EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-289 LHCb-PAPER-2017-032 November 15, 2017

First observation of $B^{+}\rightarrow D_{s}^{+}K^{+}K^{-}$ decays and a
search for $B^{+}\rightarrow D_{s}^{+}\phi$ decays

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

A search for $B^{+}\rightarrow D_{s}^{+}K^{+}K^{-}$ decays is performed using
$pp$ collision data corresponding to an integrated luminosity of 4.8 fb-1,
collected at centre-of-mass energies of 7, 8 and
13$\mathrm{\,Te\kern-1.00006ptV}$ with the LHCb experiment. A significant
signal is observed for the first time and the branching fraction is determined
to be

$\mathcal{B}(B^{+}\rightarrow D_{s}^{+}K^{+}K^{-})=(7.1\pm 0.5\pm 0.6\pm
0.7)\times 10^{-6},$

where the first uncertainty is statistical, the second systematic and the
third due to the uncertainty on the branching fraction of the normalisation
mode $B^{+}\rightarrow D_{s}^{+}\overline{\kern-1.99997ptD}^{0}$. A search is
also performed for the pure annihilation decay $B^{+}\rightarrow
D_{s}^{+}\phi$. No significant signal is observed and a limit of

$\mathcal{B}(B^{+}\rightarrow D_{s}^{+}\phi)<4.9\times 10^{-7}~{}(4.2\times
10^{-7})$

is set on the branching fraction at 95% (90%) confidence level.

Published in JHEP 01 (2018) 131

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

##  1 Introduction

The decay ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ is
mediated by a ${\overline{b}}\\!\rightarrow{\overline{u}}$ transition shown in
Fig. 1 and is therefore suppressed in the Standard Model (SM) due to the small
size of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{{u}{b}}$. The
branching fraction for this decay is currently not measured, however a similar
decay, ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{0}}$, has been observed
with a branching fraction of
$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{0}})=(1.5\pm
0.5)\times 10^{-5}$ [1].

In the SM, the decay ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ proceeds
dominantly via the annihilation diagram shown in Fig. 1. This suppressed
topology requires the wave functions of the incoming quarks to overlap
sufficiently to annihilate into a virtual $W^{+}$ boson. The decay is further
suppressed by the small magnitude of the CKM matrix element $V_{{u}{b}}$
associated with the annihilation vertex. In addition, unlike many rare
hadronic decays including
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$, possible
contributions from rescattering effects are expected to be small, for example
contributions from intermediate states such as
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\omega$ [2]. Several SM predictions
have been made for the branching fraction of the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decay [3, 4, 5, 6], using input
from lattice calculations [7, 8, 9]. These predictions are in the range
$(1-7)\times 10^{-7}$, where the limit on the precision is dominated by
hadronic uncertainties. However, additional diagrams contributing to this
decay can arise in some extensions of the SM, such as supersymmetric models
with R-parity violation. They could enhance the branching fraction and/or
produce large $C\\!P$ asymmetries [4, 5], which makes the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decay a promising place to search
for new physics beyond the SM.111Charge conjugation is implied throughout this
paper. Furthermore, $\phi$ denotes the $\phi(1020)$ resonance.

Figure 1: Dominant diagram for the (left)
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decay and (right)
annihilation diagram for the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
decay in the Standard Model.

The LHCb experiment reported evidence for the decay
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ using $pp$ collision data
corresponding to an integrated luminosity of 1$\mbox{\,fb}^{-1}$ taken during
2011, at a centre-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ [10]. A
total of $6.7^{+4.5}_{-2.6}$ candidates was observed. The branching fraction
was determined to be

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)=(1.87^{+1.25}_{-0.73}\pm
0.19\pm 0.32)\times 10^{-6},$ (1)

where the first uncertainty is statistical, the second is systematic and the
third is due to the uncertainty on the branching fraction of the decay
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$, which was used as
normalisation. Given the large uncertainties on both the theoretical and
experimental values, the previously measured value is consistent with the
range of SM values given above. The measurements presented in this paper
reanalyse the data collected in 2011, whilst adding data corresponding to an
integrated luminosity of 2$\mbox{\,fb}^{-1}$ collected at a centre-of-mass
energy 8$\mathrm{\,Te\kern-1.00006ptV}$ in 2012, along with
0.3$\mbox{\,fb}^{-1}$ from 2015 and 1.5$\mbox{\,fb}^{-1}$ from 2016, both at
13$\mathrm{\,Te\kern-1.00006ptV}$. They supersede the previous measurement
[10].

This analysis is performed in two parts: firstly
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays are
reconstructed across the entire phase space and then a dedicated search for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays is performed in a narrow
region of ${{K}^{+}}{{K}^{-}}$ invariant mass around the $\phi$ meson. The
branching fractions are determined using the decay
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$, with ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$,
as a normalisation channel. Although this ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ decay has a smaller branching
fraction than ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}$
(0.4% vs. 3.9% [11]), sharing the same final state between the signal and
normalisation channel reduces systematic uncertainties in the ratio of
detection efficiencies.

##  2 Detector and data sample

The LHCb detector [12, 13] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary $pp$ interaction vertex (PV), the impact
parameter (IP), is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger, which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction.

At the hardware trigger stage, events are required to have a muon with high
$p_{\mathrm{T}}$ or a hadron, photon or electron with high transverse energy
in the calorimeters. Two different algorithms are used in the software trigger
to select candidates for this analysis. The first uses a multivariate
algorithm [14] to identify the presence of a secondary vertex that has two,
three or four tracks and is displaced from any PV. At least one of these
charged particles must have a transverse momentum
$\mbox{$p_{\mathrm{T}}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and be
inconsistent with originating from a PV. The second algorithm selects $\phi$
candidates decaying to two charged kaons. Each kaon must have a transverse
momentum $\mbox{$p_{\mathrm{T}}$}>0.8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
be inconsistent with originating from a PV. The invariant mass of the kaon
pair must be within $20{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
$\phi$ mass [11]. This algorithm is used in both the search for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays.

Simulated events are used to determine the relative efficiencies of the signal
and normalisation channels. The samples are generated for each of the running
periods. In these simulations, $pp$ collisions are generated using Pythia [15,
16] with a specific LHCb configuration [17]. Decays of hadronic particles are
described by EvtGen [18], in which final-state radiation is generated using
Photos [19]. The interaction of the generated particles with the detector, and
its response, are implemented using the Geant4 toolkit [20,
*Agostinelli:2002hh] as described in Ref. [22].

##  3 Candidate selection

Candidate ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays are selected
using similar requirements. The $\phi$ mesons in
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates are reconstructed with
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$. Both modes are reconstructed using the
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ decay, whilst
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates are additionally
reconstructed with the decays
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ and
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ to increase the
sensitivity of the search. The ${{D}^{+}_{s}}$ ($\phi$) candidates are
required to have an invariant mass within
$25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
($40{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) of the known ${{D}^{+}_{s}}$
($\phi$) mass [11]. In the search for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays, the veto
$|m({{K}^{+}}{{K}^{-}})-m({{D}^{0}})|>25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
is applied to explicitly remove the normalisation channel from the signal
mode.

The ${{B}^{+}}$ meson candidates are formed from well reconstructed tracks
with $\chi^{2}_{\text{IP}}>4.0$, where $\chi^{2}_{\text{IP}}$ is defined as
the difference in the vertex-fit $\chi^{2}$ of the best PV reconstructed with
and without the particle being considered. The best PV is the PV that has the
smallest $\chi^{2}_{\text{IP}}$ value. For kaons from the $\phi$ or
${{B}^{+}}$ decay the momentum requirement is
$p>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. At least one track of each
${{B}^{+}}$ meson candidate must have
$\mbox{$p_{\mathrm{T}}$}>0.5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$p>5{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Loose requirements are made on particle identification (PID) to reduce
background from other $b$-hadron decays with misidentified hadrons. For the
signal, the overall efficiency of the PID requirements varies from 80% to 90%,
depending on the ${D}^{+}_{s}$ mode. Background from decays of ${{B}^{+}}$
mesons to the same final state that did not proceed via a ${D}^{+}_{s}$ meson
(referred to as charmless decays) are suppressed by applying a requirement on
the significance of the ${{B}^{+}}$ and ${D}^{+}_{s}$ vertex separation,
$\chi^{2}_{\text{FD}}$.

The residual yields of charmless decays are estimated by determining the
${{B}^{+}}$ yield in candidates that are in the invariant mass range
$25<|m(h^{+}h^{\prime-}{{\pi}^{+}})-m({{D}^{+}_{s}})|<50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$,
where $m(h^{+}h^{\prime-}{{\pi}^{+}})$ is the ${D}^{+}_{s}$ candidate mass and
$h,h^{\prime}=K,\pi$. This background estimation is performed separately for
the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ searches. For the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ normalisation channel, a two-
dimensional optimisation is performed to calculate the contribution from
decays without a ${D}^{+}_{s}$ meson, ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ meson or both. The optimal
selection requirements are chosen such that the maximum signal efficiency is
achieved for a residual charmless contribution of 2% of the normalisation
yield.

For the decay ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$,
candidates are rejected if they are consistent with
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ or ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decays, where
either a pion or a proton has been misidentified as a kaon. The candidates are
reconstructed using the alternative mass hypothesis and, for those falling
within $25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the ${D}^{+}$ or
${\mathchar 28931\relax}^{+}_{c}$ mass, particle identification requirements
are tightened on the misidentified track.

Another set of vetoes rejects decays where the tracks forming the
${D}^{+}_{s}$ candidate originate from an excited charged charm meson decay,
for example ${{D}^{*+}}\\!\rightarrow({{D}^{0}}\\!\rightarrow
h^{+}h^{\prime-}){{\pi}^{+}}$. By requiring $\Delta
m=m(h^{+}h^{\prime-}{{\pi}^{+}})-m(h^{+}h^{\prime-})>150{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
decays of this type are efficiently removed. Other specific backgrounds are
removed by mass vetoes. These vetoes remove
${{B}^{0}_{s}}\\!\rightarrow\phi\phi$ decays in which one of the $\phi$ mesons
is combined with an unrelated pion to form the ${D}^{+}_{s}$ candidate. Any
candidates within $50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${B}^{0}_{s}$ mass [11] in the four-body invariant mass
$m({{K}^{+}}{{K}^{-}}{{K}^{+}}{{K}^{-}})$ are removed to ensure a smooth
combinatorial background distribution.

In addition, a veto is applied to the invariant mass of the kaons from the
$\phi$ meson or ${{B}^{+}}$ candidate combined with any pion from the
${D}^{+}_{s}$ candidate, removing candidates within
$25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${D}^{+}_{s}$ mass.
This removes decays that include incorrectly reconstructed
${{D}^{+}_{s}}\\!\rightarrow\phi{{\pi}^{+}}$ or
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ decays, where the
$\phi$ or ${{K}^{+}}{{K}^{-}}$ pair are incorrectly assigned to have
originated from the ${{B}^{+}}$ meson rather than the ${D}^{+}_{s}$ meson. For
example, this incorrect assignment could lead to
${{{B}^{+}}}\\!\rightarrow({{D}^{+}_{s}}\\!\rightarrow\phi{{\pi}^{+}}){{K}^{+}}{{K}^{-}}$
decays being reconstructed as
${{{B}^{+}}}\\!\rightarrow({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}})\phi$
decays. The ${{B}^{+}}$ (${D}^{+}_{s}$) candidates are required to have
$\chi^{2}_{\text{IP}}<10$ ($\chi^{2}_{\text{IP}}>10$), to ensure they are
consistent (inconsistent) with being produced at the best PV.

Multivariate analyses (MVA) are used to separate genuine $\phi$ and
${D}^{+}_{s}$ candidates from random combinations of tracks [23]. The $\phi$
and ${D}^{+}_{s}$ MVAs use data samples of
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decays, respectively, where the background is statistically subtracted using
the sPlot method [24]. The training uses the $\phi$ or ${D}^{+}_{s}$ sidebands
as a background sample. A total of eight MVAs are trained to target the decays
$\phi\\!\rightarrow{{K}^{+}}{{K}^{-}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ and
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$, separately in
the Run 1 (2011 and 2012) and Run 2 (2015 and 2016) data. A preselection
including the trigger, vetoes and PID requirements previously discussed is
applied to the training samples, ensuring they are representative of the
target signal decays. The samples are split into two subsamples in a random
but reproducible way. One is used to train the corresponding MVA, the other to
test its response.

The MVA method used in this analysis is a gradient Boosted Decision Tree
(BDTG) [25]. The selection criteria for each of the BDTG classifiers are
determined by optimising the figure of merit
$\epsilon_{s}/(\frac{a}{2}+\sqrt{N_{\text{BKG}}})$ [26], with $a=5$, where
$\epsilon_{s}$ is the signal efficiency and $N_{\text{BKG}}$ is the number of
background candidates determined from fits to data, calculated in the signal
region.

The efficiencies of the MVAs are obtained from the test samples of
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decays. Additionally, a sample of ${{{B}^{+}}}\\!\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{\pi}^{+}}$ decays is used to
calculate the efficiency of ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$
decays in the normalisation channel. The efficiency calculation takes into
account the kinematic differences between the training and signal samples, as
well as any possible correlations between the ${D}^{+}_{s}$ and $\phi$
kinematics, by using input from simulation samples. Any further correlations
between the $\phi$ and ${D}^{+}_{s}$ MVA efficiencies are found to be
negligible. In the search for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays, calibration
samples are used to correct for the imperfect modelling of the PID in
simulation. These corrected samples are then used to obtain the variations in
the MVA efficiencies as a function of the phase-space position, in particular
of the $m({{K}^{+}}{{K}^{-}})$ invariant mass.

The invariant mass of the ${{B}^{+}}$ meson candidates is determined from fits
in which the ${D}^{+}_{s}$ candidate mass (and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ candidate mass for the
normalisation channel) is constrained to the known value [27]. Additionally,
the momentum vector of the ${{B}^{+}}$ meson is constrained to be parallel to
the vector connecting the PV and the ${{B}^{+}}$ meson decay vertex.

##  4 Invariant mass fits

The branching fractions of the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
and ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays are
determined from unbinned maximum likelihood fits to the invariant mass of the
${{B}^{+}}$ candidates. However, separate fit strategies are used for the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ searches.

The search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$
involves two independent fits for the signal and normalisation channels. The
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ yield is corrected
on a per-candidate basis to account for the phase-space dependence of the
signal efficiencies in this three-body decay.

In contrast, the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates are
treated as quasi-two-body decays in which all signal candidates are corrected
with the same efficiency. The ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
signal and normalisation channels are fitted simultaneously in different
categories, as are the three ${D}^{+}_{s}$ decay modes, with the
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$ mode split further
into ${{D}^{+}_{s}}\\!\rightarrow\phi{{\pi}^{+}}$ and non-$\phi$ submodes.
This exploits the high purity of the
${{D}^{+}_{s}}\\!\rightarrow\phi{{\pi}^{+}}$ decay. As the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decay involves the decay of a
pseudoscalar particle to a pseudoscalar and vector particle, the $\phi$ vector
meson ($J^{P}=1^{-}$) must be produced longitudinally polarised. For a
longitudinally polarised $\phi$ meson decaying to ${{K}^{+}}{{K}^{-}}$, the
distribution of the angle $\theta_{K}$, defined as the angle that the kaon
meson forms with the $B$ momentum in the $\phi$ rest frame, is proportional to
$\cos^{2}{\theta_{K}}$. The distribution of $\cos{\theta_{K}}$ for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ as determined from simulated
events is shown in Fig. 2.

Figure 2: Distributions of (left) $\cos{\theta_{K}}$ and (right)
$m({{K}^{+}}{{K}^{-}})$ in ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
decays, as determined from simulated events. The vertical lines represent the
limits of the two categories used for each variable. In the
$m({{K}^{+}}{{K}^{-}})$ distribution, the area within the dashed red lines
represents the $\phi$ signal region, and the two areas between the dashed red
and blue lines represent the $\phi$ sideband region. The
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ signal decays are seen to
primarily contribute to the $\phi$ signal region and the
$|\cos{\theta_{K}}|>0.4$ category.

In the simultaneous fit for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
candidates the candidates are split into two helicity categories:
$|\cos{\theta_{K}}|>0.4$ and $|\cos{\theta_{K}}|<0.4$. In simulated events,
93% of ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays are found in the
first category, whereas for the normalisation decay and background modes, as
the distributions in $\cos{\theta_{K}}$ are approximately flat, only 60% of
candidates fall into this category. Additionally, the fit further assigns
candidates into two $m({{K}^{+}}{{K}^{-}})$ invariant mass categories,
$|m({{K}^{+}}{{K}^{-}})-m_{\phi}|<10{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
and
$10<|m({{K}^{+}}{{K}^{-}})-m_{\phi}|<40{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
(Fig. 2), to help constrain the contribution from the different backgrounds in
the signal region. Background modes involving two kaons that did not originate
from a $\phi$ meson (for example ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow
D_{s}^{(*)+}K^{-}{{K}^{*0}}$) have different fractions in these two
categories, helping to distinguish them from those decays with a real $\phi$
meson. The fractions of ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
candidates in each of the categories, as determined from simulated events, are
listed in Table 1.

Table 1: Fractions of ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates expected in the helicity and $m({{K}^{+}}{{K}^{-}})$ invariant mass categories of the simultaneous fit.  $|m({{K}^{+}}{{K}^{-}})-m_{\phi}|$ (${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) | Helicity Category
---|---
$|\cos{\theta_{K}}|>0.4$ | $|\cos{\theta_{K}}|<0.4$
$<10$ | 82% | 6%
(10, 40) | 11% | 1%
Table 2: Fractions of ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ candidates assumed to contribute to each helicity and $m({{K}^{+}}{{K}^{-}})$ invariant mass categories of the simultaneous fit. The uncertainties shown are calculated from the range of fractions obtained by assuming different contributing resonances, as detailed in Sec. 4.1. $|m({{K}^{+}}{{K}^{-}})-m_{\phi}|$ (${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$) | Helicity Category
---|---
$|\cos{\theta_{K}}|>0.4$ | $|\cos{\theta_{K}}|<0.4$
$<10$ |  $(15\pm 2)$% |  $(10\pm 1)$%
(10, 40) |  $(45\pm 2)$% |  $(30\pm 1)$%

###  4.1 Signal and normalisation probability density functions

The normalisation and signal components in the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ or
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ invariant mass distributions are
each modelled using the sum of two Crystal Ball (CB) [28] probability density
functions (PDFs) with tails at lower invariant mass. The tail parameters, the
ratio of the two CB widths, and the relative fraction of each CB function are
determined from simulated events. The resolution parameter of the narrow CB
component in each ${D}^{+}_{s}$ decay mode category is a free parameter in the
fit, but the ratios of signal and normalisation widths are fixed to values
determined from simulated events. For the normalisation mode, the fraction of
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ candidates in the two helicity
bins is a free parameter in the fit, whereas for the signal the fraction in
each helicity and $m({{K}^{+}}{{K}^{-}})$ invariant mass category of the fit
is fixed to that determined from simulated events, as reported in Table 1.

The search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays includes a
component for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$
decays that did not proceed via a $\phi$ meson. The fraction of
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays expected in
each helicity angle and $m({{K}^{+}}{{K}^{-}})$ mass category, shown in Table
2, are calculated from the average of different ${{K}^{+}}{{K}^{-}}$
resonances that could contribute to
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays. These
resonances include possible contributions from the $f_{0}(980)$ and
$a_{0}(980)$ resonances. The resulting fractions are sufficiently different
from those for the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ signal such
that the two contributions can be distinguished. The range of fractions
obtained by considering the different resonances are included as uncertainties
in Table 2. A systematic uncertainty is assigned to account for the fixed
fractions assumed in the fit. No attempt is made to separate any of the
contributing resonances in the search for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ candidates.

###  4.2 Background PDFs

A number of background components are included in the fit model. The dominant
source of background under the signal is due to combinations of unrelated
tracks. An exponential function is used to parametrise this component. The
same slope parameter is used in the simultaneous fit to the signal and
normalisation modes. Partially reconstructed
${{{B}^{+}}}\\!\rightarrow{{D}^{*+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ and
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*0}}$ decays are concentrated in
the lower part of the ${{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ spectrum. They are
parametrised using analytical shapes that account for the nonreconstructed
neutral pion or photon from the excited $D$-meson decays. These shapes are
constructed from Gaussian distributions convolved with second-order
polynomials, and are analogous to those used in similar analyses [29]. An
additional component is used to model
${{{B}^{+}}}\\!\rightarrow{{D}^{*+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{*0}}$ decays where one particle
from each of the excited $D$ mesons is missed. Partially reconstructed
${{{B}^{+}}}\\!\rightarrow{{D}^{*+}_{s}}\phi$ decays can contribute to the
lower part of the ${{D}^{+}_{s}}\phi$ spectrum. These, similarly, are fitted
with analytical shapes that account for the missing neutral particle from the
${{D}^{*+}_{s}}$ decay, as well as the different helicity states for the decay
of a pseudoscalar meson to two vector particles. They are parametrised in an
analogous way to similar analyses [30]. This background component is only
included in the search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
decays. The modes ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{-}}{{K}^{*0}}$
and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{*+}_{s}}{{K}^{-}}{{K}^{*0}}$
form a background to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays when
a low-momentum pion from the ${K}^{*0}$ decay is not reconstructed.
Additionally, a neutral pion or photon can be missed from the excited
${D}^{+}_{s}$ meson decay in the case of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{*+}_{s}}{{K}^{-}}{{K}^{*0}}$.
The PDFs are determined from simulated events. The expected fractions in each
category of the ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ fit are fixed
using simulated events. The decays
${{B}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{-}_{s}}$,
${{B}^{0}_{s}}\\!\rightarrow{{D}^{*+}_{s}}{{D}^{-}_{s}}$ and
${{B}^{0}}\\!\rightarrow{{D}^{+}_{s}}{{D}^{-}}$ can form a background when a
pion is not reconstructed from a ${D}^{+}_{s}$ or ${D}^{+}$ decaying to
${{K}^{+}}{{K}^{-}}{{\pi}^{+}}$. The PDFs are also determined from simulated
events, with the fractions in each
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ fit category fixed. The result of
the fit to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$
candidates, including all the relevant background components is shown in Fig.
3. The result of the simultaneous fit to
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates in the different
helicity angle and $m({{K}^{+}}{{K}^{-}})$ mass categories is shown in Fig. 4.
The three contributing ${D}^{+}_{s}$ meson decay modes are merged.

Figure 3: Mass distribution of
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ candidates. The
result of the fit to the data using the model described in Sec. 4.1 is
overlaid, with the PDF components given in the legend.

Figure 4: Mass distribution of ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$
candidates in (top) the $\phi$ mass region, and (bottom) the $\phi$ mass
sideband. The plots on the left are in the helicity bin
$|\cos{\theta_{K}}|>0.4$ and the right are in $|\cos{\theta_{K}}|<0.4$. The
result of the fit to the data using the model described in Sec. 4.1 is
overlaid, with the PDF components given in the legend. The
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays (black) are expected to
primarily contribute to the $\phi$ region with $|\cos{\theta_{K}}|>0.4$.

##  5 Systematic uncertainties

A number of different sources of systematic uncertainty are considered. The
contribution from each source is detailed in Table 3.

Table 3: Systematic uncertainties contributing to the measurements of $\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)$ and $\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})$. The systematic uncertainty from the normalisation branching fraction is also included.  Source of uncertainty | $\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)$ | $\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})$
---|---|---
($\times 10^{-7}$) | ($\times 10^{-6}$)
Relative efficiencies | 0.08 | 0.59
Signal and normalisation PDFs | 0.04 | 0.04
Background PDFs | 0.69 | 0.02
Charmless contribution | 0.02 | 0.05
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ model | 0.38 | –
Normalisation | 0.12 | 0.72

Relative efficiencies: The calculation of the branching fractions requires a
correction to the ratio of signal and normalisation yields to account for the
difference in the selection efficiency of the two modes. All relative
selection efficiencies except the PID and MVA efficiencies are determined from
simulated events and the effect of having a limited simulation sample size is
included as a systematic uncertainty. The relative efficiency for the PID and
MVA requirements are determined from data control modes, including the samples
of ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{D}^{+}_{s}}{{\pi}^{-}}$
decays used to test the MVA responses. Systematic uncertainties are assigned
to account for the limited sizes of the control mode samples, kinematic
differences between the control modes and the signal modes and differences
between the data and simulation distributions that might affect the relative
efficiency.

Signal and normalisation PDFs: Some parameters in the signal and normalisation
PDFs are fixed to values obtained from simulation. These include the tail
parameters, relative widths, and fractional amounts of the two CB functions
that make up the PDFs. The values obtained from simulation have associated
uncertainties arising from the limited simulation sample sizes. The nominal
fits are repeated with the fixed parameters modified to values sampled from
Gaussian distributions, with a width given by the parameter uncertainties. All
parameters are changed simultaneously. For the fit to
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates, the fractions of
events expected in each category of the fit are also included in the
procedure. The resulting variation is assigned as the systematic uncertainty.

Background PDFs: Some of the PDFs for the background modes are taken directly
from simulated events using one-dimensional kernel estimations [31]. In the
nominal fit, these are smeared to account for the differences in the mass
resolution between data and simulation. To account for any systematic
uncertainty arising from the choice of resolution difference, the fit is
repeated, randomly varying the smearing resolution each time. The resulting
variation in the branching fraction is assigned as a systematic uncertainty.
Additionally, each partially reconstructed background PDF has fixed fractions
in the different categories of the signal fit. To determine the effect on the
branching fraction, these fractions are repeatedly sampled from Gaussian
distributions with widths given by the statistical uncertainty on the
fractions. For the combinatorial background shape, the choice of
parametrisation is varied and the effect included in the systematic
uncertainty.

Charmless contribution: Residual charmless and single-charm backgrounds are
expected to remain in the final selection. These contributions are neglected
in the calculation of the branching fractions. However, the shift in the
branching fraction caused by numerically including the charmless yields is
assigned as a systematic uncertainty.

${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ model assumption:
The fit to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates includes a
shape for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays
that do not proceed via a $\phi$ meson. In order to distinguish this component
from the signal, the different fractions of candidates in the four fit
categories are exploited. This requires making assumptions as to which
resonances contribute to the full
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decay model. The
shape is assumed to be dominated by $f_{0}(980)$ and $a_{0}(980)$ resonances.
Estimates of the uncertainties on the fractions are determined by considering
the range in each fraction for the models considered. The variation in the
branching fraction that results from varying these fractions within the
uncertainties is assigned as the systematic uncertainty.

##  6 Results

###  6.1 Search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$
candidates

The fit to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$
candidates finds a total yield of
$N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})=443\pm 29$
candidates. This constitutes the first observation of this decay mode. The
branching fraction is calculated as

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})=\frac{N_{\text{corr}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})}\times\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})\times\mathcal{B}({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})$
(2)

where $N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})$ is the yield of normalisation
decays, and
$N_{\text{corr}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})$ is
defined to be

$N_{\text{corr}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})=\sum\limits_{i}\frac{W_{i}}{\epsilon^{\text{ratio}}_{i}},$
(3)

where $W_{i}$ is the per-candidate weight, as determined by the sPlot
technique for candidate $i$; and $\epsilon^{\text{ratio}}_{i}$ represents the
relative efficiency of the signal and normalisation modes
$\epsilon_{i}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})/\epsilon({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})$ in the relevant bin of the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ Dalitz plot. The
corrected yield ratio can be expressed as the ratio of signal and
normalisation branching fractions using Eq. 2. The value is measured to be

$\frac{N_{\text{corr}}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})}{N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})}=\frac{\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})}{\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})\mathcal{B}({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})}=0.197\pm
0.015\pm 0.017,$

where the first uncertainty is statistical, and the second is systematic. The
branching fraction for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays is
determined to be

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})=(7.1\pm
0.5\pm 0.6\pm 0.7)\times 10^{-6},$

where the first uncertainty is statistical, the second is systematic and the
third from the branching fractions of ${{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}}$
and of the normalisation mode ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$. The values used for the
branching fractions are
$\mathcal{B}({{D}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})=(4.01\pm 0.07)\times
10^{-3}$ and $\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})=(9.0\pm 0.9)\times 10^{-3}$
[11]. The two-body projections $m(D_{s}^{+}K^{-})$ and $m(K^{+}K^{-})$ are
obtained for the signal component using the sPlot technique, shown in Fig. 5.
No significant peak is observed in the $\phi$ region of the
$m({{K}^{+}}{{K}^{-}})$ plot; rather a broad distribution of candidates is
found in the region up to $m({{K}^{+}}{{K}^{-}})\simeq
1900{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Figure 5: Projections of the background-subtracted two-body invariant masses
(left) $m({{D}^{+}_{s}}{{K}^{-}})$ and (right) $m({{K}^{+}}{{K}^{-}})$ for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays. These plots
are additionally weighted by a factor $1/\epsilon^{\text{ratio}}_{i}$ to
correct for the efficiency variation across the phase space. An expansion of
the $\phi$ region of $m({{K}^{+}}{{K}^{-}})$ is inset where the same $\phi$
signal region and $\phi$ sideband region have been represented as in Fig. 2.

###  6.2 Search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates

The fit to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ candidates finds a
total yield of $N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)=5.3\pm 6.7$,
summed across all categories and ${D}^{+}_{s}$ meson decay modes. A yield of
$N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{-}}{{K}^{+}})=65\pm 10$ is
found, consistent with the yield obtained from the full
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ measurement. The
branching fraction for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays is
calculated as

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)=R\times\frac{\mathcal{B}({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})}{\mathcal{B}(\phi\\!\rightarrow{{K}^{+}}{{K}^{-}})}\times\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}),$ (4)

where the branching fraction
$\mathcal{B}(\phi\\!\rightarrow{{K}^{+}}{{K}^{-}})=0.489\pm 0.005$ has been
used [11].

The free variable $R$ is defined to be the ratio of the signal and
normalisation yields, corrected for the selection efficiencies. The yield of
signal candidates in each ${D}^{+}_{s}$ mode is constructed from $R$ and the
normalisation yield for the given ${D}^{+}_{s}$ decay mode,
$N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})$. The product of these two
quantities is corrected by the ratio of selection efficiencies

$N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)=R\times
N({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})\times\frac{\epsilon({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)}{\epsilon({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})}.$ (5)

The simultaneous fit measures a single value of $R$ for all ${D}^{+}_{s}$
decay mode categories. From an ensemble of pseudoexperiments, $R$ is
distributed normally. It can be written as the ratio of signal and
normalisation branching fractions using Eq. 4. The value is determined to be

$R=\frac{\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)}{\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})}\times\frac{\mathcal{B}(\phi\\!\rightarrow{{K}^{+}}{{K}^{-}})}{\mathcal{B}({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})}=(1.6^{+2.2}_{-1.9}\pm
1.1)\times 10^{-3},$

where the first uncertainty is statistical and the second systematic. This
corresponds to a branching fraction for
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays of

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)=(1.2^{+1.6}_{-1.4}\pm
0.8\pm 0.1)\times 10^{-7},$

where the first uncertainty is statistical, the second systematic, and the
third results from the uncertainty on the branching fractions
$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}})$,
$\mathcal{B}(\phi\\!\rightarrow{{K}^{+}}{{K}^{-}})$ and $\mathcal{B}({{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\\!\rightarrow{{K}^{+}}{{K}^{-}})$.
Considering only the statistical uncertainty, the significance of the
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ signal is 0.8 standard deviations
($\sigma$).

Upper limits at 95% and 90% confidence levels (CL) are determined using the
Feldman-Cousins approach [32]. An ensemble of pseudoexperiments is generated
for different values of the branching fraction
$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)$. These generated
pseudoexperiments are then fitted with the nominal fit model to calculate the
fitted branching fraction and associated statistical uncertainty,
$\sigma_{\text{stat}}$. This method constructs confidence bands based on a
likelihood ratio method, calculating the probability of fitting a branching
fraction for a given generated branching fraction. This probability is assumed
to follow a Gaussian distribution with width
$\sigma=\sqrt{\sigma_{\text{stat}}^{2}+\sigma_{\text{syst}}^{2}}$, where
$\sigma_{\text{stat}}$ and $\sigma_{\text{syst}}$ are the statistical and
systematic uncertainties. The dominant source of systematic uncertainty in
this measurement is from the background PDFs. As the size of this uncertainty
is not expected to vary as a function of the generated branching fraction,
$\sigma_{\text{syst}}$ is assumed to be constant. Nuisance parameters are
accounted for using the plug-in method [33]. The generated confidence bands
are shown in Fig. 6, where the statistical-only 90% CL and 95% CL bands are
shown, along with the 95% CL band with systematic uncertainty included. This
corresponds to a statistical-only 95% (90%) CL limit of
$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)<4.4\times
10^{-7}~{}(3.9\times 10^{-7})$, and a 95% (90%) CL limit including systematic
uncertainties of

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)<4.9\times
10^{-7}~{}(4.2\times 10^{-7}).$

Figure 6: Confidence bands produced using the Feldman-Cousins approach. The
green and yellow bands represent the statistical-only 90% and 95% CL bands.
The black dotted line represents the 95% limit including systematic
uncertainties. The measured value of the branching fraction is shown by the
vertical red line, and the corresponding 95% CL limits, with and without
systematic uncertainties, are represented by the dotted red lines.

##  7 Conclusions

A search for ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays
is performed. The branching fraction is determined to be

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}})=(7.1\pm
0.5\pm 0.6\pm 0.7)\times 10^{-6},$

where the first uncertainty is statistical, the second systematic and the
third is due to the uncertainty on the branching fraction of the normalisation
mode ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$. This is the first observation
of this decay mode. A search is also performed for the pure annihilation decay
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$, but no significant signal is
observed and a limit of

$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)<4.9\times
10^{-7}~{}(4.2\times 10^{-7})$

is set on the branching fraction at 95% (90%) confidence level. The limit on
$\mathcal{B}({{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi)$ presented here
supersedes the previous result from LHCb [10].

This updated analysis benefits from the significantly larger data sample now
available at LHCb to increase the reach of these searches. The previous
measurement performed by LHCb reported evidence for the decay
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ with a significance greater than
3$\sigma$. This update determines that there is a sizeable contribution from
${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}{{K}^{+}}{{K}^{-}}$ decays that
contribute within the $\phi$-meson mass window that was previously not
considered. The result is consistent with the prediction that rescattering
contributions to ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$ decays are
small.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing
resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany),
INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),
RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF
(Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities
behind the multiple open-source software packages on which we depend.
Individual groups or members have received support from AvH Foundation
(Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
ANR, Labex P2IO, ENIGMASS and OCEVU, and Région Auvergne-Rhône-Alpes (France),
RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith
Fund, the Royal Society, the English-Speaking Union and the Leverhulme Trust
(United Kingdom).

## References

  * [1] BaBar collaboration, B. Aubert et al., _Evidence for the rare decay $B^{+}\rightarrow D^{+}_{s}\pi^{0}$_, Phys. Rev. Lett. 98 (2007) 171801, arXiv:hep-ex/0611030
  * [2] M. Gronau, D. London, and J. L. Rosner, _Rescattering contributions to rare B-meson decays_ , Phys. Rev. D87 (2013) 036008, arXiv:1211.5785
  * [3] H. Zou, R.-H. Li, X.-X. Wang, and C.-D. Lu, _The CKM suppressed $B(B_{s})\\!\rightarrow{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}_{(s)}P,{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}_{(s)}V,{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}^{*}_{(s)}P,{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}}^{*}_{(s)}V$ decays in perturbative QCD approach_, J. Phys. G37 (2010) 015002, arXiv:0908.1856
  * [4] R. Mohanta, _Searching for new physics in the rare decay $B^{+}\rightarrow D_{s}^{+}\phi$_, Phys. Lett. B540 (2002) 241, arXiv:hep-ph/0205297
  * [5] R. Mohanta and A. K. Giri, _Possible signatures of unparticles in rare annihilation type B decays_ , Phys. Rev. D76 (2007) 057701, arXiv:0707.3308
  * [6] C.-D. Lu, _Calculation of pure annihilation type decay ${{{B}^{+}}}\\!\rightarrow{{D}^{+}_{s}}\phi$_, Eur. Phys. J. C24 (2002) 121, arXiv:hep-ph/0112127
  * [7] HPQCD collaboration, R. J. Dowdall et al., _$B$ -meson decay constants from improved lattice nonrelativistic QCD and physical $u$, $d$, $s$ and $c$ quarks_, Phys. Rev. Lett. 110 (2013) 222003, arXiv:1302.2644
  * [8] ETM collaboration, A. Bussone et al., _Mass of the $b$ quark and $B$-meson decay constants from ${N}_{f}=2+1+1$ twisted-mass lattice QCD_, Phys. Rev. D93 (2016) 114505, arXiv:1603.04306
  * [9] Fermilab Lattice and MILC collaborations, A. Bazavov et al., _$B^{0}_{(s)}$ -mixing matrix elements from lattice QCD for the Standard Model and beyond_, Phys. Rev. D93 (2016) 113016, arXiv:1602.03560
  * [10] LHCb collaboration, R. Aaij et al., _First evidence for the annihilation decay mode ${{{B}^{+}}}\rightarrow{{D}^{+}_{s}}\phi$_, JHEP 02 (2013) 043, arXiv:1210.1089
  * [11] Particle Data Group, C. Patrignani et al., _Review of particle physics_ , Chin. Phys. C40 (2016) 100001
  * [12] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [13] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [14] V. V. Gligorov and M. Williams, _Efficient, reliable and fast high-level triggering using a bonsai boosted decision tree_ , JINST 8 (2013) P02013, arXiv:1210.6861
  * [15] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [16] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [17] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [18] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [19] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [20] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [21] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [22] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [23] LHCb collaboration, R. Aaij et al., _First observations of ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow{{D}^{+}}{{D}^{-}}$, ${{D}^{+}_{s}}{{D}^{-}}$ and ${{D}^{0}}{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ decays_, Phys. Rev. D87 (2013) 092007, arXiv:1302.5854
  * [24] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [25] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
  * [26] G. Punzi, _Sensitivity of searches for new signals and its optimization_ , in Statistical Problems in Particle Physics, Astrophysics, and Cosmology (L. Lyons, R. Mount, and R. Reitmeyer, eds.), p. 79, 2003.  arXiv:physics/0308063
  * [27] W. D. Hulsbergen, _Decay chain fitting with a Kalman filter_ , Nucl. Instrum. Meth. A552 (2005) 566, arXiv:physics/0503191
  * [28] T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
  * [29] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$ observables in $B^{\pm}\rightarrow D^{(\ast)}K^{\pm}$ and $B^{\pm}\rightarrow D^{(\ast)}\pi^{\pm}$ decays_, arXiv:1708.06370, submitted to Phys. Lett. B
  * [30] LHCb collaboration, R. Aaij et al., _Model-independent measurement of the CKM angle $\gamma$ using ${{B}^{0}}\rightarrow{D}{{K}^{*0}}$ decays with ${D}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{+}}{{\pi}^{-}}$ and ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{K}^{+}}{{K}^{-}}$_, JHEP 06 (2016) 131, arXiv:1604.01525
  * [31] K. S. Cranmer, _Kernel estimation in high-energy physics_ , Comput. Phys. Commun. 136 (2001) 198, arXiv:hep-ex/0011057
  * [32] G. J. Feldman and R. D. Cousins, _A unified approach to the classical statistical analysis of small signals_ , Phys. Rev. D57 (1998) 3873, arXiv:physics/9711021
  * [33] B. Sen, M. Walker, and M. Woodroofe, _On the unified method with nuisance parameters_ , Statistica Sinica 19 (2009) 301

LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, M. Atzeni42, G. Auriemma26, M. Baalouch5, I.
Babuschkin56, S. Bachmann12, J.J. Back50, A. Badalov38,m, C. Baesso62, S.
Baker55, V. Balagura7,b, W. Baldini17, A. Baranov35, R.J. Barlow56, C.
Barschel40, S. Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V.
Battista41, A. Bay41, L. Beaucourt4, J. Beddow53, F. Bedeschi24, I. Bediaga1,
A. Beiter61, L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37,
I. Belyaev32,40, E. Ben-Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A.
Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt42, F. Betti15, M.-O. Bettler40, M. van Beuzekom43, Ia. Bezshyiko42,
S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bizzeti18,u, M. Bjørn57, T.
Blake50, F. Blanc41, S. Blusk61, V. Bocci26, T. Boettcher58, A. Bondar36,w, N.
Bondar31, I. Bordyuzhin32, S. Borghi56, M. Borisyak35, M. Borsato39, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12,
T. Britton61, J. Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A.
Bursche16,f, J. Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R.
Calabrese17,g, R. Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A.
Camboni38,m, P. Campana19, D.H. Campora Perez40, L. Capriotti56, A.
Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A. Cardini16, P. Carniti21,i,
L. Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21, M. Cattaneo40, G.
Cavallero20,40,h, R. Cenci24,t, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S. Chen16, S.F.
Cheung57, S.-G. Chitic40, V. Chobanova39,40, M. Chrzaszcz42,27, A. Chubykin31,
P. Ciambrone19, X. Cid Vidal39, G. Ciezarek43, P.E.L. Clarke52, M.
Clemencic40, H.V. Cliff49, J. Closier40, J. Cogan6, E. Cogneras5, V.
Cogoni16,f, L. Cojocariu30, P. Collins40, T. Colombo40, A. Comerma-Montells12,
A. Contu40, A. Cook48, G. Coombs40, S. Coquereau38, G. Corti40, M. Corvo17,g,
C.M. Costa Sobral50, B. Couturier40, G.A. Cowan52, D.C. Craik58, A.
Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio40, F. Da Cunha
Marinho2, E. Dall’Occo43, J. Dalseno48, A. Davis3, O. De Aguiar Francisco40,
K. De Bruyn40, S. De Capua56, M. De Cian12, J.M. De Miranda1, L. De Paula2, M.
De Serio14,d, P. De Simone19, C.T. Dean53, D. Decamp4, L. Del Buono8, H.-P.
Dembinski11, M. Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F.
Dettori54, B. Dey65, A. Di Canto40, P. Di Nezza19, H. Dijkstra40, F. Dordei40,
M. Dorigo40, A. Dosil Suárez39, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour43, G. Dujany8, P. Durante40, R. Dzhelyadin37, M. Dziewiecki12, A.
Dziurda40, A. Dzyuba31, S. Easo51, M. Ebert52, U. Egede55, V. Egorychev32, S.
Eidelman36,w, S. Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53,
S. Ely61, S. Esen12, H.M. Evans49, T. Evans57, A. Falabella15, N. Farley47, S.
Farry54, D. Fazzini21,i, L. Federici25, D. Ferguson52, G. Fernandez38, P.
Fernandez Declara40, A. Fernandez Prieto39, F. Ferrari15, F. Ferreira
Rodrigues2, M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M. Fiorini17,g, M.
Firlej28, C. Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, K. Fohl40, M.
Fontana16,40, F. Fontanelli20,h, D.C. Forshaw61, R. Forty40, V. Franco Lima54,
M. Frank40, C. Frei40, J. Fu22,q, W. Funk40, E. Furfaro25,j, C. Färber40, E.
Gabriel52, A. Gallas Torreira39, D. Galli15,e, S. Gallorini23, S. Gambetta52,
M. Gandelman2, P. Gandini22, Y. Gao3, L.M. Garcia Martin70, J. García
Pardiñas39, J. Garra Tico49, L. Garrido38, P.J. Garsed49, D. Gascon38, C.
Gaspar40, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck56, M.
Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41, V. Gibson49, O.G. Girard41,
L. Giubega30, K. Gizdov52, V.V. Gligorov8, D. Golubkov32, A. Golutvin55, A.
Gomes1,a, I.V. Gorelov33, C. Gotti21,i, E. Govorkova43, J.P. Grabowski12, R.
Graciani Diaz38, L.A. Granado Cardoso40, E. Graugés38, E. Graverini42, G.
Graziani18, A. Grecu30, R. Greim9, P. Griffith16, L. Grillo21, L. Gruber40,
B.R. Gruberg Cazon57, O. Grünberg67, E. Gushchin34, Yu. Guz37, T. Gys40, C.
Göbel62, T. Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli41, C. Haen40, S.C.
Haines49, B. Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N.
Harnew57, S.T. Harnew48, C. Hasse40, M. Hatch40, J. He63, M. Hecker55, K.
Heinicke10, A. Heister9, K. Hennessy54, P. Henrard5, L. Henry70, E. van
Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57, C. Hombach56, P.H. Hopchev41,
W. Hu65, Z.C. Huard59, W. Hulsbergen43, T. Humair55, M. Hushchyn35, D.
Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten58, R. Jacobsson40, J. Jalocha57,
E. Jans43, A. Jawahery60, F. Jiang3, M. John57, D. Johnson40, C.R. Jones49, C.
Joram40, B. Jost40, N. Jurik57, S. Kandybei45, M. Karacson40, J.M. Kariuki48,
S. Karodia53, N. Kazeev35, M. Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49,
T. Ketel44, E. Khairullin35, B. Khanji12, C. Khurewathanakul41, T. Kirn9, S.
Klaver56, K. Klimaszewski29, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R.
Kopecna12, P. Koppenburg43, A. Kosmyntseva32, S. Kotriakhova31, M. Kozeiha5,
L. Kravchuk34, M. Kreps50, F. Kress55, P. Krokovny36,w, F. Kruse10, W.
Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V. Kudryavtsev36,w, A.K.
Kuonen41, T. Kvaratskheliya32,40, D. Lacarrere40, G. Lafferty56, A. Lai16, G.
Lanfranchi19, C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A.
Leflat33,40, J. Lefrançois7, R. Lefèvre5, F. Lemaitre40, E. Lemos Cid39, O.
Leroy6, T. Lesiak27, B. Leverington12, P.-R. Li63, T. Li3, Y. Li7, Z. Li61, T.
Likhomanenko68, R. Lindner40, F. Lionetto42, V. Lisovskyi7, X. Liu3, D. Loh50,
A. Loi16, I. Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39,
H. Luo52, A. Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X. Lyu63, F.
Machefert7, F. Maciuc30, V. Macko41, P. Mackowiak10, S. Maddrell-Mander48, O.
Maev31,40, K. Maguire56, D. Maisuzenko31, M.W. Majewski28, S. Malde57, B.
Malecki27, A. Malinin68, T. Maltsev36,w, G. Manca16,f, G. Mancinelli6, D.
Marangotto22,q, J. Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin
Benito38, M. Marinangeli41, P. Marino41, J. Marks12, G. Martellotti26, M.
Martin6, M. Martinelli41, D. Martinez Santos39, F. Martinez Vidal70, L.M.
Massacrier7, A. Massafferri1, R. Matev40, A. Mathad50, Z. Mathe40, C.
Matteuzzi21, A. Mauri42, E. Maurice7,b, B. Maurin41, A. Mazurov47, M.
McCann55,40, A. McNab56, R. McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6,
F. Meier10, N. Meinert67, D. Melnychuk29, M. Merk43, A. Merli22,40,q, E.
Michielin23, D.A. Milanes66, E. Millard50, M.-N. Minard4, L. Minzoni17, D.S.
Mitzel12, A. Mogini8, J. Molina Rodriguez1, T. Mombächer10, I.A. Monroy66, S.
Monteil5, M. Morandin23, M.J. Morello24,t, O. Morgunova68, J. Moron28, A.B.
Morris52, R. Mountain61, F. Muheim52, M. Mulder43, D. Müller56, J. Müller10,
K. Müller42, V. Müller10, P. Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57,
I. Nasteva2, M. Needham52, N. Neri22,40, S. Neubert12, N. Neufeld40, M.
Neuner12, T.D. Nguyen41, C. Nguyen-Mau41,n, S. Nieswand9, R. Niet10, N.
Nikitin33, T. Nikodem12, A. Nogay68, D.P. O’Hanlon50, A. Oblakowska-Mucha28,
V. Obraztsov37, S. Ogilvy19, R. Oldeman16,f, C.J.G. Onderwater71, A.
Ossowska27, J.M. Otalora Goicochea2, P. Owen42, A. Oyanguren70, P.R. Pais41,
A. Palano14,d, M. Palutan19,40, A. Papanestis51, M. Pappagallo14,d, L.L.
Pappalardo17,g, W. Parker60, C. Parkes56, G. Passaleva18,40, A. Pastore14,d,
M. Patel55, C. Patrignani15,e, A. Pearce40, A. Pellegrino43, G. Penso26, M.
Pepe Altarelli40, S. Perazzini40, P. Perret5, L. Pescatore41, K. Petridis48,
A. Petrolini20,h, A. Petrov68, M. Petruzzo22,q, E. Picatoste Olloqui38, B.
Pietrzyk4, M. Pikies27, D. Pinci26, F. Pisani40, A. Pistone20,h, A. Piucci12,
V. Placinta30, S. Playfer52, M. Plo Casasus39, F. Polci8, M. Poli Lener19, A.
Poluektov50, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce40, A.
Popov37, D. Popov11,40, S. Poslavskii37, C. Potterat2, E. Price48, J.
Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig Navarro42, H. Pullen57, G.
Punzi24,p, W. Qian50, R. Quagliani7,48, B. Quintana5, B. Rachwal28, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F.
Ratnikov35, G. Raven44, M. Ravonel Salzgeber40, M. Reboud4, F. Redi55, S.
Reichert10, A.C. dos Reis1, C. Remon Alepuz70, V. Renaudin7, S. Ricciardi51,
S. Richards48, M. Rihl40, K. Rinnert54, V. Rives Molina38, P. Robbe7, A.
Robert8, A.B. Rodrigues1, E. Rodrigues59, J.A. Rodriguez Lopez66, A.
Rogozhnikov35, S. Roiser40, A. Rollings57, V. Romanovskiy37, A. Romero
Vidal39, J.W. Ronayne13, M. Rotondo19, M.S. Rudolph61, T. Ruf40, P. Ruiz
Valls70, J. Ruiz Vidal70, J.J. Saborido Silva39, E. Sadykhov32, N. Sagidova31,
B. Saitta16,f, V. Salustino Guimaraes62, C. Sanchez Mayordomo70, B. Sanmartin
Sedes39, R. Santacesaria26, C. Santamarina Rios39, M. Santimaria19, E.
Santovetti25,j, G. Sarpis56, A. Sarti19,k, C. Satriano26,s, A. Satta25, D.M.
Saunders48, D. Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller53, H.
Schindler40, M. Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A.
Schopper40, H.F. Schreiner59, M. Schubiger41, M.-H. Schune7, R. Schwemmer40,
B. Sciascia19, A. Sciubba26,k, A. Semennikov32, E.S. Sepulveda8, A. Sergi47,
N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert40, M. Shapkin37, I.
Shapoval45, Y. Shcheglov31, T. Shears54, L. Shekhtman36,w, V. Shevchenko68,
B.G. Siddi17, R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, M. Sirendi49, N. Skidmore48, T. Skwarnicki61, E. Smith55, I.T.
Smith52, J. Smith49, M. Smith55, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, S. Sridharan40, F.
Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55, O. Steinkamp42,
S. Stemmle12, O. Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B.
Storaci42, S. Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U. Straumann42,
J. Sun3, L. Sun64, W. Sutcliffe55, K. Swientek28, V. Syropoulos44, T.
Szumlak28, M. Szymanski63, S. T’Jampens4, A. Tayduganov6, T. Tekampe10, G.
Tellarini17,g, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J. Tilley55, V.
Tisserand4, M. Tobin41, S. Tolk49, L. Tomassetti17,g, D. Tonelli24, F.
Toriello61, R. Tourinho Jadallah Aoude1, E. Tournefier4, M. Traill53, M.T.
Tran41, M. Tresch42, A. Trisovic40, A. Tsaregorodtsev6, P. Tsopelas43, A.
Tully49, N. Tuning43,40, A. Ukleja29, A. Usachov7, A. Ustyuzhanin35, U.
Uwer12, C. Vacca16,f, A. Vagner69, V. Vagnoni15,40, A. Valassi40, S. Valat40,
G. Valenti15, R. Vazquez Gomez40, P. Vazquez Regueiro39, S. Vecchi17, M. van
Veghel43, J.J. Velthuis48, M. Veltri18,r, G. Veneziano57, A. Venkateswaran61,
T.A. Verlage9, M. Vernet5, M. Vesterinen57, J.V. Viana Barbosa40, B. Viaud7,
D. Vieira63, M. Vieites Diaz39, H. Viemann67, X. Vilasis-Cardona38,m, M.
Vitti49, V. Volkov33, A. Vollhardt42, B. Voneki40, A. Vorobyev31, V.
Vorobyev36,w, C. Voß9, J.A. de Vries43, C. Vázquez Sierra39, R. Waldi67, C.
Wallace50, R. Wallace13, J. Walsh24, J. Wang61, D.R. Ward49, H.M. Wark54, N.K.
Watson47, D. Websdale55, A. Weiden42, C. Weisser58, M. Whitehead40, J.
Wicht50, G. Wilkinson57, M. Wilkinson61, M. Williams56, M.P. Williams47, M.
Williams58, T. Williams47, F.F. Wilson51,40, J. Wimberley60, M. Winn7, J.
Wishahi10, W. Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton49, K.
Wraight53, K. Wyllie40, Y. Xie65, M. Xu65, Z. Xu4, Z. Yang3, Z. Yang60, Y.
Yao61, H. Yin65, J. Yu65, X. Yuan61, O. Yushchenko37, K.A. Zarebski47, M.
Zavertyaev11,c, L. Zhang3, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V.
Zhukov33, J.B. Zonneveld52, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Universita & INFN, Milano-Bicocca, Milano, Italy
22Sezione 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
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
70Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
71Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
†Deceased