* [34] F. J. Narcowich, P. Petrushev and J. D. Ward, Localized tight frames on spheres, SIAM J. Math. Anal. 38 (2006), 574–594.
  * [35] F. J. Narcowich, P. Petrushev and J. D. Ward, Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, J. Funct. Anal. 238 (2006), 530–564.
  * [36] S. Pawelke, Über Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen, Tôhoku Math. J. 24 (1972), 473–486.
  * [37] P. Petrushev and Y. Xu, Localized polynomial frames on the interval with Jacobi weights, J. Fourier Anal. and Appl. 11 (2005), 557–575.
  * [38] P. Petrushev and Y. Xu, Localized polynomial frames on the ball, Constr. Approx. 27 (2008), 121–148.
  * [39] P. Petrushev and Y. Xu, Decomposition of spaces of distributions induced by Hermite expansion, J. Fourier Anal. and Appl. 14 (2008), 372-414.
  * [40] A. Prymak, Upper estimates of Christoffel function on convex domains, J. Math. Anal, Appl. 455 (2017), 1984–2000.
  * [41] A. Prymak, Christoffel functions on planar domains with piecewise smooth boundary, Acta Math. Hungar. 158 (2019), 216–234.
  * [42] Kh. P. Rustamov, On the approximation of functions on a sphere, (Russian), Izv. Ross. Akad. Nauk Ser. Mat. 57 (1993), 127–148; translation in Russian Acad. Sci. Izv. Math. 43 (1994), no. 2, 311– 329.
  * [43] E. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag, Berlin-Heidelberg, 1997.
  * [44] E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals Princeton University Press, Princeton, 1993.
  * [45] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, Princeton, 1971.
  * [46] G. Szegő, Orthogonal polynomials. 4th edition, Amer. Math. Soc., Providence, RI. 1975
  * [47] V. Totik, Polynomial approximation on polytopes, Mem. Amer. Math. Soc. 232 (2014), no. 1091, vi+112.
  * [48] V. Totik, Polynomial approximation in several variables, J. Approx. Theory 252: 105364 (2020).
  * [49] Y. G. Wang, Q. T. Le Gia, I. H. Sloan and R. S. Womersley, Fully discrete needlet approximation on the sphere. Appl. Comput. Harmon. Anal. 43 (2017), 292–316.
  * [50] Y. Xu, Christoffel functions and Fourier series for multivariate orthogonal polynomials. J. Approx. Theory 82 (1995), 205–239.
  * [51] Y. Xu, Summability of Fourier orthogonal series for Jacobi weight on a ball in ${\mathbb{R}}^{d}$, Trans. Amer. Math. Soc., 351 (1999), 2439–2458.
  * [52] Y. Xu, Weighted approximation of functions on the unit sphere. Const. Approx. 21 (2005), 1–28.
  * [53] Y. Xu, Fourier series in orthogonal polynomials on a cone of revolution, J. Fourier Anal. Appl., 26 (2020), Paper No. 36, 42 pp.
  * [54] Y. Xu, Orthogonal structure and orthogonal series in and on a double cone or a hyperboloid. Trans. Amer. Math. Soc., 374 (2021), 3603–3657.


EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-064 LHCb-PAPER-2015-005 March 24, 2015

Measurement of the time-dependent $C\\!P$ asymmetries in
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$

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

The first measurement of decay-time-dependent $C\\!P$ asymmetries in the decay
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and an updated measurement of the
ratio of branching fractions ${\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})/{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})$ are presented. The results are
obtained using data corresponding to an integrated luminosity of 3.0
$\mbox{\,fb}^{-1}$ of proton–proton collisions recorded with the LHCb detector
at centre-of-mass energies of 7 and 8 $\mathrm{\,Te\kern-1.00006ptV}$. The
results on the $C\\!P$ asymmetries are

$\displaystyle\mathcal{A}_{\Delta\Gamma}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$
$\displaystyle=\phantom{-}0.49\pm\>^{0.77}_{0.65}\>\>(\text{stat})\pm
0.06\>(\text{syst})\>,$ $\displaystyle
C_{\text{dir}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.28\pm
0.41\>(\text{stat})\pm 0.08\>(\text{syst})\>,$ $\displaystyle
S_{\text{mix}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.08\pm
0.40\>(\text{stat})\pm 0.08\>(\text{syst})\>.$

The ratio ${\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})/{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})$ is measured to be

$0.0431\pm 0.0017\>(\text{stat})\pm 0.0012\>(\text{syst})\pm
0.0025\>(f_{s}/f_{d})\>,$

where the last uncertainty is due to the knowledge of the ${{B}^{0}_{s}}$ and
${{B}^{0}}$ production fractions.

Published in JHEP 06 (2015) 131

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

##  1 Introduction

In decays of neutral $B$ mesons (where $B$ stands for a ${B}^{0}$ or
${B}^{0}_{s}$ meson) to a final state accessible to both ${B}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}$, the interference between the direct
decay and the decay via oscillation leads to decay-time-dependent $C\\!P$
violation. Measurements of time-dependent $C\\!P$ asymmetries provide valuable
tests of the flavour sector of the Standard Model (SM) and offer opportunities
to search for signs of non-SM physics. A measurement of this asymmetry in the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decay mode allows for a
determination of the effective $C\\!P$ phase [1, 2, 3]

$\phi_{d}^{\text{eff}}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}})\equiv{\phi_{{d}}}+\Delta{\phi_{{d}}}\>,$ (1)

where $\phi_{{d}}$ is the relative phase of the ${{B}^{0}}$–${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ mixing amplitude and the tree-
level decay process, and $\Delta{\phi_{{d}}}$ is a shift induced by the so-
called penguin topologies, which are illustrated in Fig. 1. In the Standard
Model, $\phi_{{d}}$ is equal to $2\beta$ [4], where
$\beta\equiv\arg(-V_{cd}^{\phantom{*}}V_{cb}^{*}/V_{td}^{\phantom{*}}V_{tb}^{*})$
is one of the angles of the unitarity triangle in the Cabibbo-Kobayashi-
Maskawa (CKM) quark mixing matrix [5, *Cabibbo:1963yz]. The latest average of
the Belle and BaBar measurements reads $\sin\phi_{d}^{\text{eff}}=0.665\pm
0.020$ [7], while the recently updated analysis from LHCb reports
$\sin\phi_{d}^{\text{eff}}=0.729\pm 0.035\text{(stat)}\pm 0.022\text{(syst)}$
[8].

Forthcoming data from the LHC and KEK $e^{+}e^{-}$ super $B$ factory will lead
to an unprecedented precision on the phase $\phi_{d}^{\text{eff}}$. To
translate this into an equally precise determination of the CKM phase $\beta$,
it is essential to take into account the doubly Cabibbo-suppressed
contributions from the penguin topologies, which lead to a value for
$\Delta{\phi_{{d}}}$ that might be as large as $\mathcal{O}(1^{\circ})$ [1,
3]. By relying on approximate flavour symmetries, information on
$\Delta{\phi_{{d}}}$ can be obtained from measurements of $C\\!P$ asymmetries
in decays where the penguin topologies are enhanced. The
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mode is the most promising
candidate for this task [9, 2, 3].

Assuming no $C\\!P$ violation in mixing [7], the time-dependent $C\\!P$
asymmetry in
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ takes the form

$\displaystyle a_{{C\\!P}}(t)$ $\displaystyle\equiv\frac{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}(t)\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}})-\Gamma({{B}^{0}_{s}}(t)\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}{\Gamma({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}(t)\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}})+\Gamma({{B}^{0}_{s}}(t)\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}\>,$ (2)
$\displaystyle=\frac{S_{\text{mix}}\sin\left({\Delta
m_{{s}}}\,t\right)-C_{\text{dir}}\cos\left({\Delta
m_{{s}}}\,t\right)}{\cosh\left({\Delta\Gamma_{{s}}}\,t/2\right)+\mathcal{A}_{\Delta\Gamma}\sinh\left({\Delta\Gamma_{{s}}}\,t/2\right)}\>,$
(3)

where
$\Gamma({{B}^{0}_{s}}(t)\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})$ represents the time-dependent
decay rate of the ${B}^{0}_{s}$ meson into the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}$ final state, and ${\Delta m_{{s}}}\equiv m_{\rm H}-m_{\rm L}$ and
${\Delta\Gamma_{{s}}}\equiv{\Gamma_{\rm L}}-{\Gamma_{\rm H}}$ are,
respectively, the mass and decay width difference between the heavy and light
eigenstates of the ${{B}^{0}_{s}}$ meson system. The
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables are defined
through the parameter

$\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}\equiv-e^{i{\phi_{{s}}}}\>\frac{A({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}})}{A({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}$ (4)

in terms of the complex phase ${\phi_{{s}}}$ associated with the
${B}^{0}_{s}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$
mixing process and the ratio of time-independent transition amplitudes as

$\mathcal{A}_{\Delta\Gamma}\equiv-\frac{2\,\mathcal{R}e[\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}]}{1+|\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}|^{2}}\>,\qquad
C_{\text{dir}}\equiv\frac{1-|\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}|^{2}}{1+|\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}|^{2}}\>,\qquad
S_{\text{mix}}\equiv\frac{2\,\mathcal{I}m[\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}]}{1+|\lambda_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}|^{2}}\>,$ (5)

where $C_{\text{dir}}$ and $S_{\text{mix}}$ represent direct and mixing-
induced $C\\!P$ violation, respectively. In the Standard Model
$\phi_{s}^{\text{SM}}\equiv 2\arg(-V_{ts}^{\phantom{*}}V_{tb}^{*})$. A recent
analysis [3] predicts

$\displaystyle\mathcal{A}_{\Delta\Gamma}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=$
$\displaystyle 0.957\pm 0.061\>,$ $\displaystyle
C_{\text{dir}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=$
$\displaystyle 0.003\pm 0.021\>,$ (6) $\displaystyle
S_{\text{mix}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=$
$\displaystyle 0.29\phantom{0}\pm 0.20\phantom{0}\>.$

Similar expression for Eqs. (3) and (5) are obtained for the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decay by replacing
$s\leftrightarrow d$. The observable $\mathcal{A}_{\Delta\Gamma}$ is not
applicable in the measurement of
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ because it is assumed that
${\Delta\Gamma_{{d}}}=0$ [7].

Figure 1: Decay topologies contributing to the
$B_{(s)}^{0}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ channel: (left) tree diagram and
(right) penguin diagram.

This paper presents the first measurement of the time-dependent $C\\!P$
asymmetries in
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays, as well as an updated
measurement of the ratio of time-integrated branching fractions ${\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})/{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})$. This ratio was first measured by
the CDF collaboration [10], while the previously most precise measurement was
reported by LHCb in Ref. [11]. The analysis is performed with a data sample
corresponding to an integrated luminosity of $3.0\>\mbox{\,fb}^{-1}$ of
proton–proton ($pp$) collisions, recorded by the LHCb experiment at centre-of-
mass energies of $7\>\mathrm{\,Te\kern-1.00006ptV}$ and
$8\>\mathrm{\,Te\kern-1.00006ptV}$ in 2011 and 2012, respectively.

The analysis proceeds in two steps. The first step, described in detail in
Sec. 3, consists of a multivariate selection of
${B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates. In the second step a
maximum likelihood fit is performed to the selected data. The fit model
includes a prominent
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ component, which is used to
improve the modelling of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ signal. In addition, the
measurement of $C\\!P$ asymmetries associated with
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays offers a validation of the
likelihood method’s implementation. However, the stringent event selection
necessary to isolate the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates limits the precision on
these two $C\\!P$ observables. Dedicated and more precise measurements of the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables are therefore
the subject of a separate publication [8].

For a time-dependent measurement of $C\\!P$ violation it is essential to
determine the initial flavour of the ${B}$ candidate, i.e. whether it
contained a ${b}$ or a ${\overline{b}}$ quark at production. The method to
achieve this is called _flavour tagging_ , and is discussed in Sec. 4. The
tagging information is combined with a description of the $B$ mass and decay
time distributions when performing the maximum likelihood fit, which is
described in Sec. 5. The three $C\\!P$ observables describing the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays and two $C\\!P$ observables
describing the ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays are obtained directly from
the fit. The ratio of branching fractions [12] is derived from the ratio $R$
of fitted ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ to
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ event yields as

$\frac{{\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}{{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}=R\times
f_{\text{sel}}\times\frac{f_{d}}{f_{s}}\>,$ (7)

where $f_{\text{sel}}$ is a correction factor for differences in selection
efficiency between
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays, and $f_{s}/f_{d}=0.259\pm
0.015$ [13, *LHCb-CONF-2013-011] is the ratio of ${B}^{0}_{s}$ to ${B}^{0}$
meson hadronisation fractions. The study of systematic effects on the ratio
$R$ and the $C\\!P$ observables is presented in Sec. 6. The main results for
the branching ratio measurement are reported in Sec. 7 and those for the
$C\\!P$ observables in Sec. 8.

##  2 Detector and simulation

The LHCb detector [15, 16] 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 $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter, is measured
with a resolution of $(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm
T}$ is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

In the simulation, $pp$ collisions are generated using Pythia [17,
*Sjostrand:2007gs] with a specific LHCb configuration [19]. Decays of hadronic
particles are described by EvtGen [20], in which final-state radiation is
generated using Photos [21]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [22,
*Agostinelli:2002hh] as described in Ref. [24].

##  3 Event selection

Candidate ${B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decays are considered in the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$
and ${{K}^{0}_{\rm\scriptscriptstyle S}}\\!\rightarrow{\pi}^{+}{\pi}^{-}$
final states. The event selection is based on an initial selection, followed
by a two-stage multivariate analysis consisting of artificial neural network
(NN) classifiers [25].

###  3.1 Initial selection

The online event selection is performed by a trigger, which consists of a
hardware level, based on information from the calorimeter and muon systems,
followed by a software level, which applies a full event reconstruction. The
hardware trigger selects at least one muon with a transverse momentum
$\mbox{$p_{\rm T}$}>1.48\>(1.76){\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ or two
muons with $\sqrt{\mbox{$p_{\rm T}$}(\mu_{1})\mbox{$p_{\rm
T}$}(\mu_{2})}>1.3\>(1.6){\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ in the 7 (8)
$\mathrm{\,Te\kern-1.00006ptV}$ $pp$ collisions. The software trigger consists
of two stages. In the first stage, events are required to have either two
oppositely charged muons with combined mass above
$2.7\>{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$, or at least one muon or one
high-$p_{\rm T}$ charged particle ($\mbox{$p_{\rm
T}$}>1.8\>{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$) with an impact parameter
larger than $100{\,\upmu\rm m}$ with respect to all $pp$ interaction vertices
(PVs). In the second stage of the software trigger the tracks of two or more
of the final-state particles are required to form a vertex that is
significantly displaced from the PVs, and only events containing
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$
candidates are retained.

In the offline selection, ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$
candidates are selected by requiring two muon tracks to form a good quality
vertex and have an invariant mass in the range
$[3030,3150]\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. This interval
corresponds to about eight times the ${\mu^{+}\mu^{-}}$ mass resolution at the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass and covers part of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ radiative tail.

Decays of ${{K}^{0}_{\rm\scriptscriptstyle
S}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ are reconstructed in two different
categories: the first involving ${K}^{0}_{\rm\scriptscriptstyle S}$ mesons
that decay early enough for the daughter pions to be reconstructed in the
vertex detector; and the second containing ${K}^{0}_{\rm\scriptscriptstyle S}$
that decay later such that track segments of the pions cannot be formed in the
vertex detector. These categories are referred to as _long_ and _downstream_ ,
respectively. Long ${{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates have
better mass, momentum and vertex resolution than those in the downstream
category.

The two pion tracks of the long (downstream) ${K}^{0}_{\rm\scriptscriptstyle
S}$ candidates are required to form a good quality vertex and their combined
invariant mass must be within
$35\>(64)\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known
${{K}^{0}_{\rm\scriptscriptstyle S}}$ mass [26]. To remove contamination from
$\Lambda\\!\rightarrow{p}{{\pi}^{-}}$ decays, the reconstructed mass of the
long (downstream) ${K}^{0}_{\rm\scriptscriptstyle S}$ candidates under the
assumption that one of its daughter tracks is a proton is required to be more
than $6\>(10)\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ away from the known
$\Lambda$ mass [26]. The ${K}^{0}_{\rm\scriptscriptstyle S}$ decay vertex is
required to be located downstream of the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ decay vertex, i.e. it is
required to have a positive flight distance. This removes approximately 50% of
mis-reconstructed
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ background. The remaining
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ background is heavily suppressed by the first stage
of the multivariate selection described below.

Candidate $B$ mesons are selected from combinations of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
${K}^{0}_{\rm\scriptscriptstyle S}$ candidates with mass
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}$ in the range
$[5180,5520]\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and a decay time
larger than $0.2\>{\rm\,ps}$. The reconstructed mass and decay time are
obtained from a kinematic fit [27] that constrains the masses of the
$\mu^{+}\mu^{-}$ and ${\pi}^{+}{\pi}^{-}$ pairs to the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
${K}^{0}_{\rm\scriptscriptstyle S}$ masses [26], respectively, and constrains
the $B$ candidate to originate from the PV. A good quality fit is required and
the uncertainty on the $B$ mass estimated by the kinematic fit must not exceed
$30\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. In the case that the event has
multiple PVs, a clear separation of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ decay vertex from any of the other PVs in the event is required, and
all combinations of $B$ candidates and PVs that pass the selection are
considered.

###  3.2 Multivariate selection

The first stage of the multivariate selection focuses on removing the mis-
reconstructed ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ background that survives the requirement on the
${K}^{0}_{\rm\scriptscriptstyle S}$ flight distance. It only affects the
subsample of candidates for which the ${K}^{0}_{\rm\scriptscriptstyle S}$ is
reconstructed in the long category. The NN is trained on simulated
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ (signal) and
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ (background) data and only uses information
associated with the reconstructed pions and ${K}^{0}_{\rm\scriptscriptstyle
S}$ candidate. This includes decay time, mass, momentum, impact parameter and
particle-identification properties. The requirement on the NN classifier’s
output is optimised to retain 99% of the original signal candidates in
simulation, with a background rejection on simulated
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ candidates of 99.55%. This results in an estimated
number of $18\pm 2$
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ candidates in the long
${K}^{0}_{\rm\scriptscriptstyle S}$ data sample surviving this stage of the
selection. Their yield is further reduced by the second NN classifier, and
these candidates are therefore treated as combinatorial background in the
remainder of the analysis.

The second stage of the multivariate selection aims at reducing the
combinatorial background to isolate the small
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ signal. In contrast to the first
NN, it is trained entirely on data, using the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ signal as a representative of the
signal features of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decay. Candidates for the training
sample are those populating the mass ranges
$[5180,5340]\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
$[5390,5520]\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, avoiding the
${B}^{0}_{s}$ signal region. The signal and background weights for the
training of the second NN are determined using the sPlot technique [28] and
obtained by performing an unbinned maximum likelihood fit to the $B$ mass
distribution of the candidates meeting the selection criteria on the first NN
classifier’s output. The fit function is defined as the sum of a ${B}^{0}$
signal component and a combinatorial background where the parametrisation of
the individual components matches that of the likelihood method used for the
full $C\\!P$ analysis and is described in more detail in Sec. 5.

Due to differences in the distributions of the input variables of the NN, as
well as different signal-to-background ratios, the second stage of the
multivariate selection is performed separately for the $B$ candidate samples
containing long and downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ candidates.
The NN classifiers use information on the candidate’s kinematic properties,
vertex and track quality, impact parameter, particle identification
information from the RICH and muon detectors, as well as global event
properties like track and PV multiplicities. The variables that are used in
the second NN are chosen to avoid correlations with the reconstructed $B$
mass.

Final selection requirements on the second stage NN classifier outputs are
chosen to optimise the sensitivity to the ${B}^{0}_{s}$ signal using
$N_{\text{S}}/\sqrt{N_{\text{S}}+N_{\text{B}}}$ as figure of merit, where
$N_{\text{S}}$ and $N_{\text{B}}$ are respectively the expected number of
signal and background events in a $\pm
30\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ mass range around the
${B}^{0}_{s}$ peak. After applying the final requirement on the NN classifier
output associated with the long (downstream) ${K}^{0}_{\rm\scriptscriptstyle
S}$ sample, the multivariate selection rejects, relative to the initial
selection, 99.2% of the background in both samples while keeping 72.9% (58.3%)
of the ${B}^{0}$ signal. The lower selection efficiency on the downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ sample is due to the worse signal-to-
background ratio after the initial selection, which requires a more stringent
requirement on the NN classifier output. The resulting
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mass distributions are
illustrated in Fig. 2.

Figure 2: Mass distribution of ${B}$ candidates at different stages of the
event selection for the (left) long ${K}^{0}_{\rm\scriptscriptstyle S}$ and
(right) downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ sample. The data sample
after initial selection (red, $+$), after the first neural net (green,
$\times$) and after the second neural net (black, $\bullet$) are shown.
Overlaid are projections of the fit described in Sec. 5. Shown components are
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ (dark blue, dashed),
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ (red, dotted) and combinatorial
background (turquoise, dash-dotted).

After applying the full selection, the long (downstream) $B$ candidate can
still be associated with more than one PV in about 1.5% (0.6%) of the events;
in this case, one PVs is chosen at random. Likewise, about $0.24\%$ (0.15%) of
the selected events have multiple candidates sharing one or more tracks; in
this case, one candidates is chosen at random.

##  4 Flavour tagging

At the LHC, $b$ quarks are predominantly produced in $b\bar{b}$ pairs. When
one of the two quarks hadronises to form the $B$ meson decay of interest (“the
signal $B$”), the other $b$ quark hadronises and decays independently. By
exploiting this production mechanism, the signal $B$’s initial flavour is
identified by means of two classes of flavour-tagging algorithms. The opposite
side (OS) taggers determine the flavour of the non-signal $b$-hadron [29]
while the same side kaon (SSK) tagger exploits the fact that the additional
${\overline{s}}$ (${s}$) quark produced in the fragmentation of a
${{B}^{0}_{s}}$ (${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$)
meson often forms a ${{K}^{+}}$ (${{K}^{-}}$) meson [30].

These algorithms provide tag decisions $q_{\text{OS}}$ and $q_{\text{SSK}}$,
which take the value $+1$ ($-1$) in case the signal candidate is tagged as a
$B$ (${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}}$) meson, and
predictions $\eta_{\text{OS}}$ and $\eta_{\text{SSK}}$ for the probability of
the tag to be incorrect. The latter is obtained using neural networks, which
in the case of the OS taggers are trained on
${{{B}^{+}}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays, while for the SSK tagger simulated
${{B}^{0}_{s}}\\!\rightarrow D_{s}^{-}\pi^{+}$ events are used.

The mistag probability predicted by the tagging algorithms is calibrated in
data to determine the true mistag probability $\omega$, by using control
samples of several flavour-specific ${B}$ mesons decays. This calibration is
performed individually for the OS and SSK tagging algorithms; for the latter,
different calibration parameters are used to describe the ${B}^{0}$ and
${B}^{0}_{s}$ mesons. For all events with both an OS and SSK tag decision, a
combined tag decision and mistag probability is derived as described in Ref.
[29].

The figure of merit for the optimisation of a tagging algorithm is the
effective tagging efficiency, $\varepsilon_{\rm eff}={\varepsilon_{\rm
tag}}(1-2\omega)^{2}$ where ${\varepsilon_{\rm tag}}$ is the fraction of
candidates with an assigned tag decision. In the long
${K}^{0}_{\rm\scriptscriptstyle S}$ sample for the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mode, the OS and SSK taggers yield
an $\varepsilon_{\rm eff}$ of $(2.93\pm 0.06)\%$ and $(0.97\pm 0.12)\%$,
respectively, while the sample with both an OS and SSK tagging response gives
an $\varepsilon_{\rm eff}$ of $(1.02\pm 0.10)\%$. In the respective downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ sample, the OS and SSK taggers yield an
$\varepsilon_{\rm eff}$ of $(2.74\pm 0.11)\%$ and $(1.45\pm 0.15)\%$,
respectively, while the sample with both an OS and SSK tagging response gives
an $\varepsilon_{\rm eff}$ of $(0.48\pm 0.04)\%$. The combined
$\varepsilon_{\rm eff}$ of all three overlapping samples for the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mode is measured to be $(3.80\pm
0.18)\%$ and $(4.03\pm 0.16)$% in the long and downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ sample, respectively.

In the ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mode, the main contribution is
provided by the OS taggers, where the combined $\varepsilon_{\rm eff}$ is
measured to be $(2.60\pm 0.05)\%$ and $(2.63\pm 0.05)$% in the long and
downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ sample, respectively. Although
the SSK tagging algorithm is specifically designed for ${B}^{0}_{s}$ mesons, a
small, but non-vanishing effective tagging efficiency of $(0.064\pm 0.009)\%$
and $(0.098\pm 0.013)\%$ in the long and downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ sample, respectively, is also found for
${B}^{0}$ mesons if the tag decision is reversed. This effect originates from
same-side protons mis-identified as kaons, and kaons from the decay of
${K}^{*}(892)^{0}$ mesons produced in correlation with the ${B}^{0}$. Both
tagged particles have a charge opposite to those of kaons produced in
correlation with the ${B}^{0}_{s}$, and thus require the SSK tag decision to
be inverted. Additionally, mis-identified pions carrying the same charge as
the kaons correlated with the ${B}^{0}_{s}$ dilute the effect described above.
The SSK tagging response for ${B}^{0}$ candidates is studied on
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{*}(892)^{0}}$ candidates using both data and simulated events.

##  5 Likelihood fit

The ${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables are determined
from an unbinned maximum likelihood fit. The data is fitted with a probability
density function (PDF) defined as the sum of a ${B}^{0}$ signal component, a
${B}^{0}_{s}$ signal component and a combinatorial background. In total it
depends on seven observables. The PDF describes the reconstructed $B$ mass
$(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}}\in[5180,5520]\>{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}})$, the decay time
$(t\in[0.2,15]\>\text{ps})$, and tagging responses $q_{\text{OS}}$ and
$q_{\text{SSK}}$. Additionally, it also depends on the per-candidate decay
time uncertainty estimate $\delta_{t}$ and mistag estimates $\eta_{\text{OS}}$
and $\eta_{\text{SSK}}$. The long and downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ samples are modelled using separate PDFs
but fitted simultaneously. The parameters common to both PDFs are the two
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and three
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables, as well as
the observables describing the ${B}^{0}$ and ${B}^{0}_{s}$ systems that are
listed in Table 1.

Table 1: List of the observables describing the ${B}^{0}$ and ${B}^{0}_{s}$ systems that are included as Gaussian constraints to the likelihood fit. Parameter | Value |  | Parameter | Value |
---|---|---|---|---|---
$\Delta m_{d}$ |  $0.510\pm 0.003$ |  ${\rm\,ps^{-1}}$ |  [7] | $\Delta m_{s}$ |  $17.757\pm 0.021$ |  ${\rm\,ps^{-1}}$ | [7]
$\Delta\Gamma_{d}$ |  $0\phantom{.000\pm 0.000}$ |  ${\rm\,ps^{-1}}$ |  | $\Delta\Gamma_{s}$ |  $\phantom{0}0.081\pm 0.006$ |  ${\rm\,ps^{-1}}$ | [7]
$\tau_{B_{d}}$ |  $1.520\pm 0.004$ |  ${\rm\,ps}$ |  [7] | $\tau_{B_{s}}$ |  $\phantom{0}1.509\pm 0.004$ |  ${\rm\,ps}$ | [7]

###  5.1 Mass PDF

The mass shapes of the
${B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ modes in both data and simulation
exhibit non-Gaussian tails on both sides of their signal peaks due to final-
state radiation, the detector resolution and its dependence on the momenta of
the final-state particles. Each signal shape is parametrised by a Hypatia
function [31], whose tail parameters are taken from simulation. The
${B}^{0}_{s}$ component is constrained to have the same shape as the ${B}^{0}$
PDF, but shifted by the ${B}^{0}_{s}$–${B}^{0}$ mass difference, which is a
free variable in the fit. The mass distribution of the combinatorial
background is described by an exponential function.

###  5.2 Decay time PDF

The decay time distributions of the two signal components,
$\mathcal{T}(t,q_{\text{OS}},q_{\text{SSK}}|\eta_{\text{OS}},\eta_{\text{SSK}})$,
need to be corrected for experimental effects originating from the detector
response and the event selection. This is done by convolving them with a
resolution model, $\mathcal{R}(t|\delta_{t})$, and combining the result with
an acceptance function, $\mathcal{E}(t)$, to give the experimentally observed
decay-time distribution

$\left(\int\mathcal{T}(\hat{t},q_{\text{OS}},q_{\text{SSK}}|\eta_{\text{OS}},\eta_{\text{SSK}})\times\mathcal{R}(t-\hat{t}|\delta_{t})\>\text{d}\hat{t}\right)\times\mathcal{E}(t)\>.$
(8)

The resolution model has an individual width for each candidate, described by
the per-candidate decay-time uncertainty estimate $\delta_{t}$ provided by the
kinematic fit introduced in Sec. 3. A finite resolution reduces the amplitude
of the oscillating terms in the decay-time distribution by a factor
$\mathcal{D}\equiv\exp\left(-\delta_{t}^{2}\Delta m^{2}/2\right)$ [32, 33],
and thereby affects the precision of the time-dependent $C\\!P$ observables.
This effect is larger for the rapid ${B}^{0}_{s}$–${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}$ oscillations than for the
${B}^{0}$–${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ oscillations.
The $\delta_{t}$ estimates are calibrated using a separate sample of prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decays, which are produced
directly at the PV and combined with random ${K}^{0}_{\rm\scriptscriptstyle
S}$ candidates. This sample is obtained through the same event selection as
described in Sec. 3, except for the requirement on the decay time of the $B$
candidates. The decay time distribution of the prompt
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons is modelled by the sum
of three Gaussian functions sharing a common mean. For the long (downstream)
${K}^{0}_{\rm\scriptscriptstyle S}$ sample, this resolution model leads to an
average dilution factor of $\langle\mathcal{D}\rangle=0.73\pm 0.13$ $(0.72\pm
0.04)$.

The decay time distribution of the two signal components is affected by
acceptance effects due to the decay-time bias induced by the trigger
selection, the initial selection requirements and, most importantly, the NN
classifier outputs. The shapes of the ${{B}^{0}}$ and ${{B}^{0}_{s}}$
acceptances are assumed to be equal and modelled using cubic b-splines [34].
The acceptance function is obtained directly from the data. The
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ decay time distribution is
described by a single exponential, assuming ${\Delta\Gamma}_{d}=0$. The
lifetime of the ${B}^{0}$, $\tau_{{{B}^{0}}}=1.520\pm 0.004\>\text{ps}$ [7],
is constrained in the fit using a Gaussian function whose mean is fixed to the
known lifetime and whose width accounts for the experimental uncertainty. This
allows the acceptance parameters to be directly evaluated in the fit to the
data.

The background decay-time distributions are modelled using two exponential
functions, describing empirically a short-lived and a long-lived component.

Figure 3: Decay time distribution of ${B}$ candidates in the (left) long
${K}^{0}_{\rm\scriptscriptstyle S}$ and (right) downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ sample. The fit projection is shown as
solid black line. Shown components are
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ (dark blue, dashed),
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ (red, dotted) and combinatorial
background (turquoise, dash-dotted).

###  5.3 Likelihood fit

The results are obtained from a simultaneous fit of the long and downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ samples, using both the OS and SSK tagging
information. In addition to the five $C\\!P$ observables, the nuisance
parameters describing the mass (9 parameters), acceptance (12), background
decay time (6) and event yields (18) are floated in the fit. The observables
$\Delta m_{d}$, $\tau_{{{B}^{0}}}$, $\Delta m_{s}$, $\tau_{{{B}^{0}_{s}}}$ and
$\Delta\Gamma_{s}$, parametrising the ${B}^{0}$ and ${B}^{0}_{s}$ systems, and
the effective $B$ production asymmetries $A_{\text{prod}}({{B}^{0}})$ and
$A_{\text{prod}}({{B}^{0}_{s}})$ of the long and downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ samples are constrained using Gaussian
functions. The production asymmetries are defined in terms of the $B$
production cross-section $\sigma({B})$ as
$A_{\text{prod}}({B})\equiv(\sigma({\kern
1.79993pt\overline{\kern-1.79993ptB}{}})-\sigma({B}))/(\sigma({\kern
1.79993pt\overline{\kern-1.79993ptB}{}})+\sigma({B}))$. The statistical and
systematic uncertainties on the constrained parameters are added in quadrature
and treated together; the correlation
$\rho(\Gamma_{s},\Delta\Gamma_{s})=-0.271$ [7] between the decay width and
decay width difference of the ${B}^{0}_{s}$ meson is also included. The
effective $B$ production asymmetries, specific to the data sample used in this
analysis, are obtained by reweighting the results binned in $B$ transverse
momentum and pseudorapidity given in Ref. [35]. The obtained values are listed
in Table 2.

Table 2: Effective $B$ production asymmetries specific to the data sample used in this analysis. Sample | Mode | Value
---|---|---
Long ${K}^{0}_{\rm\scriptscriptstyle S}$ | ${B}^{0}$ | $-0.0117\pm 0.0057\>(\text{stat})\pm 0.0013\>(\text{syst})$
Downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ | ${B}^{0}$ | $-0.0095\pm 0.0051\>(\text{stat})\pm 0.0013\>(\text{syst})$
Long ${K}^{0}_{\rm\scriptscriptstyle S}$ | ${B}^{0}_{s}$ | $-0.041\phantom{0}\pm 0.032\phantom{0}\>(\text{stat})\pm 0.003\phantom{0}\>(\text{syst})$
Downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ | ${B}^{0}_{s}$ | $-0.022\phantom{0}\pm 0.024\phantom{0}\>(\text{stat})\pm 0.003\phantom{0}\>(\text{syst})$

The likelihood fit is cross-checked using two independent implementations, and
is validated with large sets of pseudoexperiments to thoroughly test several
aspects of the analysis. These also include the use of stand-alone event
generators that produce samples independently of the fit implementations. In
addition, the fit model is tested on simulated data, with signal only and with
both signal and background components present. The results from the fit to the
full data sample are compared to those from various subsamples, and to those
obtained from a weighted fit to the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ candidates only. All tests agree
with the expectations and no biases in the fit are found.

###  5.4 Fit results

The results of the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ asymmetries are

$\displaystyle
C_{\text{dir}}\left({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.028\pm
0.034\>(\text{stat})\>,$ $\displaystyle
S_{\text{mix}}\left({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$
$\displaystyle=\phantom{-}0.719\pm 0.034\>(\text{stat})\>,$

where the uncertainties are statistical only. They are compatible with the
BaBar [36], Belle [37] and latest LHCb [8] results. The results of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ asymmetries are

$\displaystyle\mathcal{A}_{\Delta\Gamma}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$
$\displaystyle=\phantom{-}0.49\pm\>^{0.77}_{0.65}\>\>(\text{stat})\>,$
$\displaystyle
C_{\text{dir}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.28\pm
0.41\>(\text{stat})\>,$ $\displaystyle
S_{\text{mix}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.08\pm
0.40\>(\text{stat})\>,$

where the uncertainties are statistical only, and the observed event yields
are summarised in Table 3. The fit projections for the mass and decay time
distributions are shown in Figs. 2 and 3, respectively. The statistical
correlations between the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables are
$\rho(\mathcal{A}_{\Delta\Gamma},C_{\text{dir}})=-0.07$,
$\rho(\mathcal{A}_{\Delta\Gamma},S_{\text{mix}})=-0.01$ and
$\rho(C_{\text{dir}},S_{\text{mix}})=-0.06$. In addition, there is a
$\mathcal{O}(10\%)$ correlation between $\mathcal{A}_{\Delta\Gamma}$ and the
average decay width $\Gamma_{s}$ and decay width difference
${\Delta\Gamma_{{s}}}$, and a $\mathcal{O}(10\%)$ correlation between
$S_{\text{mix}}$ and the ${{B}^{0}_{s}}$ production asymmetries. The
confidence intervals for the three
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ asymmetries are also
calculated with the Feldman–Cousins method [38, 39], which gives consistent
results with the point estimates given above.

Table 3: Fitted yields from the unbinned maximum likelihood fit. The uncertainties are statistical only. Yield |  Long ${K}^{0}_{\rm\scriptscriptstyle S}$ | Downstream ${K}^{0}_{\rm\scriptscriptstyle S}$
---|---|---
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ | $27\>801\pm 168$ | $51\>351\pm 231$
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ | $307\pm 20\phantom{0}$ | $601\pm 30\phantom{0}$
Combinatorial background | $658\pm 37\phantom{0}$ | $2\>852\pm 74\phantom{0}$

##  6 Systematic uncertainties

A number of systematic uncertainties affecting the determination of the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables and the ratio
of event yields $R$ are considered. The main sources of systematic uncertainty
are due to assumptions for modelling the different components of the
multivariate PDF. These uncertainties are estimated using large sets of
simulated pseudoexperiments, in which the shapes and parameters of the
individual PDF components are varied. In the generation of the
pseudoexperiments, the values of the parameters are fixed to the ones obtained
in the fit to the data. For each individual pseudoexperiment, the fitted
values of the $C\\!P$ observables and event yields are compared between the
nominal fit and an alternative fit in which some of the shapes or nuisance
parameters are varied. The resulting differences between the fit values form a
Gaussian-like distribution. The mean and width of this distribution are added
in quadrature and assigned as a systematic uncertainty.

Following this strategy, the systematic uncertainty due to the chosen mass
model is evaluated by varying the Hypatia tail parameters within their
uncertainties, replacing the signal model with a double Crystal Ball function
[40], and replacing the background model with a second-order Chebychev
polynomial. The latter variation has the largest impact on the $C\\!P$
observables and yield ratio, and is used to assign a systematic uncertainty.

The systematic uncertainty associated with the decay time resolution is
evaluated by varying the dilution of the resolution model, through changes of
the resolution parameters, and by comparing the nominal model with one that
includes a scale offset in the calibration functions for the per-candidate
decay time uncertainty estimates. The largest impact on the $C\\!P$
observables and yield ratio originates from the limited knowledge on the decay
time resolution of the long ${K}^{0}_{\rm\scriptscriptstyle S}$ sample. This
forms the dominant systematic uncertainty to the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ $C\\!P$ observables.

Systematic effects due to the modelling of the decay time acceptance mainly
affect $\mathcal{A}_{\Delta\Gamma}$, and are evaluated by varying the
empirical model for $\mathcal{E}(t)$.

The systematic uncertainty associated with the tagging calibration is obtained
by comparing the nominal calibration with the largest and smallest effective
tagging efficiency that can be obtained through changes of the calibration
parameters within their respective uncertainties.

The mass resolution is assumed to be identical for the ${B}^{0}$ and
${B}^{0}_{s}$ signal modes, but it could depend on the mass of the
reconstructed $B$ candidate. This effect is studied by multiplying the width
of the ${B}^{0}_{s}$ mass PDF by different scale factors, obtained by
comparing ${B}^{0}$ and ${B}^{0}_{s}$ signal shapes in simulation. These
variations mainly affect the ratio of event yields.

Finally, a correlation between the reconstructed $B$ mass and decay time
resolution is observed in simulated data. The impact of neglecting this
correlation in the fit to data is also evaluated with the simulated
experiments.

The total systematic uncertainty and its sources are summarised in Table 4.

Table 4: Summary of systematic uncertainties. |  |  |  | Long | Downstream
---|---|---|---|---|---
Source | $\mathcal{A}_{\Delta\Gamma}$ | $C_{\text{dir}}$ | $S_{\text{mix}}$ | $R\times 10^{5}$ | $R\times 10^{5}$
Mass modelling | 0.045 | 0.009 | 0.009 | 15.5 | 17.2
Decay-time resolution | 0.038 | 0.066 | 0.070 |  10.6 |  10.3
Decay-time acceptance | 0.022 | 0.004 | 0.004 |  10.6 |  10.5
Tagging calibration | 0.002 | 0.021 | 0.023 |  10.1 |  10.2
Mass resolution | 0.010 | 0.005 | 0.006 | 12.6 |  18.0
Mass–time correlation | 0.003 | 0.037 | 0.036 |  10.2 |  10.1
Total | 0.064 | 0.079 | 0.083 | 20.0 | 19.0

##  7 Branching ratio measurement

The measured ratio of branching fractions is calculated from the event yields
using Eq. (7). The selection efficiencies and their ratio $f_{\text{sel}}$ are
evaluated using simulated data. As the simulated data are generated with
different values for the lifetime $\tau_{{{B}^{0}_{s}}}$, decay width
difference ${\Delta\Gamma_{{s}}}$ and acceptance parameters compared to those
measured in the collision data, correction factors are applied. This leads to
a ratio of total selection efficiencies of $f_{\text{sel}}=0.972\pm 0.029$ for
the long ${K}^{0}_{\rm\scriptscriptstyle S}$ sample and
$f_{\text{sel}}=0.987\pm 0.040$ for the downstream
${K}^{0}_{\rm\scriptscriptstyle S}$ samples.

Combining the results in Table 3 with the systematic uncertainties in Table 4
yields

$\displaystyle R\>\text{(long)}$ $\displaystyle=0.01104\pm
0.00072\>(\text{stat})\pm 0.00020\>(\text{syst})\>,$ $\displaystyle
R\>\text{(downstream)}$ $\displaystyle=0.01170\pm 0.00059\>(\text{stat})\pm
0.00019\>(\text{syst})$

for the long and downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ samples,
respectively. A weighted average of the combinations $R\times f_{\text{sel}}$
for the long and downstream ${K}^{0}_{\rm\scriptscriptstyle S}$ samples is
performed, assuming that they are uncorrelated measurements. The measured
ratio of branching fractions is then given by

$\frac{{\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}{{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}=0.0431\pm
0.0017\>(\text{stat})\pm 0.0012\>(\text{syst})\pm 0.0025\>(f_{s}/f_{d})\>.$

where the third uncertainty is due to the uncertainty in $f_{s}/f_{d}$.

Combining the ratio of branching fractions with the known
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}}$ branching fraction ${\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}})=(8.97\pm 0.35)\times 10^{-4}$ [26], which accounts for the
difference in production rates for the ${B}^{+}$${B}^{-}$ and ${B}^{0}$${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ pairs at the $\mathchar
28935\relax{(4S)}$ resonance, i.e.
$\Gamma({{B}^{+}}{}{{B}^{-}})/\Gamma({{B}^{0}}{}{{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}})=1.058\pm 0.024$ [7], the
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ branching fraction is

$\displaystyle{\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})=$ $\displaystyle\left[1.93\pm
0.08\>(\text{stat})\pm 0.05\>(\text{syst})\pm 0.11\>(f_{s}/f_{d})\pm
0.07\>({\cal B}({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}})\right]\times 10^{-5}\>,$

where the last uncertainty comes from the
${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{}{{K}^{0}}$ branching fraction.

##  8 Conclusion

This paper presents the first measurement of the time-dependent $C\\!P$
violation observables in the decay
${{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and an updated measurement of its
time-integrated branching fraction. Both measurements are performed using a
data set corresponding to an integrated luminosity of 3.0 $\mbox{\,fb}^{-1}$
of $pp$ collisions recorded by the LHCb detector at centre-of-mass energies of
7 and 8 $\mathrm{\,Te\kern-1.00006ptV}$.

The results on the $C\\!P$ observables are

$\displaystyle\mathcal{A}_{\Delta\Gamma}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$
$\displaystyle=\phantom{-}0.49\pm\>^{0.77}_{0.65}\>\>(\text{stat})\pm
0.06\>(\text{syst})\>,$ $\displaystyle
C_{\text{dir}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.28\pm
0.41\>(\text{stat})\pm 0.08\>(\text{syst})\>,$ $\displaystyle
S_{\text{mix}}\left({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}\right)$ $\displaystyle=-0.08\pm
0.40\>(\text{stat})\pm 0.08\>(\text{syst})\>.$

The large statistical uncertainties on these results do not allow for a
conclusive comparison with the predictions in Eq. (1) nor do they provide
constraints on the shift parameter $\Delta{\phi_{{d}}}$ affecting $C\\!P$
measurements in ${{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$.

The ratio of time-integrated branching fractions is measured to be

$\frac{{\cal
B}({{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}{{\cal
B}({{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}})}=0.0431\pm
0.0017\>(\text{stat})\pm 0.0012\>(\text{syst})\pm 0.0025\>(f_{s}/f_{d})\>.$

This result is the single most precise measurement of this quantity, and
supersedes the previous LHCb measurement [11].

## Acknowledgements

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

## References

  * [1] S. Faller, M. Jung, R. Fleischer, and T. Mannel, _The golden modes $B^{0}\rightarrow J/\psi K_{S,L}$ in the era of precision flavor physics_, Phys. Rev. D79 (2009) 014030, arXiv:0809.0842
  * [2] K. De Bruyn, R. Fleischer, and P. Koppenburg, _Extracting $\gamma$ and penguin topologies through $C\\!P$ violation in ${B}^{0}_{s}$ $\rightarrow$ ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$${K}^{0}_{\rm\scriptscriptstyle S}$_, Eur. Phys. J. C70 (2010) 1025, arXiv:1010.0089
  * [3] K. De Bruyn and R. Fleischer, _A roadmap to control penguin effects in ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and ${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{}\phi$_, JHEP 1503 (2015) 145, arXiv:1412.6834
  * [4] I. I. Y. Bigi and A. I. Sanda, _Notes on the observability of $C\\!P$ violation in B decays_, Nucl. Phys. B193 (1981) 85
  * [5] M. Kobayashi and T. Maskawa, _CP violation in the renormalizable theory of weak interaction_ , Prog. Theor. Phys. 49 (1973) 652
  * [6] N. Cabibbo, _Unitary symmetry and leptonic decays_ , Phys. Rev. Lett. 10 (1963) 531
  * [7] Heavy Flavour Averaging Group (HFAG), Y. Amhis et al., _Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014_, arXiv:1412.7515, updated results and plots available at http://www.slac.stanford.edu/xorg/hfag/
  * [8] LHCb collaboration, R. Aaij et al., _Measurement of $CP$ violation in ${B}^{0}$ $\rightarrow$ ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$${K}^{0}_{\rm\scriptscriptstyle S}$ decays_, arXiv:1503.07089, to appear in PRL
  * [9] R. Fleischer, _Extracting $\gamma$ from $B_{(s/d)}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ and $B_{(d/s)}\rightarrow D^{+}_{(d/s)}D^{-}_{(d/s)}$_, Eur. Phys. J. C10 (1999) 299, arXiv:hep-ph/9903455
  * [10] CDF collaboration, T. Aaltonen et al., _Observation of ${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{}K^{\ast}(892)^{0}$ and ${B}^{0}_{s}$ $\rightarrow$ ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$${K}^{0}_{\rm\scriptscriptstyle S}$ decays_, Phys. Rev. D83 (2011) 052012, arXiv:1102.1961
  * [11] LHCb collaboration, R. Aaij et al., _Measurement of the effective ${{B}^{0}_{s}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{}{{K}^{0}_{\rm\scriptscriptstyle S}}$ lifetime_, Nucl. Phys. B873 (2013) 275, arXiv:1304.4500
  * [12] K. De Bruyn et al., _Branching ratio measurements of $B_{s}$ decays_, Phys. Rev. D86 (2012) 014027, arXiv:1204.1735
  * [13] LHCb collaboration, R. Aaij et al., _Measurement of the fragmentation fraction ratio $f_{s}/f_{d}$ and its dependence on $B$ meson kinematics_, JHEP 04 (2013) 001, arXiv:1301.5286
  * [14] LHCb collaboration, _Updated average $f_{s}/f_{d}$ $b$-hadron production fraction ratio for $7~{}T\kern-0.50003pteV$ $pp$ collisions_, LHCb-CONF-2013-011
  * [15] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [16] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015), no. 07 1530022, arXiv:1412.6352
  * [17] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [18] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [19] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [20] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [21] 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
  * [22] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [23] Geant4 collaboration, S. Agostinelli et al., _Geant4: a simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [24] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [25] M. Feindt, _A neural Bayesian estimator for conditional probability densities_ , arXiv:physics/0402093
  * [26] Particle Data Group, K. A. Olive et al., _Review of particle physics_ , Chin. Phys. C38 (2014) 090001
  * [27] W. D. Hulsbergen, _Decay chain fitting with a Kalman filter_ , Nucl. Instrum. Meth. A552 (2005) 566, arXiv:physics/0503191
  * [28] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083
  * [29] LHCb collaboration, R. Aaij et al., _Opposite-side flavour tagging of $B$ mesons at the LHCb experiment_, Eur. Phys. J. C72 (2012) 2022, arXiv:1202.4979
  * [30] LHCb collaboration, _Optimization and calibration of the same-side kaon tagging algorithm using hadronic ${{B}^{0}_{s}}$ decays in 2011 data_, LHCb-CONF-2012-033
  * [31] D. M. Santos and F. Dupertuis, _Mass distributions marginalized over per-event errors_ , Nucl. Instrum. Meth. A764 (2014) 150, arXiv:1312.5000
  * [32] H. G. Moser and A. Roussarie, _Mathematical methods for ${B}^{0}$ ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ oscillation analyses_, Nucl. Instrum. Meth. A384 (1997) 491
  * [33] LHCb collaboration, R. Aaij et al., _Measurement of $CP$ violation and the $B^{0}_{s}$ meson decay width difference with $B_{s}^{0}\rightarrow J/\psi K^{+}K^{-}$ and $B_{s}^{0}\rightarrow J/\psi\pi^{+}\pi^{-}$ decays_, Phys. Rev. D87 (2013) 112010, arXiv:1304.2600
  * [34] T. M. Karbach, G. Raven, and M. Schiller, _Decay time integrals in neutral meson mixing and their efficient evaluation_ , arXiv:1407.0748
  * [35] LHCb collaboration, R. Aaij et al., _Measurement of the $\bar{B}^{0}$–$B^{0}$ and $\bar{B}^{0}_{s}$–$B^{0}_{s}$ production asymmetries in $pp$ collisions at $\sqrt{s}=7$ TeV_, Phys. Lett. B739 (2014) 218, arXiv:1408.0275
  * [36] BaBar collaboration, B. Aubert et al., _Measurement of time-dependent $C\\!P$ asymmetry in $B^{0}\rightarrow c\bar{c}K^{(*)0}$ decays_, Phys. Rev. D79 (2009) 072009, arXiv:0902.1708
  * [37] Belle collaboration, I. Adachi et al., _Precise measurement of the $C\\!P$ violation parameter $\sin 2\phi_{1}$ in $B^{0}\rightarrow(c\bar{c})K^{0}$ decays_, Phys. Rev. Lett. 108 (2012) 171802, arXiv:1201.4643
  * [38] 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
  * [39] T. M. Karbach, _Feldman-Cousins confidence levels – toy MC method_ , arXiv:1109.0714
  * [40] 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

LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle53, A.A. Alves Jr57, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, M. Andreotti16,f, J.E. Andrews58, R.B.
Appleby54, O. Aquines Gutierrez10, F. Archilli38, A. Artamonov35, M. Artuso59,
E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S. Bachmann11, J.J. Back48, A.
Badalov36, C. Baesso60, W. Baldini16,38, R.J. Barlow54, C. Barschel38, S.
Barsuk7, W. Barter38, V. Batozskaya28, V. Battista39, A. Bay39, L. Beaucourt4,
J. Beddow51, F. Bedeschi23, I. Bediaga1, L.J. Bel41, I. Belyaev31, E. Ben-
Haim8, G. Bencivenni18, S. Benson38, J. Benton46, A. Berezhnoy32, R. Bernet40,
A. Bertolin22, M.-O. Bettler38, M. van Beuzekom41, A. Bien11, S. Bifani45, T.
Bird54, A. Bizzeti17,i, T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59, V.
Bocci25, A. Bondar34, N. Bondar30,38, W. Bonivento15, S. Borghi54, A.
Borgia59, M. Borsato7, T.J.V. Bowcock52, E. Bowen40, C. Bozzi16, S. Braun11,
D. Brett54, M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, A.
Bursche40, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M.
Calvo Gomez36,p, P. Campana18, D. Campora Perez38, L. Capriotti54, A.
Carbone14,d, G. Carboni24,l, R. Cardinale19,j, A. Cardini15, P. Carniti20, L.
Carson50, K. Carvalho Akiba2,38, R. Casanova Mohr36, G. Casse52, L.
Cassina20,k, L. Castillo Garcia38, M. Cattaneo38, Ch. Cauet9, G. Cavallero19,
R. Cenci23,t, M. Charles8, Ph. Charpentier38, M. Chefdeville4, S. Chen54,
S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26, X. Cid Vidal38, G.
Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47, J. Closier38, V.
Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15,e, L. Cojocariu29, G.
Collazuol22, P. Collins38, A. Comerma-Montells11, A. Contu15,38, A. Cook46, M.
Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f, I. Counts56, B.
Couturier38, G.A. Cowan50, D.C. Craik48, A.C. Crocombe48, M. Cruz Torres60, S.
Cunliffe53, R. Currie53, C. D’Ambrosio38, J. Dalseno46, P.N.Y. David41, A.
Davis57, K. De Bruyn41, S. De Capua54, M. De Cian11, J.M. De Miranda1, L. De
Paula2, W. De Silva57, P. De Simone18, C.-T. Dean51, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach55, O. Deschamps5, F.
Dettori38, B. Dey40, A. Di Canto38, F. Di Ruscio24, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A.
Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P. Durante38, R.
Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V.
Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L.
Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, H.M. Evans47, T.
Evans55, A. Falabella14, C. Färber11, C. Farinelli41, N. Farley45, S. Farry52,
R. Fay52, D. Ferguson50, V. Fernandez Albor37, F. Ferreira Rodrigues1, M.
Ferro-Luzzi38, S. Filippov33, M. Fiore16,38,f, M. Fiorini16,f, M. Firlej27, C.
Fitzpatrick39, T. Fiutowski27, P. Fol53, M. Fontana10, F. Fontanelli19,j, R.
Forty38, O. Francisco2, M. Frank38, C. Frei38, M. Frosini17, J. Fu21,38, E.
Furfaro24,l, A. Gallas Torreira37, D. Galli14,d, S. Gallorini22,38, S.
Gambetta19,j, M. Gandelman2, P. Gandini55, Y. Gao3, J. García Pardiñas37, J.
Garofoli59, J. Garra Tico47, L. Garrido36, D. Gascon36, C. Gaspar38, U.
Gastaldi16, R. Gauld55, L. Gavardi9, G. Gazzoni5, A. Geraci21,v, E.
Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A. Gianelle22, S.
Gianì39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C. Göbel60, D.
Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, C. Gotti20,k, M. Grabalosa
Gándara5, R. Graciani Diaz36, L.A. Granado Cardoso38, E. Graugés36, E.
Graverini40, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P.
Griffith45, L. Grillo11, O. Grünberg63, E. Gushchin33, Yu. Guz35,38, T. Gys38,
C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S. Hall53, B.
Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N. Harnew55, S.T.
Harnew46, J. Harrison54, J. He38, T. Head39, V. Heijne41, K. Hennessy52, P.
Henrard5, L. Henry8, J.A. Hernando Morata37, E. van Herwijnen38, M. Heß63, A.
Hicheur2, D. Hill55, M. Hoballah5, C. Hombach54, W. Hulsbergen41, T. Humair53,
N. Hussain55, D. Hutchcroft52, D. Hynds51, M. Idzik27, P. Ilten56, R.
Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, A. Jawahery58, F. Jing3, M.
John55, D. Johnson38, C.R. Jones47, C. Joram38, B. Jost38, N. Jurik59, S.
Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38, S. Karodia51, M.
Kelsey59, I.R. Kenyon45, M. Kenzie38, T. Ketel42, B. Khanji20,38,k, C.
Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O. Kochebina7, M. Kolpin11,
I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M. Korolev32, L. Kravchuk33,
K. Kreplin11, M. Kreps48, G. Krocker11, P. Krokovny34, F. Kruse9, W.
Kucewicz26,o, M. Kucharczyk26, V. Kudryavtsev34, K. Kurek28, T.
Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38, G. Lafferty54, A. Lai15, D.
Lambert50, R.W. Lambert42, G. Lanfranchi18, C. Langenbruch48, B. Langhans38,
T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P. Lees4, R.
Lefèvre5, A. Leflat32, J. Lefrançois7, O. Leroy6, T. Lesiak26, B.
Leverington11, Y. Li7, T. Likhomanenko64, M. Liles52, R. Lindner38, C. Linn38,
F. Lionetto40, B. Liu15, S. Lohn38, I. Longstaff51, J.H. Lopes2, P. Lowdon40,
D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A.
Malinin64, G. Manca15,e, G. Mancinelli6, P. Manning59, A. Mapelli38, J.
Maratas5, J.F. Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,38,t,
R. Märki39, J. Marks11, G. Martellotti25, M. Martinelli39, D. Martinez
Santos42, F. Martinez Vidal66, D. Martins Tostes2, A. Massafferri1, R.
Matev38, Z. Mathe38, C. Matteuzzi20, A. Mauri40, B. Maurin39, A. Mazurov45, M.
McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. McSkelly52, B.
Meadows57, F. Meier9, M. Meissner11, M. Merk41, D.A. Milanes62, M.-N. Minard4,
J. Molina Rodriguez60, S. Monteil5, M. Morandin22, P. Morawski27, A. Mordà6,
M.J. Morello23,t, J. Moron27, A.-B. Morris50, R. Mountain59, F. Muheim50, K.
Müller40, M. Mussini14, B. Muster39, P. Naik46, T. Nakada39, R. Nandakumar49,
I. Nasteva2, M. Needham50, N. Neri21, S. Neubert11, N. Neufeld38, M. Neuner11,
A.D. Nguyen39, T.D. Nguyen39, C. Nguyen-Mau39,q, V. Niess5, R. Niet9, N.
Nikitin32, T. Nikodem11, A. Novoselov35, D.P. O’Hanlon48, A. Oblakowska-
Mucha27, V. Obraztsov35, S. Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, C.J.G.
Onderwater67, B. Osorio Rodrigues1, J.M. Otalora Goicochea2, A. Otto38, P.
Owen53, A. Oyanguren66, A. Palano13,c, F. Palombo21,u, M. Palutan18, J.
Panman38, A. Papanestis49, M. Pappagallo51, L.L. Pappalardo16,f, C. Parkes54,
G. Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, A. Pearce54,49,
A. Pellegrino41, G. Penso25,m, M. Pepe Altarelli38, S. Perazzini14,d, P.
Perret5, L. Pescatore45, K. Petridis46, A. Petrolini19,j, E. Picatoste
Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50,
M. Plo Casasus37, T. Poikela38, F. Polci8, A. Poluektov48,34, I. Polyakov31,
E. Polycarpo2, A. Popov35, D. Popov10, B. Popovici29, C. Potterat2, E.
Price46, J.D. Price52, J. Prisciandaro39, A. Pritchard52, C. Prouve46, V.
Pugatch44, A. Puig Navarro39, G. Punzi23,s, W. Qian4, R. Quagliani7,46, B.
Rachwal26, J.H. Rademacker46, B. Rakotomiaramanana39, M. Rama23, M.S. Rangel2,
I. Raniuk43, N. Rauschmayr38, G. Raven42, F. Redi53, S. Reichert54, M.M.
Reid48, A.C. dos Reis1, S. Ricciardi49, S. Richards46, M. Rihl38, K.
Rinnert52, V. Rives Molina36, P. Robbe7,38, A.B. Rodrigues1, E. Rodrigues54,
J.A. Rodriguez Lopez62, P. Rodriguez Perez54, S. Roiser38, V. Romanovsky35, A.
Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, H. Ruiz36, P. Ruiz
Valls66, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B. Saitta15,e, V.
Salustino Guimaraes2, C. Sanchez Mayordomo66, B. Sanmartin Sedes37, R.
Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A. Sarti18,m, C.
Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32, M. Schiller38, H.
Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O. Schneider39, A.
Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A. Sciubba25,m, A.
Semennikov31, I. Sepp53, N. Serra40, J. Serrano6, L. Sestini22, P. Seyfert11,
M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T. Shears52, L. Shekhtman34,
V. Shevchenko64, A. Shires9, R. Silva Coutinho48, G. Simi22, M. Sirendi47, N.
Skidmore46, I. Skillicorn51, T. Skwarnicki59, N.A. Smith52, E. Smith55,49, E.
Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D. Sokoloff57,38, F.J.P.
Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B. Spaan9, P.
Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl38, O.
Steinkamp40, O. Stenyakin35, F. Sterpka59, S. Stevenson55, S. Stoica29, S.
Stone59, B. Storaci40, S. Stracka23,t, M. Straticiuc29, U. Straumann40, R.
Stroili22, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4,
M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J.
van Tilburg41, V. Tisserand4, M. Tobin39, J. Todd57, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, K. Trabelsi39, M.T. Tran39, M. Tresch40, A. Trisovic38, A.
Tsaregorodtsev6, P. Tsopelas41, N. Tuning41,38, M. Ubeda Garcia38, A.
Ukleja28, A. Ustyuzhanin65, U. Uwer11, C. Vacca15,e, V. Vagnoni14, G.
Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez Regueiro37, C. Vázquez
Sierra37, S. Vecchi16, J.J. Velthuis46, M. Veltri17,h, G. Veneziano39, M.
Vesterinen11, J.V. Viana Barbosa38, B. Viaud7, D. Vieira2, M. Vieites Diaz37,
X. Vilasis-Cardona36,p, A. Vollhardt40, D. Volyanskyy10, D. Voong46, A.
Vorobyev30, V. Vorobyev34, C. Voß63, J.A. de Vries41, R. Waldi63, C.
Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59, D.R. Ward47,
N.K. Watson45, D. Websdale53, A. Weiden40, M. Whitehead48, D. Wiedner11, G.
Wilkinson55,38, M. Wilkinson59, M. Williams38, M.P. Williams45, M. Williams56,
H.W. Wilschut67, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M.
Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38, Y. Xie61, Z.
Xu39, Z. Yang3, X. Yuan34, O. Yushchenko35, M. Zangoli14, M. Zavertyaev10,b,
L. Zhang3, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3.

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

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