Search for the lepton-flavour-violating decays $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ and $B^{0}\to\tau^{\pm}\mu^{\mp}$

TL;DR

This study searches for lepton-flavour-violating decays of B mesons into tau and muon, setting the first limits on B_s decay and the best limits on B decay, with no significant signals observed.

Contribution

It provides the first experimental limits on the branching fractions of $B^{0}_{s} o au^{ mootnotesize ext{±}} ext{ mootnotesize ext{μ}} ext{ mootnotesize ext{∓}}$ decays and the most stringent limits on $B^{0} o au^{ mootnotesize ext{±}} ext{ mootnotesize ext{μ}} ext{ mootnotesize ext{∓}}$ decays, using LHCb data.

Findings

No significant signal observed for the decays.

Upper limit on $B^{0}_{s} o au^{ mootnotesize ext{±}} ext{ mootnotesize ext{μ}} ext{ mootnotesize ext{∓}}$ branching fraction: < 4.2×10⁻⁵.

Upper limit on $B^{0} o au^{ mootnotesize ext{±}} ext{ mootnotesize ext{μ}} ext{ mootnotesize ext{∓}}$ branching fraction: < 1.4×10⁻⁵.

Abstract

A search for $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ and $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays is performed using data corresponding to an integrated luminosity of 3 fb$^{-1}$ of proton-proton collisions, recorded with the LHCb detector in 2011 and 2012. For this search, the $\tau$ lepton is reconstructed in the $\tau^{-}\to\pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ channel. No significant signal is observed. Assuming no contribution from $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays, an upper limit is set on the $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ branching fraction of $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right) < 4.2\times 10^{-5}$ at $95\%$ confidence level. If instead no contribution from $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ decays is assumed, a limit of $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right) < 1.4\times 10^{-5}$ is obtained at $95\%$ confidence level. These are the first limit on $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right)$ and the world's best limit on $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right)$.

Figures

Tables

Table 1. Table 1: Expected and observed 90 % percent 90 90\% and 95 % percent 95 95\% CL limits on the B ( s ) 0 → τ ± ​ μ ∓ → subscript superscript 𝐵 0 𝑠 superscript 𝜏 plus-or-minus superscript 𝜇 minus-or-plus {{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}  branching fraction.

Mode	Limit	$90\%$ CL	$95\%$ CL
$B_s^0\to {\tau }^{\pm }{\mu }^{\mp }$	Observed	$3.4\times {10}^{-5}$	$4.2\times {10}^{-5}$
	Expected	$3.9\times {10}^{-5}$	$4.7\times {10}^{-5}$
$B^0\to {\tau }^{\pm }{\mu }^{\mp }$	Observed	$1.2\times {10}^{-5}$	$1.4\times {10}^{-5}$
	Expected	$1.6\times {10}^{-5}$	$1.9\times {10}^{-5}$

Equations

$${\mathcal{B}}\left(\mbox{${{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$}\right)=\alpha_{(s)}^{\text{norm}}\cdot N^{\text{sig}}_{(s)},$$

$$\alpha_{(s)}^{\text{norm}}=\frac{f_{{B}^{0}}}{f_{{B}^{0}_{(s)}}}\cdot\frac{{\mathcal{B}}\left(\mbox{${{B}^{0}}\!\rightarrow{{D}^{-}}(\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}){{\pi}^{+}}$}\right)}{{\mathcal{B}}\left(\mbox{${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$}\right)}\cdot\frac{\epsilon_{B\rightarrow D\pi}}{\epsilon_{{{B}^{0}_{({s})}}\rightarrow{\tau}\mu}}\cdot\frac{1}{N^{\text{norm}}},$$

$$\begin{array}{rl}{\alpha }_s^{\text{norm}}& =(4.32\pm 0.19\pm 0.45\pm 0.36)\times 10^{-7}\text{ and}\\ {\alpha }^{\text{norm}}& =(1.25\pm 0.06\pm 0.13\pm 0.08)\times 10^{-7},\end{array}$$

$$\begin{split}N^{\text{sig}}_{\mbox{${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$}}&=-16\pm 38\text{ and}\\ N^{\text{sig}}_{\mbox{${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$}}&=-65\pm 58,\end{split}$$

Full text

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

​​​

CERN-EP-2019-076

LHCb-PAPER-2019-016

November 29, 2019

Search for the lepton-flavour-violating decays ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$

LHCb collaboration

Results are reported from a search for the rare decays ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$, where the tau lepton is reconstructed in the channel ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$. These processes are effectively forbidden in the standard model, but they can potentially occur at detectable rates in models of new physics that can induce lepton-flavor-violating decays. The search is based on a data sample corresponding to 3$\mbox{\,fb}^{-1}$ of proton-proton collisions recorded by the LHCb experiment in 2011 and 2012. The event yields observed in the signal regions for both processes are consistent with the expected standard model backgrounds. Because of the limited mass resolution arising from the undetected tau neutrino, the ${B}^{0}_{s}$ and ${B}^{0}$ signal regions are highly overlapping. Assuming no contribution from ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$, the upper limit {\mathcal{B}}\left(\mbox{{{B}^{0}{s}}!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}}\right)<4.2\times 10^{-5} is obtained at 95% confidence level. If no contribution from ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ is assumed, a limit of {\mathcal{B}}\left(\mbox{{{B}^{0}}!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}}\right)<1.4\times 10^{-5} is obtained at 95% confidence level. These results represent the first limit on {\mathcal{B}}\left(\mbox{{{B}^{0}{s}}!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}}\right) and the most stringent limit on {\mathcal{B}}\left(\mbox{{{B}^{0}}!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}}\right).

Published in Phys. Rev. Lett. 123 (2019) 211801

© 2024 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

Lepton-flavor-violating decays of mesons containing $b$ quarks, such as ${{B}^{0}}(b\overline{d})\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}_{s}}(b\overline{s})\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$, are extremely suppressed in the Standard Model (SM), with expected branching fractions of order 10*-54* [1]. (The inclusion of charge-conjugate processes is implied throughout this Letter.) These processes involve not only quantum loops, but also neutrino oscillations. Signals at the level expected in the SM lie far below current and foreseen experimental sensitivities. However, many theoretical models proposed to explain possible experimental tensions observed in other $B$-meson decays (discussed below) naturally allow for branching fractions that are within current sensitivity. Among them, models containing a heavy neutral gauge boson (${Z}^{{}^{\prime}}$) could lead to a ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ branching fraction of up to $10^{-8}$  [2, 3] when only left-handed or right-handed couplings to quarks are considered, or of the order of $10^{-6}$ [3] if both are allowed. In models with either scalar or vector leptoquarks, the largest predictions for the ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ branching fraction range from $10^{-9}$ to $10^{-5}$, depending on the assumed leptoquark mass [4, 5, 6]. The three-site Pati-Salam gauge model favours values for this branching fraction in the range 10*-4*–10*-6* [7, 8].

The SM predicts that the electroweak couplings for the three lepton families are universal, a result referred to as Lepton Flavor Universality (LFU). Experimental tests of LFU performed using ${b}\rightarrow s\ell^{+}\ell^{-}$ and $b\rightarrow c\ell^{-}\overline{\nu}$ processes show tensions with respect to the SM predictions for the observables $R_{{K}^{(*)}}$ [9, 10] and ${\cal R}(D^{(*)})$ [11]. For the latter, the observed discrepancy with respect to the SM prediction is greater than 3 standard deviations. Because theoretical models that can account for the possible LFU effects observed in data often predict Lepton Flavor Violation (LFV) as well [12], searches for LFV processes provide a powerful signature for probing these models.

An upper limit {\mathcal{B}}\left(\mbox{{{B}^{0}}!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}}\right)<2.2\times 10^{-5} at $90\%$ confidence level (CL) was obtained by the BaBar collaboration [13]. There are currently no experimental results for the ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ mode.

This Letter reports results from the first search for the decay ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$, along with the most stringent limit on the process ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$. The analysis is performed on data corresponding to an integrated luminosity of $3\mbox{\,fb}^{-1}$ of proton-proton ($pp$) collisions, recorded with the LHCb detector during the years 2011 and 2012 at centre-of-mass energies of $7$ and $8\mathrm{\,Te\kern-1.00006ptV}$, respectively. The $\tau$ leptons are reconstructed through the decay ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$, which mainly proceeds via the production of two intermediate resonances, $a_{1}(1260)^{-}\rightarrow\pi^{+}\pi^{-}\pi^{-}$ and $\rho(770)^{0}\rightarrow\pi^{+}\pi^{-}$ [14], which help in the signal selection. In this mode, the $\tau$ decay vertex can be precisely reconstructed, facilitating a good reconstruction of the $B$-meson invariant mass despite the undetected neutrino. To avoid experimenter bias, the $B$-meson invariant-mass signal region was not examined until the selection and fit procedures were finalised. The signal yield is determined by performing an unbinned maximum-likelihood fit to the reconstructed $B$-meson invariant-mass distribution and is converted into a branching fraction using the decay ${{B}^{0}}\!\rightarrow{{D}^{-}}(\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}){{\pi}^{+}}$ as a normalisation channel.

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 $4{\mathrm{\,Tm}}$, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of the momentum, $p$, of charged particles with a relative uncertainty varying 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 (PV), the impact parameter (IP), is measured with a resolution of $(15+29/p_{\mathrm{T}}){\,\upmu\mathrm{m}}$, 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 and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.

The on-line event selection is performed by a trigger [17] consisting of a hardware stage based on information from the calorimeter and muon systems, followed by a software stage, which performs a full event reconstruction. At the hardware trigger stage, signal candidates are required to have a muon with high $p_{\mathrm{T}}$, while, for the normalisation sample, events are required to have a hadron with high transverse energy in the calorimeters. The software trigger requires a two-, three-, or four-track secondary vertex with a significant displacement from any primary $pp$ interaction vertex. A multivariate algorithm [18] is used to identify secondary vertices consistent with the decay of a $b$ hadron. At least one charged particle must have a transverse momentum $p_{\mathrm{T}}>1.0\>(1.6){\mathrm{\,Ge\kern-1.00006ptV\!/}c}$ for muons (hadrons), and must be inconsistent with originating from a PV.

Simulation is used to optimise the selection, determine the signal model for the fit and obtain the selection efficiencies. In the simulation, $pp$ collisions are generated using Pythia [19, *Sjostrand:2007gs] with a specific LHCb configuration [21]. The $\tau$ decay is simulated using the Tauola decay library tuned with BaBar data [22], while the decays of all other unstable particles are described by EvtGen [23]. Final-state radiation is accounted for using Photos [24]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [25, *Agostinelli:2002hh], as described in Ref. [27].

Both signal and normalisation candidates are formed using tracks that are inconsistent with originating from any PV. Candidate ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$ and ${{D}^{-}}\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ decays are reconstructed from three tracks forming a good-quality vertex and with particle identification information corresponding to their assumed particle hypotheses. Candidate ${{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ decays are formed by combining a reconstructed $\tau$ lepton and an oppositely charged track identified as a muon. A control sample of same-sign candidates, which are formed by a $\tau$ lepton and a muon with identical charges, is also selected to serve, during the selection process, as a proxy for the large component of the background in which the muon and the tau candidate charges are uncorrelated. For the normalisation mode, ${{B}^{0}}\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates are made out of a reconstructed $D$ meson and an oppositely charged track identified as a pion. The decay vertex of the signal or normalisation $B$ candidate is determined through a fit to all reconstructed particles in the decay chain [28], which is required to be of good quality. The $B$-meson $p_{\mathrm{T}}$ is required to be greater than $5{\mathrm{\,Ge\kern-1.00006ptV\!/}c}$ for both signal and normalisation modes.

While the neutrino from the $\tau$ decay escapes detection, its momentum vector can be constrained from the measured positions of the primary and $\tau$ decay vertices, the momenta of the muon and the three pions, and the trajectory of the muon. Then, by imposing the requirements that the mass of the system formed from the three pions and the unobserved neutrino corresponds to the mass of the tau lepton, and by requiring that the $B$ decay vertex lies on the trajectories of the muon, of the tau lepton, and of the $B$ meson, the invariant mass of the ${B}^{0}_{({s})}$ candidate can be determined analytically up to a twofold ambiguity. Because of the quadratic nature of the equation, the computed masses may be unphysical. This occurs in 32% of the selected signal in the simulated event sample due to measurement resolutions and in 48% of the same-sign candidates in data. These candidates are removed, thereby improving the signal-to-background ratio. The solution whose distribution shows the largest separation between signal and background is used as the reconstructed $B$ invariant mass, $M_{B}$, in the analysis. The distributions of $M_{B}$ for candidates satisfying the previously described initial selection in the simulated signal samples and in the opposite-sign control sample in the data are shown in Fig. 1.

To reduce the data to a manageable level and focus on the rejection of the most difficult backgrounds, the low-mass region with ${M_{B}}<4{\mathrm{\,Ge\kern-1.00006ptV\!/}c^{2}}$ is discarded. The signal loss due to this requirement is negligible.

To further reduce the background, additional requirements, optimised with same-sign candidates and simulated samples, are applied to the selected ${{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ decays. Taking advantage of the resonant structure of the ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$ decay, candidates with both combinations of oppositely charged pions with invariant-masses below $550{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ are removed. Candidates with a three-pion invariant mass greater than $1.8{\mathrm{\,Ge\kern-1.00006ptV\!/}c^{2}}$ are discarded to veto the background contribution due to ${{D}^{+}}\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$ decays.

A set of isolation variables is used to reduce background from decays with additional reconstructed particles. The first class of isolation variables exploits the presence of activity in the calorimeter to identify the contribution of neutral particles contained in a cone centred on the $B$ or $\tau$ flight directions. The second class is based on the presence of additional tracks consistent with originating from the $B$ or $\tau$ decay vertices, or uses a multivariate classifier, trained on simulated data, to discriminate against candidates whose decay products are compatible with forming good-quality vertices with other tracks in the event. These variables are combined using a Boosted Decision Tree (BDT) [29], trained on same-sign candidates and simulated ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ decays. Candidates with a BDT output compatible with that of background are discarded. A second BDT is used to reduce to a negligible level the contribution of combinatorial background, which extends over the whole mass range but dominates at higher masses. It uses variables related to vertex quality and reconstructed particle opening angles and is trained on samples of same-sign candidates with ${M_{B}}>6.2{\mathrm{\,Ge\kern-1.00006ptV\!/}c^{2}}$ and simulated ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ decays.

Some background processes, such as ${{B}^{0}_{({s})}}\!\rightarrow{{D}^{-}_{({s})}}(\!\rightarrow{\mu^{-}}{{\overline{\nu}}_{\mu}}){{\pi}^{+}}{{\pi}^{-}}{{\pi}^{+}}$, have $M_{B}$ distributions peaking in the signal region. In these decays, the three pions come from the $B$ decay vertex, and therefore the reconstructed $B$ and $\tau$ decay vertices are very close. Discarding candidates with a reconstructed $\tau$ decay-time significance lower than $1.8$ reduces this type of background to a negligible level while keeping $\sim$75$\%$ of signal, according to studies performed on simulation. All previously described selection criteria also suppress a possible contribution from the ${{B}^{0}}\!\rightarrow{a_{1}(1260)^{-}}{\mu^{+}}{{\nu}_{\mu}}$ mode, whose selection efficiency is 60 times lower than that of the signal. Its rate is currently unmeasured, but, given that the largest known $b\rightarrow u$ semileptonic decay branching fractions are of the order of $10^{-4}$, its branching fraction is not expected to be much higher. Events from the decay ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{0}}{{\nu}_{\tau}}$ passing the selection are also included as signal.

The selection procedure retains 17 746 candidates. According to studies based on simulations, the remaining background is dominated by ${{B}^{0}_{({s})}}\!\rightarrow{D}_{(s)}^{(*)}\mu\nu\text{X}$ decays.

The selection efficiencies for the signal and normalisation modes, $\epsilon_{{{B}^{0}_{({s})}}\rightarrow{\tau}\mu}$ and $\epsilon_{B\rightarrow D\pi}$, respectively, are estimated using simulation or, whenever possible, data. The efficiency $\epsilon_{{{B}^{0}_{({s})}}\rightarrow{\tau}\mu}$ includes those for both ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}$ and ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{0}}{{\nu}_{\tau}}$ decays, where the latter is weighted by the ratio of the two branching fractions. The ${\tau^{-}}\!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{0}}{{\nu}_{\tau}}$ channel contributes by $\sim 16\%$ to the extracted signal yield. The tracking and particle identification efficiencies are determined using data [30, 31]. The trigger efficiency for the normalisation channel is estimated using a trigger-unbiased subsample made of events which have been triggered independently of the normalisation candidate. For the signal, muons from ${{{B}^{+}}}\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}(\!\rightarrow{\mu^{+}}{\mu^{-}}){{K}^{+}}$ decays are used to evaluate the muon trigger efficiency and corrections are applied to the simulated signal samples. To account for differences between the control and the signal samples, the efficiency is computed as a function of the muon $p_{\mathrm{T}}$ and IP. Simulation as well as ${{{B}^{+}}}\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}(\!\rightarrow{\mu^{+}}{\mu^{-}}){{K}^{+}}$ decays is used to determine the software-trigger efficiency and its systematic uncertainty.

The signal yield for the normalisation mode is obtained from a fit to the invariant-mass distribution of the ${{B}^{0}}\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ candidates. In the fit the signal is modelled by the sum of two Crystal Ball (CB) [32] functions, with tails on opposite sides, having common means and widths, but independent tail parameters. The tail parameters are fixed to values determined from a fit to a sample of ${{B}^{0}}\!\rightarrow{{D}^{-}}(\!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}){{\pi}^{+}}$ simulated decays, while all other parameters are left free. The small background contribution is described by an exponential function. The measured yield of the ${{B}^{0}}\!\rightarrow{{D}^{-}}{{\pi}^{+}}$ mode is $N^{\text{norm}}=22\;588\pm 176$ where the uncertainty is statistical only.

The ${{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ branching fractions can be written as

[TABLE]

where $N^{\text{sig}}_{(s)}$ is the number of observed ${{B}^{0}_{({s})}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ decays and $\alpha_{(s)}^{\text{norm}}$ a normalisation factor. The latter is defined by

[TABLE]

using externally measured quantities: the ratio of $b$-quark hadronisation fractions to ${B}^{0}_{s}$ and ${B}^{0}$ mesons, $f_{{B}^{0}_{s}}/f_{{B}^{0}}=0.259\pm 0.015$ [33], {\mathcal{B}}\left(\mbox{{{B}^{0}}!\rightarrow{{D}^{-}}(!\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}){{\pi}^{+}}}\right)=(2.26\pm 0.14)\times 10^{-4} [34] and {\mathcal{B}}\left(\mbox{{\tau^{-}}!\rightarrow{{\pi}^{-}}{{\pi}^{+}}{{\pi}^{-}}{{\nu}_{\tau}}}\right)=(9.02\pm 0.05)\% [34]. The measured values of $\alpha_{(s)}^{\text{norm}}$ for the ${B}^{0}_{s}$ and ${B}^{0}$ modes are, respectively,

[TABLE]

where the three quoted uncertainties are the statistical uncertainty due to the sizes of the signal and normalisation simulated and data samples, the systematic uncertainty on the selection efficiencies (dominated by the trigger efficiency contribution, $\sim$11$\%$) and the total uncertainty on the externally measured quantities.

A final BDT is built to split the selected candidates into four samples with different signal-to-background ratios. It combines 16 discriminating variables, none of which are correlated with the $B$-meson invariant mass. The most important ones are the invariant masses of the three-pion system and of the two combinations of oppositely charged pions, the $B$-meson IP and flight distance significances, and the output of the BDT based on isolation variables. The output of the BDT is transformed to have a uniform distribution between 0 and 1 for ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}(\!\rightarrow{{\pi}^{\pm}}{{\pi}^{\mp}}{{\pi}^{\pm}}{{\nu}_{\tau}}){{\mu}^{\mp}}$ simulated decays. As a consequence, its distribution for the background peaks at low BDT values. All samples are divided into four bins of equal width in BDT output. Their distributions are shown in Fig. 2.

The signal yield is evaluated by performing a simultaneous unbinned maximum-likelihood fit to the $M_{B}$ distributions in the range $[4.6,5.8]{\mathrm{\,Ge\kern-1.00006ptV\!/}c^{2}}$ of the four samples corresponding to different BDT bins. In each bin, the data are described by the sum of a signal and a background component. The background shape is modelled by the upper tail of a reversed CB function, whose peak position and tail parameters are shared among BDT bins. For the determination of the systematic uncertainties, different sets of constrained parameters or alternative background models, such as the sum of two Gaussian functions, are considered. The signal shapes are described by double-sided Hypatia functions [35] whose parameters are initialized to the values obtained from a fit to the ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ simulated samples and allowed to vary within Gaussian constraints accounting for possible discrepancies between data and simulation. The width of the Hypatia functions are $\sim 330{\mathrm{\,Me\kern-1.00006ptV\!/}c^{2}}$ for both signal modes in the most sensitive BDT bin. As the separation between ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ signal shapes is limited, two independent fits are performed while assuming the contribution of either the ${B}^{0}_{s}$ or the ${B}^{0}$ signal only. The signal fractional yields in each BDT bin are Gaussian constrained according to their expected values and uncertainties. The fit result corresponding to the hypothesis of the ${B}^{0}_{s}$ signal only is shown in Fig. 3.

The fit procedure is validated by performing fits to a set of pseudoexperiments where the mass distributions are randomly generated according to the background model observed in the data. The pulls of all fitted parameters are normally distributed except those of the signal yields $N^{\text{sig}}$, which have the expected widths but exhibit a very small bias of $-3\pm 1$ ($2\pm 2$) events for the ${B}^{0}_{s}$ (${B}^{0}$) mode. This effect is accounted for by adding the bias to $N^{\text{sig}}$ in the simultaneous fits to the four BDT regions for both ${B}^{0}$ and ${B}^{0}_{s}$. The obtained signal yields are

[TABLE]

where the uncertainties account for the statistical ones as well as those on the signal and background shape parameters. They show no evidence of any signal excess.

Using the calculated values of the normalisation factors $\alpha^{\text{norm}}$ and $\alpha_{s}^{\text{norm}}$ from Eq. 1 together with Eq. 3, the observed yields from the likelihood fits are translated into upper limits on the branching fractions using the CLs method [36, 37]. The total uncertainty on the normalisation factor is accounted for as an additional Gaussian constraint in the simultaneous fit. Furthermore, a systematic uncertainty on the signal yield of 34 (41) for the ${B}^{0}_{s}$ (${B}^{0}$) mode, derived using different sets of constrained parameters or alternative background models, is added to account for the uncertainties in the background shape. The expected and observed CLs values as a function of the branching fraction are shown in the Supplemental Material [38]. The corresponding limits on the ${B}^{0}_{s}$ and ${B}^{0}$ branching fractions at $90\%$ and $95\%$ CL are given in Table 1 assuming negligible contribution from the ${{B}^{0}}\!\rightarrow{a_{1}(1260)^{-}}{\mu^{+}}{{\nu}_{\mu}}$ mode. A possible residual contribution of this background would lower the expected limits by $\sim$16\%\times({\mathcal{B}}(\mbox{{{B}^{0}}!\rightarrow{a_{1}(1260)^{-}}{\mu^{+}}{{\nu}_{\mu}}})/10^{-4}).

The impact of systematic uncertainties on the final limits is about 35$\%$, dominated by the uncertainty on the background model.

These results represent the best upper limits to date. They constitute a factor $\sim$2 improvement with respect to the BaBar result for the ${B}^{0}$ mode [13] and the first measurement for the ${B}^{0}_{s}$ mode. The allowed range on the ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ branching fraction preferred by the three-site Pati-Salam model [7, 8] is significantly reduced by the results presented in this Letter.

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 (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (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 and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United Kingdom).

Supplemental material for LHCb-PAPER-2019-016

Figures 4 and 5 show the expected and observed CLs values as a function of the ${{B}^{0}_{s}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ and ${{B}^{0}}\!\rightarrow{{\tau}^{\pm}}{{\mu}^{\mp}}$ branching fractions.

LHCb collaboration

R. Aaij30, C. Abellán Beteta47, B. Adeva44, M. Adinolfi51, C.A. Aidala78, Z. Ajaltouni8, S. Akar62, P. Albicocco21, J. Albrecht13, F. Alessio45, M. Alexander56, A. Alfonso Albero43, G. Alkhazov36, P. Alvarez Cartelle58, A.A. Alves Jr44, S. Amato2, Y. Amhis10, L. An20, L. Anderlini20, G. Andreassi46, M. Andreotti19, J.E. Andrews63, F. Archilli21, J. Arnau Romeu9, A. Artamonov42, M. Artuso65, K. Arzymatov40, E. Aslanides9, M. Atzeni47, B. Audurier25, S. Bachmann15, J.J. Back53, S. Baker58, V. Balagura10,b, W. Baldini19,45, A. Baranov40, R.J. Barlow59, S. Barsuk10, W. Barter58, M. Bartolini22,h, F. Baryshnikov74, V. Batozskaya34, B. Batsukh65, A. Battig13, V. Battista46, A. Bay46, F. Bedeschi27, I. Bediaga1, A. Beiter65, L.J. Bel30, V. Belavin40, S. Belin25, N. Beliy4, V. Bellee46, K. Belous42, I. Belyaev37, G. Bencivenni21, E. Ben-Haim11, S. Benson30, S. Beranek12, A. Berezhnoy38, R. Bernet47, D. Berninghoff15, H.C. Bernstein65, E. Bertholet11, A. Bertolin26, C. Betancourt47, F. Betti18,e, M.O. Bettler52, Ia. Bezshyiko47, S. Bhasin51, J. Bhom32, M.S. Bieker13, S. Bifani50, P. Billoir11, A. Birnkraut13, A. Bizzeti20,u, M. Bjørn60, M.P. Blago45, T. Blake53, F. Blanc46, S. Blusk65, D. Bobulska56, V. Bocci29, O. Boente Garcia44, T. Boettcher61, A. Bondar41,w, N. Bondar36, S. Borghi59,45, M. Borisyak40, M. Borsato15, M. Boubdir12, T.J.V. Bowcock57, C. Bozzi19,45, S. Braun15, A. Brea Rodriguez44, M. Brodski45, J. Brodzicka32, A. Brossa Gonzalo53, D. Brundu25,45, E. Buchanan51, A. Buonaura47, C. Burr59, A. Bursche25, J.S. Butter30, J. Buytaert45, W. Byczynski45, S. Cadeddu25, H. Cai69, R. Calabrese19,g, S. Cali21, R. Calladine50, M. Calvi23,i, M. Calvo Gomez43,m, A. Camboni43,m, P. Campana21, D.H. Campora Perez45, L. Capriotti18,e, A. Carbone18,e, G. Carboni28, R. Cardinale22,h, A. Cardini25, P. Carniti23,i, K. Carvalho Akiba30, A. Casais Vidal44, G. Casse57, M. Cattaneo45, G. Cavallero22, R. Cenci27,p, M.G. Chapman51, M. Charles11,45, Ph. Charpentier45, G. Chatzikonstantinidis50, M. Chefdeville7, V. Chekalina40, C. Chen3, S. Chen25, S.-G. Chitic45, V. Chobanova44, M. Chrzaszcz45, A. Chubykin36, P. Ciambrone21, X. Cid Vidal44, G. Ciezarek45, F. Cindolo18, P.E.L. Clarke55, M. Clemencic45, H.V. Cliff52, J. Closier45, J.L. Cobbledick59, V. Coco45, J.A.B. Coelho10, J. Cogan9, E. Cogneras8, L. Cojocariu35, P. Collins45, T. Colombo45, A. Comerma-Montells15, A. Contu25, G. Coombs45, S. Coquereau43, G. Corti45, C.M. Costa Sobral53, B. Couturier45, G.A. Cowan55, D.C. Craik61, A. Crocombe53, M. Cruz Torres1, R. Currie55, C.L. Da Silva64, E. Dall’Occo30, J. Dalseno44,51, C. D’Ambrosio45, A. Danilina37, P. d’Argent15, A. Davis59, O. De Aguiar Francisco45, K. De Bruyn45, S. De Capua59, M. De Cian46, J.M. De Miranda1, L. De Paula2, M. De Serio17,d, P. De Simone21, J.A. de Vries30, C.T. Dean56, W. Dean78, D. Decamp7, L. Del Buono11, B. Delaney52, H.-P. Dembinski14, M. Demmer13, A. Dendek33, D. Derkach75, O. Deschamps8, F. Desse10, F. Dettori25, B. Dey6, A. Di Canto45, P. Di Nezza21, S. Didenko74, H. Dijkstra45, F. Dordei25, M. Dorigo27,x, A.C. dos Reis1, A. Dosil Suárez44, L. Douglas56, A. Dovbnya48, K. Dreimanis57, L. Dufour45, G. Dujany11, P. Durante45, J.M. Durham64, D. Dutta59, R. Dzhelyadin42,†, M. Dziewiecki15, A. Dziurda32, A. Dzyuba36, S. Easo54, U. Egede58, V. Egorychev37, S. Eidelman41,w, S. Eisenhardt55, U. Eitschberger13, R. Ekelhof13, S. Ek-In46, L. Eklund56, S. Ely65, A. Ene35, S. Escher12, S. Esen30, T. Evans62, A. Falabella18, C. Färber45, N. Farley50, S. Farry57, D. Fazzini10, M. Féo45, P. Fernandez Declara45, A. Fernandez Prieto44, F. Ferrari18,e, L. Ferreira Lopes46, F. Ferreira Rodrigues2, S. Ferreres Sole30, M. Ferro-Luzzi45, S. Filippov39, R.A. Fini17, M. Fiorini19,g, M. Firlej33, C. Fitzpatrick45, T. Fiutowski33, F. Fleuret10,b, M. Fontana45, F. Fontanelli22,h, R. Forty45, V. Franco Lima57, M. Franco Sevilla63, M. Frank45, C. Frei45, J. Fu24,q, W. Funk45, E. Gabriel55, A. Gallas Torreira44, D. Galli18,e, S. Gallorini26, S. Gambetta55, Y. Gan3, M. Gandelman2, P. Gandini24, Y. Gao3, L.M. Garcia Martin77, J. García Pardiñas47, B. Garcia Plana44, J. Garra Tico52, L. Garrido43, D. Gascon43, C. Gaspar45, G. Gazzoni8, D. Gerick15, E. Gersabeck59, M. Gersabeck59, T. Gershon53, D. Gerstel9, Ph. Ghez7, V. Gibson52, O.G. Girard46, P. Gironella Gironell43, L. Giubega35, K. Gizdov55, V.V. Gligorov11, C. Göbel67, D. Golubkov37, A. Golutvin58,74, A. Gomes1,a, I.V. Gorelov38, C. Gotti23,i, E. Govorkova30, J.P. Grabowski15, R. Graciani Diaz43, L.A. Granado Cardoso45, E. Graugés43, E. Graverini46, G. Graziani20, A. Grecu35, R. Greim30, P. Griffith25, L. Grillo59, L. Gruber45, B.R. Gruberg Cazon60, C. Gu3, E. Gushchin39, A. Guth12, Yu. Guz42,45, T. Gys45, T. Hadavizadeh60, C. Hadjivasiliou8, G. Haefeli46, C. Haen45, S.C. Haines52, P.M. Hamilton63, Q. Han6, X. Han15, T.H. Hancock60, S. Hansmann-Menzemer15, N. Harnew60, T. Harrison57, C. Hasse45, M. Hatch45, J. He4, M. Hecker58, K. Heijhoff30, K. Heinicke13, A. Heister13, K. Hennessy57, L. Henry77, M. Heß71, J. Heuel12, A. Hicheur66, R. Hidalgo Charman59, D. Hill60, M. Hilton59, P.H. Hopchev46, J. Hu15, W. Hu6, W. Huang4, Z.C. Huard62, W. Hulsbergen30, T. Humair58, M. Hushchyn75, D. Hutchcroft57, D. Hynds30, P. Ibis13, M. Idzik33, P. Ilten50, A. Inglessi36, A. Inyakin42, K. Ivshin36, R. Jacobsson45, S. Jakobsen45, J. Jalocha60, E. Jans30, B.K. Jashal77, A. Jawahery63, F. Jiang3, M. John60, D. Johnson45, C.R. Jones52, C. Joram45, B. Jost45, N. Jurik60, S. Kandybei48, M. Karacson45, J.M. Kariuki51, S. Karodia56, N. Kazeev75, M. Kecke15, F. Keizer52, M. Kelsey65, M. Kenzie52, T. Ketel31, B. Khanji45, A. Kharisova76, C. Khurewathanakul46, K.E. Kim65, T. Kirn12, V.S. Kirsebom46, S. Klaver21, K. Klimaszewski34, S. Koliiev49, M. Kolpin15, A. Kondybayeva74, A. Konoplyannikov37, P. Kopciewicz33, R. Kopecna15, P. Koppenburg30, I. Kostiuk30,49, O. Kot49, S. Kotriakhova36, M. Kozeiha8, L. Kravchuk39, M. Kreps53, F. Kress58, S. Kretzschmar12, P. Krokovny41,w, W. Krupa33, W. Krzemien34, W. Kucewicz32,l, M. Kucharczyk32, V. Kudryavtsev41,w, G.J. Kunde64, A.K. Kuonen46, T. Kvaratskheliya37, D. Lacarrere45, G. Lafferty59, A. Lai25, D. Lancierini47, G. Lanfranchi21, C. Langenbruch12, T. Latham53, C. Lazzeroni50, R. Le Gac9, R. Lefèvre8, A. Leflat38, F. Lemaitre45, O. Leroy9, T. Lesiak32, B. Leverington15, H. Li68, P.-R. Li4,aa, X. Li64, Y. Li5, Z. Li65, X. Liang65, T. Likhomanenko73, R. Lindner45, F. Lionetto47, V. Lisovskyi10, G. Liu68, X. Liu3, D. Loh53, A. Loi25, J. Lomba Castro44, I. Longstaff56, J.H. Lopes2, G. Loustau47, G.H. Lovell52, D. Lucchesi26,o, M. Lucio Martinez44, Y. Luo3, A. Lupato26, E. Luppi19,g, O. Lupton53, A. Lusiani27,t, X. Lyu4, F. Machefert10, F. Maciuc35, V. Macko46, P. Mackowiak13, S. Maddrell-Mander51, O. Maev36,45, K. Maguire59, D. Maisuzenko36, M.W. Majewski33, S. Malde60, B. Malecki45, A. Malinin73, T. Maltsev41,w, H. Malygina15, G. Manca25,f, G. Mancinelli9, D. Marangotto24,q, J. Maratas8,v, J.F. Marchand7, U. Marconi18, C. Marin Benito10, M. Marinangeli46, P. Marino46, J. Marks15, P.J. Marshall57, G. Martellotti29, L. Martinazzoli45, M. Martinelli45,23,i, D. Martinez Santos44, F. Martinez Vidal77, A. Massafferri1, M. Materok12, R. Matev45, A. Mathad47, Z. Mathe45, V. Matiunin37, C. Matteuzzi23, K.R. Mattioli78, A. Mauri47, E. Maurice10,b, B. Maurin46, M. McCann58,45, A. McNab59, R. McNulty16, J.V. Mead57, B. Meadows62, C. Meaux9, N. Meinert71, D. Melnychuk34, M. Merk30, A. Merli24,q, E. Michielin26, D.A. Milanes70, E. Millard53, M.-N. Minard7, O. Mineev37, L. Minzoni19,g, D.S. Mitzel15, A. Mödden13, A. Mogini11, R.D. Moise58, T. Mombächer13, I.A. Monroy70, S. Monteil8, M. Morandin26, G. Morello21, M.J. Morello27,t, J. Moron33, A.B. Morris9, R. Mountain65, H. Mu3, F. Muheim55, M. Mukherjee6, M. Mulder30, D. Müller45, J. Müller13, K. Müller47, V. Müller13, C.H. Murphy60, D. Murray59, P. Naik51, T. Nakada46, R. Nandakumar54, A. Nandi60, T. Nanut46, I. Nasteva2, M. Needham55, N. Neri24,q, S. Neubert15, N. Neufeld45, R. Newcombe58, T.D. Nguyen46, C. Nguyen-Mau46,n, S. Nieswand12, R. Niet13, N. Nikitin38, N.S. Nolte45, A. Oblakowska-Mucha33, V. Obraztsov42, S. Ogilvy56, D.P. O’Hanlon18, R. Oldeman25,f, C.J.G. Onderwater72, J. D. Osborn78, A. Ossowska32, J.M. Otalora Goicochea2, T. Ovsiannikova37, P. Owen47, A. Oyanguren77, P.R. Pais46, T. Pajero27,t, A. Palano17, M. Palutan21, G. Panshin76, A. Papanestis54, M. Pappagallo55, L.L. Pappalardo19,g, W. Parker63, C. Parkes59,45, G. Passaleva20,45, A. Pastore17, M. Patel58, C. Patrignani18,e, A. Pearce45, A. Pellegrino30, G. Penso29, M. Pepe Altarelli45, S. Perazzini18, D. Pereima37, P. Perret8, L. Pescatore46, K. Petridis51, A. Petrolini22,h, A. Petrov73, S. Petrucci55, M. Petruzzo24,q, B. Pietrzyk7, G. Pietrzyk46, M. Pikies32, M. Pili60, D. Pinci29, J. Pinzino45, F. Pisani45, A. Piucci15, V. Placinta35, S. Playfer55, J. Plews50, M. Plo Casasus44, F. Polci11, M. Poli Lener21, M. Poliakova65, A. Poluektov9, N. Polukhina74,c, I. Polyakov65, E. Polycarpo2, G.J. Pomery51, S. Ponce45, A. Popov42, D. Popov50, S. Poslavskii42, E. Price51, C. Prouve44, V. Pugatch49, A. Puig Navarro47, H. Pullen60, G. Punzi27,p, W. Qian4, J. Qin4, R. Quagliani11, B. Quintana8, N.V. Raab16, B. Rachwal33, J.H. Rademacker51, M. Rama27, M. Ramos Pernas44, M.S. Rangel2, F. Ratnikov40,75, G. Raven31, M. Ravonel Salzgeber45, M. Reboud7, F. Redi46, S. Reichert13, F. Reiss11, C. Remon Alepuz77, Z. Ren3, V. Renaudin60, S. Ricciardi54, S. Richards51, K. Rinnert57, P. Robbe10, A. Robert11, A.B. Rodrigues46, E. Rodrigues62, J.A. Rodriguez Lopez70, M. Roehrken45, S. Roiser45, A. Rollings60, V. Romanovskiy42, A. Romero Vidal44, J.D. Roth78, M. Rotondo21, M.S. Rudolph65, T. Ruf45, J. Ruiz Vidal77, J.J. Saborido Silva44, N. Sagidova36, B. Saitta25,f, V. Salustino Guimaraes67, C. Sanchez Gras30, C. Sanchez Mayordomo77, B. Sanmartin Sedes44, R. Santacesaria29, C. Santamarina Rios44, M. Santimaria21,45, E. Santovetti28,j, G. Sarpis59, A. Sarti21,k, C. Satriano29,s, A. Satta28, M. Saur4, D. Savrina37,38, S. Schael12, M. Schellenberg13, M. Schiller56, H. Schindler45, M. Schmelling14, T. Schmelzer13, B. Schmidt45, O. Schneider46, A. Schopper45, H.F. Schreiner62, M. Schubiger30, S. Schulte46, M.H. Schune10, R. Schwemmer45, B. Sciascia21, A. Sciubba29,k, A. Semennikov37, E.S. Sepulveda11, A. Sergi50,45, N. Serra47, J. Serrano9, L. Sestini26, A. Seuthe13, P. Seyfert45, M. Shapkin42, T. Shears57, L. Shekhtman41,w, V. Shevchenko73, E. Shmanin74, B.G. Siddi19, R. Silva Coutinho47, L. Silva de Oliveira2, G. Simi26,o, S. Simone17,d, I. Skiba19, N. Skidmore15, T. Skwarnicki65, M.W. Slater50, J.G. Smeaton52, E. Smith12, I.T. Smith55, M. Smith58, M. Soares18, L. Soares Lavra1, M.D. Sokoloff62, F.J.P. Soler56, B. Souza De Paula2, B. Spaan13, E. Spadaro Norella24,q, P. Spradlin56, F. Stagni45, M. Stahl15, S. Stahl45, P. Stefko46, S. Stefkova58, O. Steinkamp47, S. Stemmle15, O. Stenyakin42, M. Stepanova36, H. Stevens13, S. Stone65, S. Stracka27, M.E. Stramaglia46, M. Straticiuc35, U. Straumann47, S. Strokov76, J. Sun3, L. Sun69, Y. Sun63, K. Swientek33, A. Szabelski34, T. Szumlak33, M. Szymanski4, Z. Tang3, T. Tekampe13, G. Tellarini19, F. Teubert45, E. Thomas45, M.J. Tilley58, V. Tisserand8, S. T’Jampens7, M. Tobin5, S. Tolk45, L. Tomassetti19,g, D. Tonelli27, D.Y. Tou11, E. Tournefier7, M. Traill56, M.T. Tran46, A. Trisovic52, A. Tsaregorodtsev9, G. Tuci27,45,p, A. Tully52, N. Tuning30, A. Ukleja34, A. Usachov10, A. Ustyuzhanin40,75, U. Uwer15, A. Vagner76, V. Vagnoni18, A. Valassi45, S. Valat45, G. Valenti18, M. van Beuzekom30, H. Van Hecke64, E. van Herwijnen45, C.B. Van Hulse16, J. van Tilburg30, M. van Veghel30, R. Vazquez Gomez45, P. Vazquez Regueiro44, C. Vázquez Sierra30, S. Vecchi19, J.J. Velthuis51, M. Veltri20,r, A. Venkateswaran65, M. Vernet8, M. Veronesi30, M. Vesterinen53, J.V. Viana Barbosa45, D. Vieira4, M. Vieites Diaz44, H. Viemann71, X. Vilasis-Cardona43,m, A. Vitkovskiy30, M. Vitti52, V. Volkov38, A. Vollhardt47, D. Vom Bruch11, B. Voneki45, A. Vorobyev36, V. Vorobyev41,w, N. Voropaev36, R. Waldi71, J. Walsh27, J. Wang3, J. Wang5, M. Wang3, Y. Wang6, Z. Wang47, D.R. Ward52, H.M. Wark57, N.K. Watson50, D. Websdale58, A. Weiden47, C. Weisser61, M. Whitehead12, G. Wilkinson60, M. Wilkinson65, I. Williams52, M. Williams61, M.R.J. Williams59, T. Williams50, F.F. Wilson54, M. Winn10, W. Wislicki34, M. Witek32, G. Wormser10, S.A. Wotton52, K. Wyllie45, Z. Xiang4, D. Xiao6, Y. Xie6, H. Xing68, A. Xu3, L. Xu3, M. Xu6, Q. Xu4, Z. Xu7, Z. Xu3, Z. Yang3, Z. Yang63, Y. Yao65, L.E. Yeomans57, H. Yin6, J. Yu6,z, X. Yuan65, O. Yushchenko42, K.A. Zarebski50, M. Zavertyaev14,c, M. Zeng3, D. Zhang6, L. Zhang3, S. Zhang3, W.C. Zhang3,y, Y. Zhang45, A. Zhelezov15, Y. Zheng4, Y. Zhou4, X. Zhu3, V. Zhukov12,38, J.B. Zonneveld55, S. Zucchelli18,e.

*1**Centro 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

4University of Chinese Academy of Sciences, Beijing, China

5Institute Of High Energy Physics (IHEP), Beijing, China

6Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China

7Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France

8Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

9Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

10LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

11LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France

12I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany

13Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany

14Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany

15Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

16School of Physics, University College Dublin, Dublin, Ireland

17INFN Sezione di Bari, Bari, Italy

18INFN Sezione di Bologna, Bologna, Italy

19INFN Sezione di Ferrara, Ferrara, Italy

20INFN Sezione di Firenze, Firenze, Italy

21INFN Laboratori Nazionali di Frascati, Frascati, Italy

22INFN Sezione di Genova, Genova, Italy

23INFN Sezione di Milano-Bicocca, Milano, Italy

24INFN Sezione di Milano, Milano, Italy

25INFN Sezione di Cagliari, Monserrato, Italy

26INFN Sezione di Padova, Padova, Italy

27INFN Sezione di Pisa, Pisa, Italy

28INFN Sezione di Roma Tor Vergata, Roma, Italy

29INFN Sezione di Roma La Sapienza, Roma, Italy

30Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands

31Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands

32Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland

33AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

34National Center for Nuclear Research (NCBJ), Warsaw, Poland

35Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

36Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI), Gatchina, Russia

37Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow, Russia, Moscow, Russia

38Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia

40Yandex School of Data Analysis, Moscow, Russia

41Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia

42Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI), Protvino, Russia, Protvino, Russia

43ICCUB, Universitat de Barcelona, Barcelona, Spain

44Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain

45European Organization for Nuclear Research (CERN), Geneva, Switzerland

46Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

47Physik-Institut, Universität Zürich, Zürich, Switzerland

48NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine

49Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine

50University of Birmingham, Birmingham, United Kingdom

51H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

52Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

53Department of Physics, University of Warwick, Coventry, United Kingdom

54STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

55School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom

56School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

57Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

58Imperial College London, London, United Kingdom

59Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

60Department of Physics, University of Oxford, Oxford, United Kingdom

61Massachusetts Institute of Technology, Cambridge, MA, United States

62University of Cincinnati, Cincinnati, OH, United States

63University of Maryland, College Park, MD, United States

64Los Alamos National Laboratory (LANL), Los Alamos, United States

65Syracuse University, Syracuse, NY, United States

66Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria, associated to 2

67Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

68South China Normal University, Guangzhou, China, associated to 3

69School of Physics and Technology, Wuhan University, Wuhan, China, associated to 3

70Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to 11

71Institut für Physik, Universität Rostock, Rostock, Germany, associated to 15

72Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 30

73National Research Centre Kurchatov Institute, Moscow, Russia, associated to 37

74National University of Science and Technology “MISIS”, Moscow, Russia, associated to 37

75National Research University Higher School of Economics, Moscow, Russia, associated to 40

76National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 37

77Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain, associated to 43

78University of Michigan, Ann Arbor, United States, associated to 65

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, Vietnam

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

vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines

wNovosibirsk State University, Novosibirsk, Russia

xINFN Sezione di Trieste, Trieste, Italy

ySchool of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, China

zPhysics and Micro Electronic College, Hunan University, Changsha City, China

aaLanzhou University, Lanzhou, China

†Deceased *