconstructed background from ${B}^{0}$ and ${B}^{+}$ decays with a missing
pion hardly enter the fit region; any residual contributions are absorbed in
the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$
mass shape.

There remain 11 parameters that are varied in the fit to the
${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ sample: the yields for
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ decays, combinatorial
and partially reconstructed backgrounds; the fractional yields of the
combinatorial background in each NN2 bin; the exponential slope parameter of
the combinatorial background and the relative normalisation and ratio of
widths of the two CB functions. The results of this fit are summarised in
Table 1 and shown in Fig. 2. The statistical significance of the
${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ peak, obtained from the square root of twice
the change in negative log likelihood from the value obtained in a fit with
zero signal yield, is $11\,\sigma$.

Figure 2: Weighted invariant mass distribution of candidates in the (left) ${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ and (right) ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ data samples. Data points and fit functions are weighted as described in the text. The components are as detailed in the legend.  Table 1: Yields and statistical uncertainties obtained from fits to the ${{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ and ${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ data samples. | ${{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ | ${{D}^{+}}{{K}^{+}}{{\pi}^{-}}$
---|---|---
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ | — |  $\phantom{11}164$$\;\pm\;$ | $21$
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ |  $3101$$\;\pm\;$ | $66$ | —
Combinatorial background |  $3710$$\;\pm\;$ | $110$ |  $5945$$\;\pm\;$ | $89$
Partially reconstructed background |  $1676$$\;\pm\;$ | $57$ |  $1425$$\;\pm\;$ | $54$
${{{B}^{+}}}\rightarrow D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$ |  $\phantom{11}548$$\;\pm\;$ | $67$ | —
${{{B}^{+}}}\rightarrow{{D}^{-}_{s}}{{K}^{+}}{{\pi}^{+}}$ |  $\phantom{11}342$$\;\pm\;$ | $42$ | —

Systematic uncertainties on the ratio ${{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}/{{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}$ arise
due to approximations made in the signal and background shapes used in the fit
and uncertainties in the relative efficiencies. The largest uncertainties are
associated with the particle identification and hardware trigger efficiencies
($5.9\,\%$), the modelling of the combinatorial background in $B$ candidate
mass and NN2 bins ($4.4\,\%$) and the NN2 distributions of signal and
partially reconstructed background ($4.2\,\%$). Other sources, including the
modelling of the
${{B}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$ background
and potential biases that are either intrinsic to the fit procedure or related
to the treatment of multiple candidates, contribute systematic uncertainties
of $2.0\,\%$ or less.

With all sources combined in quadrature, the total systematic uncertainty on
the ratio of branching fractions is found to be $9.0\,\%$. The likelihood
function is convolved with a Gaussian of width corresponding to the size of
the systematic uncertainties that affect the signal yield, and the total
significance of the signal is found to be $8\,\sigma$.

The relative branching fraction of
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ decays is determined
from

$\frac{{\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}{{\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}=\frac{N^{\rm
corr}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}{N^{\rm
corr}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}\,,$ (1)

where the efficiency-corrected yield is $N^{\rm
corr}=\sum_{i}W_{i}/\epsilon_{i}$. Here the index $i$ runs over all candidates
in the fit range, $W_{i}$ is the signal weight for candidate $i$, determined
using the sPlot procedure [35], from the fits shown in Fig. 2, and
$\epsilon_{i}$ is the efficiency for candidate $i$ as a function of its Dalitz
plot position.

The average efficiencies are defined as $\bar{\epsilon}=N/N^{\rm
corr}=\sum_{i}W_{i}/N^{\rm corr}$ and are found to be
$\bar{\epsilon}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)=(0.057\pm
0.014)\,\%$ and
$\bar{\epsilon}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)=(0.079\pm
0.003)\,\%$. These values include contributions from the LHCb detector
acceptance, selection and trigger. The trigger efficiency and most selection
efficiencies are calculated from simulated samples with data-driven
corrections applied, while the particle identification efficiency is measured
from a data control sample [36]. The difference between the efficiencies is
mainly caused by the different Dalitz plot distributions of the data in each
channel.

From Eq. (1), the ratio of branching fractions is determined to be

$\frac{{\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}{{\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}=0.073\pm
0.012\mathrm{\,(stat)}\pm 0.007\mathrm{\,(syst)}\,.$

Taking ${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)=(7.31\pm
0.19\pm 0.22\pm 0.39)\times 10^{-5}$ [11] gives

${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)=(5.31\pm
0.90\pm 0.48\pm 0.35)\times 10^{-6}\,,$

where the third uncertainty is from ${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)$, which
arises mainly from the precision with which ${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{\pi}^{+}}{{\pi}^{+}}\right)$ [31] is
known.

The Dalitz plot distribution of
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ candidates in the region
$5260<\nobreak m({{D}^{+}}{{K}^{+}}{{\pi}^{-}})<\nobreak
5310{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is shown in Fig. 3.
Combinatorial background has been subtracted using the distribution of
candidates in a sideband
($5400<m({{D}^{+}}{{K}^{+}}{{\pi}^{-}})<5800{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$),
while the signal region has been chosen to minimise the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$
background contribution. The Dalitz plot variables are calculated with a
constraint imposed on the $B$ mass; the combinatorial background distribution
is not significantly distorted by this procedure. Some excesses are seen at
low $m(D\pi)$ and low $m(K\pi)$, but these do not appear to be from narrow
structures; rather, there seems to be a broad S-wave $D\pi$ contribution. The
apparent structure at high $m(D\pi)$ may arise from imperfect background
subtraction.

Figure 3: Background-subtracted Dalitz plot distribution of
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ candidates in the region
$5260<m({{D}^{+}}{{K}^{+}}{{\pi}^{-}})<5310{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$
from all NN2 bins. Areas of boxes are proportional to signal yields. Negative
yields are indicated by crosses.

Although the ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ yield is
not sufficient for a Dalitz plot analysis, it is possible to gain information
about the contributions from narrow resonances. Two-body mass requirements can
reduce the contributions from other intermediate states, but not to a
negligible level. Therefore it is necessary to use the angular decay
distributions to isolate particular resonances. The
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ normalisation mode is
again used to reduce potential sources of systematic bias.

Contributions from different partial waves can be determined by weighting the
data according to the value of the Legendre polynomial of order $L$, $P_{L}$,
evaluated as a function of the cosine of the helicity angle of the
${{K}^{+}}{{\pi}^{-}}$ or ${{D}^{+}}{{\pi}^{-}}$ system. The helicity angle is
defined as the angle between the momentum vectors of the pion and the
${{B}^{+}}$ candidate in the ${{K}^{+}}{{\pi}^{-}}$ or ${{D}^{+}}{{\pi}^{-}}$
rest frame. Event-by-event efficiency corrections, determined as a function of
Dalitz plot position, are also applied. The helicity angles and two-body
invariant masses are calculated with a constraint on the $B$ mass imposed on
the decay chain. If only resonances up to spin $J_{\rm max}$ are present in a
certain mass region, the $P_{2J_{\rm max}}$ moment will isolate the highest
spin state. Thus, in the limit that only ${{D}^{+}}{{\pi}^{-}}$ resonances
contribute, weighting by $P_{4}$ will isolate the $D_{2}^{*}(2460)^{0}$
component, as shown in Ref. [11], where a more detailed description of
contributions to each moment can be found. Similarly, at low
$m({{K}^{+}}{{\pi}^{-}})$, weighting by $P_{2}$ can be used to determine the
contribution from the $K^{*}(892)^{0}$ resonance. Higher moments may be
present, due to tails of higher spin resonances or reflections from resonances
in the other two-particle combination; these will also cause an excess of
events in regions away from the resonance peak and therefore can be accounted
for by sideband subtraction.

Candidates are selected within regions corresponding to approximately $\pm
2\Gamma$, where $\Gamma$ is the natural width [31], around the peaks of the
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993ptD$}{}_{2}^{*}(2460)^{0}$ resonance in
$m({{D}^{\pm}}{{\pi}^{\mp}})$ and of the $K^{*}(892)^{0}$ resonance in
$m({{K}^{+}}{{\pi}^{-}})$. The data are efficiency-corrected and weighted
according to the corresponding Legendre polynomial functions. Yields, denoted
$\widetilde{N}$, are then obtained from binned minimum $\chi^{2}$ fits to the
${{B}^{+}}$ candidate mass distribution. A variable-width binning scheme is
used with bin widths chosen to avoid empty bins. The same procedure is applied
for candidates in low and high sideband regions, between about $3\Gamma$ and
$5\Gamma$ from the peak. For the normalisation of the search for
${{D}^{+}}K^{*}(892)^{0}$ decays, the full efficiency-corrected
${{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ sample is used without weighting by angular
moment. The results are used to measure the ratios of branching fractions

$\displaystyle\frac{{\cal B}\left({{{B}^{+}}}\\!\rightarrow
D^{*}_{2}(2460)^{0}K^{+}\right)}{{\cal B}\left({{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}\right)}\equiv\left(r_{B}(D^{*}_{2}(2460)K^{+})\right)^{2}=\frac{\widetilde{N}^{\rm
corr}\left({{{B}^{+}}}\\!\rightarrow
D^{*}_{2}(2460)^{0}K^{+}\right)}{\widetilde{N}^{\rm
corr}\left({{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}\right)}\,,$
(2) $\displaystyle\frac{{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{+}}K^{*}(892)^{0}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}{{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}=\frac{\widetilde{N}^{\rm
corr}\left({{{B}^{+}}}\\!\rightarrow{{D}^{+}}K^{*}(892)^{0}\right)\cdot\left(\frac{5}{2}\right)}{\widetilde{N}^{\rm
corr}\left({{{B}^{+}}}\\!\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)\epsilon(K^{*}(892)^{0})}\,\,,$
(3)

where $\widetilde{N}^{\rm corr}$ are the yields obtained from the fit after
accounting for subtraction of higher moments as estimated from the sideband
regions. In Eq. (3) the correction of $\frac{5}{2}$ arises from the
normalisation of the Legendre polynomial functions and the factor of
$\epsilon(K^{*}(892)^{0})=0.857\pm 0.006$ is due to the efficiency of the
$K^{*}(892)^{0}$ signal region
($801.0<m({{K}^{+}}{{\pi}^{-}})<990.6{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$)
requirement. All efficiency, $D^{*}_{2}$ branching fraction and normalisation
effects cancel in Eq. (2).

The fit models used are based on those described above, but with some
important simplifications. The angular weighting by $P_{2}$ or $P_{4}$
significantly reduces the combinatorial background, and therefore candidates
in all NN2 bins are combined; moreover a linear shape is used instead of an
exponential function in order to allow for the possibility that the weighted
background can fluctuate to negative values. The ${{{B}^{+}}}\rightarrow
D^{(*)-}{{\pi}^{+}}{{\pi}^{+}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$
background shapes are given by non-parametric functions obtained from
simulated samples with angular moment weighting applied. No component is
included for misidentified
${{{B}^{+}}}\rightarrow{{D}^{-}_{s}}{{K}^{+}}{{\pi}^{+}}$ decays, as it is
found to be removed by the weighting procedure.

The analysis method is validated using the
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ channel and simulated
pseudoexperiments. The fit fraction for ${{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}$ decays
obtained from a full Dalitz plot analysis in Ref. [11] is reproduced within
the expected range. The procedure is tested by searching for a fake
${{K}^{*}}$ resonance in $m({{K}^{+}}{{\pi}^{+}})$, and the yield is found to
be consistent with zero.

The results of the fits to $P_{4}$-weighted and efficiency-corrected
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ and
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ data samples in the
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993ptD$}{}_{2}^{*}(2460)^{0}$ resonance region are shown in
Fig. 4. The procedure isolates the ${{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}$ decay, as
expected, but no evidence is seen for the suppressed
${{{B}^{+}}}\\!\rightarrow D^{*}_{2}(2460)^{0}K^{+}$ channel. The
corresponding fits for the ${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$
search are also shown in Fig. 4; there is no evidence for this decay. The
yields are given in Table 2.

Figure 4: Results of binned minimum $\chi^{2}$ fits to the ${{B}^{+}}$
candidate invariant mass distributions of (left)
${{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}$ and (right)
${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$ candidates with
efficiency corrections and angular weights applied. Candidates in the ranges
(top)
$2217.6<m(D^{\pm}\pi^{\mp})<2315.6{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$
and (bottom right)
$801.0<m({{K}^{+}}{{\pi}^{-}})<990.6{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$
are shown, while in the bottom left plot the whole $m({{K}^{+}}{{\pi}^{+}})$
range is included. The components are as described in the legend.  Table 2:
Results of the binned minimum $\chi^{2}$ fits to efficiency-corrected
${{{B}^{+}}}$ candidate invariant mass distributions in each resonance region
and with weighting according to angular distributions as described in the
text.

| Lower sideband | Signal region | Upper sideband | $\widetilde{N}^{\rm corr}$
---|---|---|---|---
$\widetilde{N}({{{B}^{+}}}\rightarrow D_{2}^{*}(2460)^{0}{{K}^{+}})$ |  $-200$$\,\pm\,$ | $\phantom{1}2\,500$ |  $500$$\,\pm\,$ | $\phantom{11}3\,000$ |  $200$$\,\pm\,$ | $2\,200$ |  $500$$\,\pm\,$ | $\phantom{1}4\,500$
$\widetilde{N}({{{B}^{+}}}\rightarrow{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}_{2}^{*}(2460)^{0}{{K}^{+}})$ |  $28\,000$$\,\pm\,$ | $14\,000$ |  $293\,000$$\,\pm\,$ | $\phantom{1}24\,000$ |  $-600$$\,\pm\,$ | $4\,200$ |  $266\,000$$\,\pm\,$ | $28\,000$
$\widetilde{N}({{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0})$ |  $1\,700$$\,\pm\,$ | $\phantom{1}1\,900$ |  $-3\,000$$\,\pm\,$ | $\phantom{11}5\,000$ |  $9\,500$$\,\pm\,$ | $4\,000$ |  $-14\,000$$\,\pm\,$ | $\phantom{1}7\,000$
$\widetilde{N}({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}})$ | — |  $4\,670\,000$$\,\pm\,$ | $110\,000$ | — | —

Systematic uncertainties arise due to the fit models and background
subtraction used to determine $\widetilde{N}^{\rm corr}$ in Eqs. (2) and (3).
The uncertainties are evaluated from the effects on the yields of the
following variations: the combinatorial background shape is changed from
linear to flat; the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$
background component is removed; all other fit components are varied in the
same way as described previously. The limited precision of the knowledge of
the efficiencies as functions of Dalitz plot position also causes a small
uncertainty. An uncertainty is assigned due to the effect of changing the
sideband regions from the default of $3\Gamma\leftrightarrow 5\Gamma$ to
$4\Gamma\leftrightarrow 6\Gamma$. The uncertainty in
$\epsilon(K^{*}(892)^{0})$ of Eq. (3) is also accounted for. The total
systematic uncertainty is obtained by combining all sources in quadrature.

The ratio of branching fractions is thus measured to be

$\frac{{\cal B}\left({{{B}^{+}}}\\!\rightarrow
D^{*}_{2}(2460)^{0}K^{+}\right)}{{\cal B}\left({{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}\right)}=0.002\pm
0.015\mathrm{\,(stat)}\pm 0.005\mathrm{\,(syst)}\,,$

which in turn gives

$r_{B}(D^{*}_{2}(2460)K^{+})=0.04\pm 0.18\mathrm{\,(stat)}\pm
0.06\mathrm{\,(syst)}\,.$

Assuming Gaussian uncertainties, upper limits at $90\,(95)\,\%$ confidence
level (CL) are obtained by integrating the likelihood in the region of
positive branching fraction,

$\left(r_{B}(D^{*}_{2}(2460)K^{+})\right)^{2}<0.027~{}(0.033)\quad{\rm
and}\quad r_{B}(D^{*}_{2}(2460){{K}^{+}})<0.30~{}(0.36)\,.$

The result for $\left(r_{B}(D^{*}_{2}(2460)K^{+})\right)^{2}$ and the product
branching fraction ${\cal B}\left({{{B}^{+}}}\\!\rightarrow{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}K^{+}\right)\times{\cal
B}\left({\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*}_{2}(2460)^{0}\\!\rightarrow{{D}^{-}}{{\pi}^{+}}\right)=(23.2\pm
1.1\pm 0.6\pm 1.0\pm 1.6)\times 10^{-6}$ [11] give

$\displaystyle{\cal B}\left({{{B}^{+}}}\\!\rightarrow
D^{*}_{2}(2460)^{0}K^{+}\right)\times{\cal
B}\left(D^{*}_{2}(2460)^{0}\\!\rightarrow{{D}^{+}}{{\pi}^{-}}\right)$
$\displaystyle=$ $\displaystyle(0.4\pm 3.5\pm 1.1\pm 0.1)\times 10^{-7}\,,$
$\displaystyle<$ $\displaystyle 6.3~{}(7.5)\times 10^{-7}\ {\rm at}\
90\,(95)\,\%\ {\rm CL.}$

These are the first experimental results on this decay mode. Similarly for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}}K^{*}(892)^{0}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$,

$\displaystyle\frac{{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{+}}K^{*}(892)^{0}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}\right)}{{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)}$
$\displaystyle=$ $\displaystyle-0.0079\pm 0.0039\mathrm{\,(stat)}\pm
0.0028\mathrm{\,(syst)}\,,$ $\displaystyle<$ $\displaystyle 0.0044~{}(0.0055)\
{\rm at}\ 90\,(95)\,\%\ {\rm CL.}$

The measured value ${\cal
B}\left({{{B}^{+}}}\rightarrow{{D}^{-}}{{K}^{+}}{{\pi}^{+}}\right)=(7.31\pm
0.19\pm 0.22\pm 0.39)\times 10^{-5}$ [11] and the isospin relation ${\cal
B}\left(K^{*}(892)^{0}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}\right)=\frac{2}{3}$
give

$\displaystyle{\cal
B}\left({{{B}^{+}}}\\!\rightarrow{{D}^{+}}K^{*}(892)^{0}\right)$
$\displaystyle=$ $\displaystyle(-8.7\pm 4.3\pm 3.1\pm 0.4)\times 10^{-7}\,,$
$\displaystyle<$ $\displaystyle 4.9~{}(6.1)\times 10^{-7}\ {\rm at}\
90\,(95)\,\%\ {\rm CL,}$

where the third uncertainty is due to the normalisation channel branching
fraction. This result supersedes the previous limit, which was obtained with a
subset of the data [12].

In summary, the rare ${{{B}^{+}}}\rightarrow{{D}^{+}}{{K}^{+}}{{\pi}^{-}}$
decay has been observed for the first time with $8\,\sigma$ significance,
based on a data sample of $3.0\mbox{\,fb}^{-1}$ of $pp$ collision data
collected with the LHCb detector. The Dalitz plot appears to be dominated by
broad structures. Searches for ${{{B}^{+}}}\rightarrow
D_{2}^{*}(2460)^{0}{{K}^{+}}$ and
${{{B}^{+}}}\rightarrow{{D}^{+}}K^{*}(892)^{0}$ decays have been carried out
by weighting the data according to the decay angle distributions, but no
significant signals are seen. These results indicate that further studies,
with larger data samples, of the Dalitz plot distribution of this mode will be
of interest to understand the potential for a measurement of $\gamma$ from
${{{B}^{+}}}\rightarrow{D}{{K}^{+}}{{\pi}^{0}}$ decays.

## 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 (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. 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 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 (Russia), GVA, XuntaGal and GENCAT (Spain), The
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

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LHCb collaboration

R. Aaij39, C. Abellán Beteta41, B. Adeva38, M. Adinolfi47, A. Affolder53, Z.
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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.
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d’Argent12, A. Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,n, M.
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Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F.
Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,k, I.
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Berezhnoy33, R. Bernet41, A. Bertolin23, M.-O. Bettler39, M. van Beuzekom42,
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Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, A. Bondar35, N.
Bondar31,39, W. Bonivento16, S. Borghi55, M. Borisyak66, 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. Bursche41, J.
Buytaert39, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,k, M. Calvo Gomez37,p,
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Carboni25,l, R. Cardinale20,j, A. Cardini16, P. Carniti21,k, L. Carson51, K.
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Niet10, N. Nikitin33, T. Nikodem12, A. Novoselov36, D.P. O’Hanlon49, A.
Oblakowska-Mucha28, V. Obraztsov36, S. Ogilvy52, O. Okhrimenko45, R.
Oldeman16,f, C.J.G. Onderwater68, B. Osorio Rodrigues1, J.M. Otalora
Goicochea2, A. Otto39, P. Owen54, A. Oyanguren67, 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. Qian4, R.
Quagliani7,47, B. Rachwal27, J.H. Rademacker47, M. Rama24, M. Ramos Pernas38,
M.S. Rangel2, I. Raniuk44, N. Rauschmayr39, 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 Lopez63, P. Rodriguez Perez55, S. Roiser39, V.
Romanovsky36, A. Romero Vidal38, J. W. Ronayne13, M. Rotondo23, T. Ruf39, P.
Ruiz Valls67, J.J. Saborido Silva38, N. Sagidova31, B. Saitta16,f, V.
Salustino Guimaraes2, C. Sanchez Mayordomo67, 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.
Shevchenko65, A. Shires10, B.G. Siddi17, R. Silva Coutinho41, L. Silva de
Oliveira2, G. Simi23,s, M. Sirendi48, N. Skidmore47, T. Skwarnicki60, E.
Smith56,50, 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, N. Torr56, 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. Ustyuzhanin66,65, 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. Voß64, J.A. de
Vries42, R. Waldi64, 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. Xie62, Z. Xu40, Z. Yang3, J. Yu62, X. Yuan35, O. Yushchenko36,
M. Zangoli15, M. Zavertyaev11,c, L. Zhang3, Y. Zhang3, A. Zhelezov12, 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
62Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
63Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
64Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
65National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
66Yandex School of Data Analysis, Moscow, Russia, associated to 32
67Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
68Van 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