EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-208 LHCb-PAPER-2021-038 May 12, 2022

Tests of lepton universality using
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ decays

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

This paper is dedicated to the memory of our friend and colleague Sheldon
Stone.

Tests of lepton universality in
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ decays where
$\ell$ is either an electron or a muon are presented. The differential
branching fractions of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays are measured in
intervals of the dilepton invariant mass squared. The measurements are
performed using proton-proton collision data recorded by the LHCb experiment,
corresponding to an integrated luminosity of 9$\text{\,fb}^{-1}$. The results
are consistent with the Standard Model and previous tests of lepton
universality in related decay modes. The first observation of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays is reported.

Published in Phys. Rev. Lett. 128, 191802

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

The ${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ decays, where
$\ell$ refers to either an electron or a muon, are flavour-changing neutral
current (FCNC) transitions involving the transformation of a beauty quark into
a strange quark.111Charge conjugate processes are implied throughout. These
decays proceed via higher order electroweak processes in the Standard Model
(SM) due to the absence of first order FCNC transitions, making them highly
suppressed. Therefore, these decays may receive significant contributions from
new quantum fields that lie beyond the Standard Model (BSM) and hence are
promising laboratories for new physics (NP) searches.

In recent years, studies of similar
${{b}\\!\rightarrow{s}{\ell^{+}}{\ell^{-}}}$ transitions, most prominently
${{{{B}^{+}}}\\!\rightarrow{{K}^{+}}{\ell^{+}}{\ell^{-}}}$ and
${{{B}^{0}}\\!\rightarrow{{K}^{*0}}{\ell^{+}}{\ell^{-}}}$ decays, have
revealed tensions with the SM predictions. Deviations have been seen in ratios
of branching fractions

$R_{H}\equiv\dfrac{\displaystyle\int^{q^{2}_{\rm\max}}_{q^{2}_{\rm\min}}\dfrac{\mathrm{d}\mathcal{B}\left({{B}\\!\rightarrow
H{\mu^{+}}{\mu^{-}}}\right)}{\mathrm{d}{q^{2}}}\mathrm{d}{q^{2}}}{\displaystyle\int^{q^{2}_{\rm\max}}_{q^{2}_{\rm\min}}\dfrac{\mathrm{d}\mathcal{B}\left({{B}\\!\rightarrow
H{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}\mathrm{d}{q^{2}}},$ (1)

where $B$ denotes a ${{B}^{+}}$ or a ${B}^{0}$ meson, $H$ is either a $K$ or a
${K}^{*}$ meson, and $q^{2}$ is the dilepton invariant mass squared. In the SM
the charged leptons have identical interaction strengths, which is referred to
as lepton universality. The only exception is their interaction with the Higgs
field, which determines their differing masses. Therefore, these ratios are
predicted to be very close to unity [1], with corrections from QED up to
$\mathcal{O}(10^{-2})$ [2, 3] and further small corrections due to the muon-
electron mass difference. Furthermore, these ratios benefit from precise
cancellation of the hadronic uncertainties that affect predictions of the
branching fractions and angular observables, which affect the ratios at
$\mathcal{O}(10^{-4})$ [4]. Significant deviation from unity in such ratios
would therefore constitute unambiguous evidence of BSM physics.

The ratio $R_{{{K}^{*0}}}$, measured by the LHCb collaboration using the data
collected in the $q^{2}$ regions
$0.045<{q^{2}}<1.1$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ and
$1.1<{q^{2}}<6.0$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ [5], is in tension
with the SM predictions at 2.2–2.4 and 2.4–2.5 standard deviations ($\sigma$),
respectively, where the ranges are due to the use of different Standard Model
predictions. A measurement of $R_{{{K}^{+}}}$ performed in the region
$1.1<{q^{2}}<6.0$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ deviates from the
SM by 3.1 standard deviations [6]. The analogous ratio measured using
${{{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{p}{{K}^{-}}{\ell^{+}}{\ell^{-}}}$ decays,
$R_{{p}{K}}$, is consistent with the SM within one standard deviation [7]. All
four measurements show a deficit of ${{b}\\!\rightarrow{s}{\mu^{+}}{\mu^{-}}}$
decays with respect to ${{b}\\!\rightarrow{s}{e^{+}e^{-}}}$ decays.

In addition, angular observables [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19] and branching fractions [20, 21, 22, 23] of
${{b}\\!\rightarrow{s}{\mu^{+}}{\mu^{-}}}$ decays have been measured, with
several in tension with the SM. However, the extent to which they may be
affected by residual quantum chromodynamics contributions remains uncertain
[24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34].

Intriguingly, it is possible to account for all these anomalies simultaneously
through the modification of the ${{b}\\!\rightarrow{s}}$ coupling in a model-
independent way [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]. Such a
modification can be generated by the presence of a heavy neutral boson [47,
48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63] or a
leptoquark [64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90], as well as in models with
supersymmetry [91, 92, 93], extra dimensions [94], and extended Higgs sectors
[95, 96, 97, 98, 99].

The ${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ decays are the
isospin partners of ${{{{B}^{+}}}\\!\rightarrow{{K}^{+}}{\ell^{+}}{\ell^{-}}}$
and ${{{B}^{0}}\\!\rightarrow{{K}^{*0}}{\ell^{+}}{\ell^{-}}}$ decays and are
expected to be affected by the same NP contributions. Testing lepton
universality by measuring the ratios $R_{{{K}^{0}_{\mathrm{S}}}}$ and
$R_{{{K}^{*+}}}$ can therefore provide important additional evidence for or
against NP. However, while these decays have similar branching fractions to
their isospin partners, $\mathcal{O}(10^{-6})$ to $\mathcal{O}(10^{-7})$, they
suffer from a reduced experimental efficiency at LHCb due to the presence of a
long-lived ${K}^{0}_{\mathrm{S}}$ meson in the final state. These ratios have
previously been measured by the BaBar [100] and Belle [101, 102]
collaborations. The differential branching fractions of the muon modes,
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$, were found to be
lower although still consistent with predictions at low $q^{2}$ in a
measurement performed by the LHCb collaboration [22]. No single experiment has
unambiguously observed the electron decay modes to date.

In this Letter, measurements of the ratios $R_{{{K}^{0}_{\mathrm{S}}}}$ and
$R_{{{K}^{*+}}}$ and the differential branching fractions of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays are presented. The
measurements are performed using proton-proton ($pp$) collision data
corresponding to an integrated luminosity of 9$\text{\,fb}^{-1}$ recorded by
the LHCb experiment in 2011, 2012 (Run 1) and 2016–2018 (Run 2) at centre-of-
mass energies of 7, 8 and 13 TeV, respectively. The ${K}^{0}_{\mathrm{S}}$ and
${K}^{*+}$ mesons are reconstructed in the ${\pi}^{+}$ ${\pi}^{-}$ and
${K}^{0}_{\mathrm{S}}$ ${\pi}^{+}$ final states, respectively. The ratio
$R_{{{K}^{0}_{\mathrm{S}}}}$ and the branching fraction
$\mathcal{B}({{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}})$ are
measured in the region
$1.1<{q^{2}}<6.0$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$, while
$R_{{{K}^{*+}}}$ and
$\mathcal{B}({{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}})$ are
determined in the range
$0.045<{q^{2}}<6.0$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$. A wider range
is used in the case of the ${{B}^{+}}$ decay, the differential branching
fraction of which is enhanced at low $q^{2}$ by the photon pole, since the
${K}^{*+}$ is a vector meson. Splitting the $q^{2}$ range into two bins at 1.1
$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$, as was done in the
$R_{{{K}^{*0}}}$ measurement, is not possible due to the limited data sample.

The analysis is designed to minimise systematic uncertainties, particularly
those associated with differences in the detector response between electrons
and muons. The ratios and differential branching fractions are normalised to
the control modes,
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{0}_{\mathrm{S}}}}$,
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right){{K}^{0}_{\mathrm{S}}}}$,
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}$,
and
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right){{K}^{*+}}}$,
the branching fractions of which are known to respect lepton universality to
an excellent approximation [103] and are taken to be equal for the muon and
the electron decays of a given $B$ meson. The parameters
$R^{-1}_{{{K}^{0}_{\mathrm{S}}}}$ and $R^{-1}_{{{K}^{*+}}}$ are measured as
double ratios

$\displaystyle R^{-1}_{{K}^{(*)}}$ $\displaystyle=$
$\displaystyle\frac{\mathcal{B}({{B}\\!\rightarrow
K^{(*)}{e^{+}e^{-}}})}{\mathcal{B}({{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right)K^{(*)}})}\Big{/}\frac{\mathcal{B}({{B}\\!\rightarrow
K^{(*)}{\mu^{+}}{\mu^{-}}})}{\mathcal{B}({{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right)K^{(*)}})}$
(2) $\displaystyle=$
$\displaystyle\left(\frac{N_{\text{sig}}^{ee}}{\epsilon_{\text{sig}}^{ee}}\cdot\frac{\epsilon_{\text{con}}^{ee}}{N_{\text{con}}^{ee}}\right)\Big{/}\left(\frac{N_{\text{sig}}^{\mu\mu}}{\epsilon_{\text{sig}}^{\mu\mu}}\cdot\frac{\epsilon_{\text{con}}^{\mu\mu}}{N_{\text{con}}^{\mu\mu}}\right),$

where $K^{(*)}$ is either a ${K}^{0}_{\mathrm{S}}$ or ${K}^{*+}$ meson, $N$ is
the measured yield, and $\epsilon$ is the total efficiency for signal (sig)
and control (con) decays. The inverse ratio $R^{-1}_{{K}^{(*)}}$ is measured
as its uncertainty better represents a Gaussian distribution due to the low
yield of the electron decay mode. Many sources of systematic bias cancel in
the ratio between the signal and control modes. The differential branching
fractions of the signal electron modes are measured as

$\frac{\mathrm{d}\mathcal{B}\left({{B}\\!\rightarrow
K^{(*)}{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}=\frac{N_{\text{sig}}^{ee}}{\epsilon_{\text{sig}}^{ee}}\frac{\epsilon_{\text{con}}^{ee}}{N_{\text{con}}^{ee}}\frac{\mathcal{B}\left({{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right)K^{(*)}}\right)}{q^{2}_{\rm\max}-q^{2}_{\rm\min}}.$
(3)

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, described in detail in Refs. [104, 105]. The
simulated events used in this analysis are produced with the software
described in Refs. [106, *Sjostrand:2006za, 108, 109, 110,
*Agostinelli:2002hh, 112]. In particular, final-state radiation is simulated
using Photos [113].

The candidates used in the analysis must first pass a hardware trigger, which
requires the presence of at least one muon with high transverse momentum,
$p_{\mathrm{T}}$, in the case of ${{B}\\!\rightarrow
K^{(*)}{\mu^{+}}{\mu^{-}}}$ candidates, or in the case of ${{B}\\!\rightarrow
K^{(*)}{e^{+}e^{-}}}$ candidates at least one electron or hadron with large
energy deposits in the electromagnetic calorimeter (ECAL) or hadronic
calorimeter (HCAL), respectively. Further ${{B}\\!\rightarrow
K^{(*)}{e^{+}e^{-}}}$ candidates are selected where the hardware trigger
requirements are satisfied by objects from the underlying $pp$ collision that
do not form part of the reconstructed candidate. Candidates are then required
to pass a software trigger, the first stage of which requires the presence of
at least one track with high $p_{\mathrm{T}}$ that is well separated from the
primary $pp$ interaction vertex (PV), followed by a second stage that imposes
topological requirements on the final-state tracks to determine whether they
are consistent with the decay of a $b$ hadron.

Muons are initially identified from tracks that penetrate the calorimeters and
the iron absorber plates of the muon system and further separated from hadrons
(primarily pions and kaons) by a multivariate classifier that combines
information from the other subdetectors. Electrons are identified from tracks
with an associated deposit of energy in the ECAL, and separated from hadrons
using a similar multivariate classifier.

Due to their small mass, electrons lose energy via bremsstrahlung radiation as
they traverse the detector material, leading to a degradation in their energy
and momentum resolution. A bremsstrahlung recovery procedure is used to
identify energy deposits in the ECAL that are consistent with photons radiated
from electron candidate tracks upstream of the magnet. This is done by
extrapolating the direction of the electron track before the magnet to a
position in the ECAL and then searching for energy deposits without associated
tracks at that location. When such a deposit is identified, its energy is used
to correct the electron’s energy and momentum. This leads to an improvement in
the $B$ candidate invariant mass resolution, although the resolution for
electronic modes remains larger than for the equivalent muonic channels.

Candidate ${K}^{0}_{\mathrm{S}}$ mesons are reconstructed from two oppositely
charged tracks identified as pions, using either a pair of tracks that
originate in the vertex locator (long tracks), or two tracks that originate
downstream of the vertex locator in the first silicon-strip detector
(downstream tracks). Around a third of reconstructed ${K}^{0}_{\mathrm{S}}$
mesons are formed from long tracks. Candidate
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ decays
are formed from two oppositely charged tracks identified as either muons or
electrons combined with a candidate ${K}^{0}_{\mathrm{S}}$ meson. In the case
of ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ candidates, the
additional charged pion is required to result in a
${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$ mass within
300$\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the ${K}^{*+}$ mass [103]. An
estimated S-wave contribution in this ${K}^{*+}$ mass window of approximately
22% based on previous studies of
${{{B}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{\mu^{+}}{\mu^{-}}}$ decays by
the LHCb collaboration [20] is included in the analysis. When measuring the
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ differential branching
fraction, the
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}$
control mode is selected with a ${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$ mass in
the range $792-992$ $\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ in order to be
consistent with the selection used in previous measurements of
$\mathcal{B}\left({{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}}{{K}^{*+}}\right)$
[114, 115], the world average of which is taken as external input [103].
Background is further suppressed by requirements on the quality of the $B$
decay vertex, the flight distance significance of the $B$ candidate, how
consistent the $B$ candidate is with having originated at the PV, the
invariant masses of the ${K}^{0}_{\mathrm{S}}$, ${K}^{*+}$ and $B$ candidates,
and the $p_{\mathrm{T}}$ and separation from the PV of the final-state tracks.
In an additional step, the invariant masses of $B$ candidates are recalculated
with the ${K}^{0}_{\mathrm{S}}$ meson mass constrained to its measured value
[103], leading to an improvement in the $B$ mass resolution.

Various requirements on decay kinematics, decay time, and particle
identification (PID) information are used to reject potential background
originating from misidentified $b$-hadron ($H_{b}$) decays. Background to
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ decays
includes $H_{b}\rightarrow hh^{\prime}{\ell^{+}}{\ell^{-}}$ decays (where $h$
refers to a hadron), ${{{\mathchar
28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar
28931\relax}{\ell^{+}}{\ell^{-}}}$ and
${{{B}^{0}}\\!\rightarrow{{D}^{-}}({{K}^{0}_{\mathrm{S}}}X)Y}$ decays, where
both $X$ and $Y$ represent either an electron-neutrino pair or a pion.
Background to ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$
decays includes
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ decays
combined with a random additional pion,
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\ell^{+}}{\ell^{-}}\right){{K}^{*+}}}$
and
${{{B}^{+}}\\!\rightarrow{\psi{(2S)}}\left({\ell^{+}}{\ell^{-}}\right){{K}^{*+}}}$
decays where the companion pion from the ${K}^{*+}$ is swapped with a lepton
from the ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ or $\psi{(2S)}$ meson,
$H_{b}\rightarrow hh^{\prime}\pi{\ell^{+}}{\ell^{-}}$ decays, decays with
${\mathchar 28931\relax}$ baryons in the final state, and
${{{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}X)Y}$
decays. These selection requirements reduce all these background sources to
levels that have a negligible (sub-percent) effect on the measured signal
yields. The
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{{\pi}^{+}}{{\pi}^{-}}}$ decays, where
the pions are misidentified as electrons, are significantly reduced by the
electron particle identification requirements and included as components in
the mass fits.

Multivariate classifiers based on boosted decision tree (BDT) algorithms [116]
are used to suppress background from coincidental track combinations
(combinatorial background). Separate classifiers are trained for each signal
decay mode, the two data-taking periods (Run 1, Run 2) and whether the
${K}^{0}_{\mathrm{S}}$ meson was reconstructed from long or downstream tracks.
Each classifier is trained on a signal sample of simulated ${{B}\\!\rightarrow
K^{(*)}{\ell^{+}}{\ell^{-}}}$ decays, and a background sample taken from data
with a reconstructed invariant $B$ mass greater than
5500$\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ and $q^{2}$ regions consistent with
either a ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ or $\psi{(2S)}$ meson removed. The
classifiers combine information on the $B$ candidate’s fit quality, distance
of closest approach to the PV, flight distance, $p_{\mathrm{T}}$ and decay
time; the decay time of the dilepton pair; the $p_{\mathrm{T}}$ and decay time
of the ${K}^{0}_{\mathrm{S}}$ candidate; how isolated the $B$, dilepton and
${K}^{0}_{\mathrm{S}}$ candidates are from other tracks in the event; and the
distance of closest approach to the PV of long tracks forming the
${K}^{0}_{\mathrm{S}}$ candidate. Requirements on the classifier outputs are
optimised to provide the maximum signal significance, defined as
$S/\sqrt{S+B}$, where $S$ is the expected signal calculated from the control
mode yield in data, the signal-to-control mode efficiency ratio from
simulation and the signal-to-control mode branching fraction ratio [103], and
$B$ is the background yield in the signal region, extrapolated from a fit to
the data mass sidebands.

The muon and electron control modes are selected in the ranges of
$8.98<{q^{2}}<10.21$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ and
$6.0<{q^{2}}<11.0$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$, respectively,
and the spectra of their invariant masses
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}})$ and
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})$ are
shown in Fig. 1. Their yields are determined using fits to the $B$ candidate
mass, calculated with the masses of the ${K}^{0}_{\mathrm{S}}$ and
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ mesons constrained to their measured values
[103], improving the resolution. The mass distribution of each control mode is
modelled with a sum of two Crystal Ball functions [117] with common mean and
opposite-side power law tails (referred to as a double Crystal Ball or DCB),
with parameters fixed to values obtained from fits to simulated events. The
muon control modes are modelled using a single DCB function, while the
electron control modes are modelled using a sum of three DCB functions, where
the shape of each component and their relative fractions are determined from
fits to simulation in three different categories according to the number of
bremsstrahlung photons added to the candidate’s electrons: 0, 1, or $\geq 2$.
In the fit to data, shifts in the DCB means and widths are allowed to vary
freely with respect to those obtained from simulation in order to accommodate
data-simulation differences in the mass scale and resolution. Combinatorial
background is modelled with an exponential function. In the case of the
${B}^{0}$ control modes,
${{{B}^{0}_{s}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\ell^{+}}{\ell^{-}}\right){{K}^{0}_{\mathrm{S}}}}$
decays are modelled with the ${B}^{0}$ DCB function with its mean offset by
the measured $m_{{{B}^{0}_{s}}}-m_{{{B}^{0}}}$ mass difference [103] and with
its yield allowed to vary freely. The lower limit of the mass range excludes
partially reconstructed background from higher $K^{*}$ resonances, which are
not modelled. The structures visible in the range
$5400\text{\,Me\kern-1.00006ptV\\!/}c^{2}<m({{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}})<5500\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
are due to small amounts of residual contamination from ${\mathchar
28931\relax}^{0}_{b}$ decays, which have a negligible effect on the measured
yields of
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right){{K}^{0}_{\mathrm{S}}}}$
and
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{0}_{\mathrm{S}}}}$
decays. The results of the fit are shown in Fig. 1 and the yields of
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right){{K}^{0}_{\mathrm{S}}}}$,
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{0}_{\mathrm{S}}}}$,
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right){{K}^{*+}}}$,
and
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}$
decays are found to be $118\,750\pm 360$, $21\,080\pm 170$, $75\,420\pm 290$,
and $14\,330\pm 170$, respectively.

Figure 1: Distributions of (top left)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}$
mass, (top right)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}$
mass, (bottom left)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass and (bottom right)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass with the fit models used to determine the control mode yields.

The spectra of the invariant masses
$m({{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}})$,
$m({{K}^{0}_{\mathrm{S}}}{e^{+}}{e^{-}})$,
$m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$, and
$m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{e^{+}}{e^{-}})$ of the muon and electron
signal modes are shown in Fig. 2. The yields of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$ decays are
determined using fits to the ${{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}$ and
${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ mass distributions. The
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$ signal decays are
modelled using DCB functions where the shape parameters are determined from
fits to simulation, with shifts in their means and widths taken from the
corresponding control mode fits to data. Combinatorial background is modelled
using an exponential function, while partially reconstructed background is
excluded by the lower mass limit.

Figure 2: Distributions of (top left)
${{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}$ and (top right)
${{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}$ mass with the fit models used to
determine the
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$ yield and
$R^{-1}_{{{K}^{0}_{\mathrm{S}}}}$, and (bottom left)
${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and (bottom right)
${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{e^{+}e^{-}}$ mass with the fit models used
to determine the ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$
yield and $R^{-1}_{{{K}^{*+}}}$.

The ratios and branching fractions are determined using fits to
${{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}$ and
${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{e^{+}e^{-}}$ mass spectra, with the
${K}^{0}_{\mathrm{S}}$ candidate’s mass constrained to its measured value. The
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ signal decays are modelled
using the sum of three DCB functions, each corresponding to different numbers
of recovered bremsstrahlung photons. The DCB parameters are taken from
simulation with shifts in the means and widths taken from the control mode
fits to data without a ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ mass constraint.
Partially reconstructed background from higher $K^{*}$ resonances is modelled
using a DCB function with shape parameters constrained from simulation in the
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ fit, and
Gaussian kernel density estimations (KDE) determined from simulation in the
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ fit, with their yields
allowed to vary freely. Leakage from the ${J\mskip-3.0mu/\mskip-2.0mu\psi}$
control modes into the signal region is modelled using KDE functions, with
their yields constrained based on the control mode fits and the efficiency in
simulation. Residual contamination from
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{{\pi}^{+}}{{\pi}^{-}}}$ decays is
modelled in each fit by a DCB function determined from simulated events, with
its yield constrained using the control mode yields, the control mode and
background branching fractions, and the efficiencies taken from simulation.
Combinatorial background is modelled with an exponential function.

The efficiencies used in the measurements of the ratios and differential
branching fractions are calculated using simulation, to which various
corrections are applied to improve the agreement with data. The PID
efficiencies for each channel are calculated from calibration data samples of
electrons, muons and pions, and are applied as per-candidate weights to the
simulation. Similarly, the electron tracking efficiency is corrected using
calibration samples. The $p_{\mathrm{T}}$ and pseudorapidity of the $B$ mesons
generated by Pythia 8 [106], and the occupancy of the underlying events are
corrected by comparing their distributions between data and simulation using
the muon control modes to calculate per-candidate weights, which are applied
to both electron and muon samples. Similarly, the trigger efficiency is
corrected by comparing the efficiency as a function of the $p_{\mathrm{T}}$ of
the muons, the transverse energy of the electrons and pions, and the
$p_{\mathrm{T}}$ of the $B$ meson, between control mode data and simulation.
Further weights are applied to correct any residual mismodelling of the BDT
classifier response. Finally, the simulated $q^{2}$ distribution is corrected
using control mode data to account for the larger observed resolution in data.

Multiple sources of systematic uncertainty are evaluated, the largest of which
comes from the statistical uncertainties of the efficiencies due to the sizes
of the available samples of simulated events. These affect the
$R^{-1}_{{K}^{(*)}}$ ratios and the differential branching fractions at 2–3%.
The next largest are associated with the mass fit models, in particular the
limited size of the simulation samples used to determine the shape parameters,
and the choices of models used for the partially reconstructed and
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ leakage background, which affect the
observables by 1–2%. The remaining sources of systematic uncertainty are found
to be close to or below the 1% level. These include: the limited amount of
data and simulation used to calculate correction weights; the choices of
binning schemes used to evaluate the PID efficiency weights and potential
biases in this procedure due to correlations in the PID response between the
two electrons; the choice of methods used to calculate the trigger efficiency;
imperfect modelling of the muon track reconstruction efficiency; residual
mismodelling of the BDT classifier response in simulation; residual bias in
the fitting procedure evaluated using pseudoexperiments, and residual
contamination from
${{{B}^{0}}\\!\rightarrow{{D}^{-}}({{K}^{0}_{\mathrm{S}}}X)Y}$ and
${{{{B}^{+}}}\\!\rightarrow{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}X)Y}$
decays. Other sources of residual background contamination were found to have
a negligible effect on the measurements. All systematic uncertainties, as well
as the statistical precision of the efficiencies and various parameters used
in the maximum likelihood fits, are included as Gaussian constraints in the
fit. Finally, the statistical precision on each observable is scaled by
factors determined from pseudoexperiments (with values in the range
1.01–1.02), in order to guarantee proper coverage.

A number of checks are performed to ensure that efficiencies are accurately
estimated. The ratios $R^{-1}_{{\psi{(2S)}}K^{(*)}}$, where the signal modes
in Eq. (2) are substituted for
${{B}\\!\rightarrow{\psi{(2S)}}\left({\mu^{+}}{\mu^{-}}\right)K^{(*)}}$ and
${{B}\\!\rightarrow{\psi{(2S)}}\left({e^{+}e^{-}}\right)K^{(*)}}$ decays,
selected in the $q^{2}$ ranges
$[12.86,14.33]$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ and
$[11.0,15.0]$$\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$, respectively, are
found to be $R^{-1}_{{\psi{(2S)}}{{K}^{0}_{\mathrm{S}}}}=1.014\pm
0.030\left(\text{stat.}\right)\pm 0.020\left(\text{syst.}\right)$ and
$R^{-1}_{{\psi{(2S)}}{{K}^{*+}}}=1.017\pm 0.045\left(\text{stat.}\right)\pm
0.023\left(\text{syst.}\right)$, consistent with unity as expected due to
lepton universality in ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ and $\psi{(2S)}$
decays [6]. Additionally, the single ratios

$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}}\equiv\frac{\mathcal{B}\left({{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right)K^{(*)}}\right)}{\mathcal{B}\left({{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({\mu^{+}}{\mu^{-}}\right)K^{(*)}}\right)}=\frac{N_{\text{con}}^{ee}}{N_{\text{con}}^{\mu\mu}}\frac{\epsilon_{\text{con}}^{\mu\mu}}{\epsilon_{\text{con}}^{ee}},$
(4)

which do not benefit from cancellation of systematic biases between signal and
control modes, and are therefore a stringent check of the efficiencies, are
found to be
$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}}}=0.977\pm
0.008\left(\text{stat.}\right)\pm 0.027\left(\text{syst.}\right)$ and
$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{*+}}}=0.965\pm
0.011\left(\text{stat.}\right)\pm 0.032\left(\text{syst.}\right)$, again
consistent with unity in both cases. Furthermore, differential measurements of
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}}$ as functions of a range of
variables that are differently distributed in the signal and control decays
are performed. The most powerful of these tests measures
$r_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}}$ as a function of the response
of a BDT classifier trained on simulated candidates to distinguish signal and
control decays. All these differential distributions are found to be flat
within the statistical precision, providing further confidence that the yields
and efficiencies are well estimated [118].

In order to avoid experimenter’s bias, the results of the analysis and the
electron signal mode mass spectra were not examined until the full procedure
had been finalised and checks had been performed to ensure that the muon
signal mode branching fractions were in agreement between the different data-
taking years and also with the results of the previous measurements made by
LHCb [22]. The fits to the
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$,
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$,
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$ invariant-mass
spectra are shown in Fig. 2. The fitted yields of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$ decays are $45\pm
10$, $155\pm 15$, $67\pm 13$ and $221\pm 17$, respectively. The ratios
$R^{-1}_{{{K}^{0}_{\mathrm{S}}}}$ and $R^{-1}_{{{K}^{*+}}}$ are measured to be

$\displaystyle R^{-1}_{{{K}^{0}_{\mathrm{S}}}}=\hskip 2.84544pt$
$\displaystyle
1.51\,^{+0.40}_{-0.35}\left(\text{stat.}\right)^{+0.09}_{-0.04}\left(\text{syst.}\right),$
$\displaystyle R^{-1}_{{{K}^{*+}}}=\hskip 2.84544pt$ $\displaystyle
1.44\,^{+0.32}_{-0.29}\left(\text{stat.}\right)^{+0.09}_{-0.06}\left(\text{syst.}\right),$

in the $q^{2}$ ranges $[1.1,6.0]$ $\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$
and $[0.045,6.0]$ $\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$, respectively.
These ratios are consistent with the SM at $1.5$ and $1.4$ standard
deviations, respectively, evaluated using Wilks’ theorem [119]. To aid
comparison with other lepton-universality ratios, $R_{{{K}^{0}_{\mathrm{S}}}}$
and $R_{{{K}^{*+}}}$ are calculated by inverting the results above, yielding

$\displaystyle R_{{{K}^{0}_{\mathrm{S}}}}=\hskip 2.84544pt$ $\displaystyle
0.66\,^{+0.20}_{-0.14}\left(\text{stat.}\right)^{+0.02}_{-0.04}\left(\text{syst.}\right),$
$\displaystyle R_{{{K}^{*+}}}=\hskip 2.84544pt$ $\displaystyle
0.70\,^{+0.18}_{-0.13}\left(\text{stat.}\right)^{+0.03}_{-0.04}\left(\text{syst.}\right).$

The differential branching fractions of the signal electron decays are found
to be

$\displaystyle\frac{\mathrm{d}\mathcal{B}\left({{{B}^{0}}\\!\rightarrow{{K}^{0}}{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}=$
$\displaystyle\,\left(2.6\pm 0.6\left(\text{stat.}\right)\pm
0.1\left(\text{syst.}\right)\right)\times 10^{-8}\hskip
2.84544pt\text{\,Ge\kern-1.00006ptV}^{-2}c^{4},$
$\displaystyle\frac{\mathrm{d}\mathcal{B}\left({{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}=$
$\displaystyle\,\left(9.2\,^{+1.9}_{-1.8}\left(\text{stat.}\right)^{+0.8}_{-0.6}\left(\text{syst.}\right)\right)\times
10^{-8}\hskip 2.84544pt\text{\,Ge\kern-1.00006ptV}^{-2}c^{4},$

in the $q^{2}$ ranges $[1.1,6.0]$ $\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$
and $[0.045,6.0]$ $\text{\,Ge\kern-1.00006ptV}^{2}\\!/c^{4}$ and where the
significances of the
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays evaluated using
Wilks’ theorem [119] are 5.3$\sigma$ and 6.0$\sigma$, respectively. Since the
control mode branching fraction of
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}}}$ decays
$(8.91\pm 0.21)\times 10^{-4}$ [103] is used, the differential branching
fraction of ${{{B}^{0}}\\!\rightarrow{{K}^{0}}{e^{+}e^{-}}}$ instead of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ decays is
reported. A combination of the $R^{-1}_{{{K}^{0}_{\mathrm{S}}}}$ and
$R^{-1}_{{{K}^{*+}}}$ measurements is performed using the flavio software
package [120] to fit for a single muon-specific Wilson coefficient
$C_{9}^{\text{NP}}=-C_{10}^{\text{NP}}$, while fixing all other Wilson
coefficients to their SM values. This scenario is used in several existing
fits to ${{b}\\!\rightarrow{s}{\ell^{+}}{\ell^{-}}}$data, and is chosen
specifically as the ratios $R_{{K}^{(*)}}$ have poor sensitivity in
discriminating between the Wilson Coefficients $C_{9}$ and $C_{10}$. The fit
results in $C_{9}^{\text{NP}}=-C_{10}^{\text{NP}}=-0.8^{+0.4}_{-0.3}$ and a
significance of 2.0 standard deviations with respect to the SM under this
specific scenario. It should be noted that this fit is model-dependent and the
result could change if data-driven estimates of the hadronic uncertainties
were used.

These measurements constitute the most precise tests of lepton universality in
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\ell^{+}}{\ell^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\ell^{+}}{\ell^{-}}}$ decays to date,
the most precise measurements of their differential branching fractions at low
$q^{2}$, and the first observations of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$ and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays. While these
measurements are individually consistent with the SM, the central values
exhibit the same deficit of muonic decays relative to electronic decays as
seen in the other lepton universality tests performed by the LHCb
collaboration [5, 6, 7].

## 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); MICINN (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 NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

##  Appendix A Supplemental material

This appendix contains supplemental material to the measurements. Eq. 5 gives
the the ${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$differential branching
fractions divided by the branching fractions of their respective normalisation
modes. Fig. 3 shows the total efficiencies for the four signal decay modes as
function of $q^{2}$. Figs. 4 and 5 show differential measurements of
$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}}$. Figs. 6 and 7 show the
profile likelihood scans for $R^{-1}_{{K}^{(*)}}$ and the differential
branching fractions. Fig. 8 compares the measurements of $R^{-1}_{{K}^{(*)}}$
presented in this Letter with previous measurements by the Belle
collaboration. Fig. 9 shows the ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}$
invariant mass spectra and the maximum likelihood fits use to determine the
${{B}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}K^{(*)}}$control mode
yields with a linear scale. Figs. 10 and 11 show the ${\psi{(2S)}}K^{(*)}$
invariant mass spectra and the maximum likelihood fits use to determine the
${{B}\\!\rightarrow{\psi{(2S)}}K^{(*)}}$ mode yields with linear and
logarithmic scales.

In the main text, the differential branching fractions of
${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$and
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$decays are reported. These
are normalised using the world-average branching fractions for
${{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{0}}}$
and
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}$
respectively [103]. The ratios of signal and control mode branching fractions
used in this calculation are

$\displaystyle\frac{\mathrm{d}\mathcal{B}\left({{{B}^{0}}\\!\rightarrow{{K}^{0}}{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}\,\big{/}\,\mathcal{B}\left({{{B}^{0}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{0}}}\right)$
$\displaystyle=\,$
$\displaystyle\left(4.9\,^{+1.2}_{-1.1}\left(\text{stat.}\right)\pm
0.2\left(\text{syst.}\right)\right)$ $\displaystyle\times 10^{-4}\hskip
2.84544pt\text{\,Ge\kern-1.00006ptV}^{-2}c^{4},$
$\displaystyle\frac{\mathrm{d}\mathcal{B}\left({{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}\right)}{\mathrm{d}{q^{2}}}\,\big{/}\,\mathcal{B}\left({{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}\right)$
$\displaystyle=\,$
$\displaystyle\left(1.08\,^{+0.22}_{-0.21}\left(\text{stat.}\right)\,^{+0.06}_{-0.04}\left(\text{syst.}\right)\right)$
$\displaystyle\times 10^{-3}\hskip
2.84544pt\text{\,Ge\kern-1.00006ptV}^{-2}c^{4},$ (5)

where ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$candidates are
selected with $m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})$ within 300
$\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the world-average ${K}^{*+}$ mass,
whereas
${{{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}\left({e^{+}e^{-}}\right){{K}^{*+}}}$candidates
are selected in the range
$792<m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})/\text{\,Me\kern-1.00006ptV\\!/}c^{2}<992$.

Figure 3:  Total selection efficiencies as a function of $q^{2}$, for (top
left) ${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{\mu^{+}}{\mu^{-}}}$,
(top right) ${{{B}^{0}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{e^{+}e^{-}}}$,
(bottom left) ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{\mu^{+}}{\mu^{-}}}$, and
(bottom right) ${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays. The
efficiencies are evaluated using simulated candidates that have been corrected
to improve agreement with data. These efficiencies account for detector
resolution effects including the effect of bremsstrahlung, which may cause a
candidate to be reconstructed in a different bin of $q^{2}$ than would be
dictated by its ‘true’ value.

Figure 4:  Single ratios (left)
$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}}}$ and
(right) $r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{*+}}}$ as a function
of the opening angle of the two leptons, normalised to their average value.

Figure 5:  Single ratios (left)
$r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{0}_{\mathrm{S}}}}$ and
(right) $r^{-1}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{*+}}}$ as a function
of the output of an MVA trained to separate the signal and control modes,
normalised to their average value.

Figure 6:  Scans of the profile likelihoods as a function of (left)
$R^{-1}_{{{K}^{0}_{\mathrm{S}}}}$, and (right) $R^{-1}_{{{K}^{*+}}}$.

Figure 7:  Scans of the profile likelihoods as a function of the differential
branching fractions for (left)
${{{B}^{0}}\\!\rightarrow{{K}^{0}}{e^{+}e^{-}}}$ decays, and (right)
${{{{B}^{+}}}\\!\rightarrow{{K}^{*+}}{e^{+}e^{-}}}$ decays. Figure 8:
Measurements of $R_{{{K}^{0}_{\mathrm{S}}}}$ and $R_{{{K}^{*+}}}$ performed by
the LHCb and Belle collaborations [101, 102].

Figure 9: Distributions of (top left)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}$
mass, (top right)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}$
mass, (bottom left)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass and (bottom right)
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass with the fit models used to determine the control mode yields.

Figure 10: Distributions of (top left)
${\psi{(2S)}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}$ mass, (top right)
${\psi{(2S)}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}$ mass, (bottom left)
${\psi{(2S)}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$ mass and
(bottom right) ${\psi{(2S)}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass with the fit models used to determine the $\psi{(2S)}$ control mode
yields.

Figure 11: Distributions of (top left)
${\psi{(2S)}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}$ mass, (top right)
${\psi{(2S)}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}$ mass, (bottom left)
${\psi{(2S)}}({\mu^{+}}{\mu^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$ mass and
(bottom right) ${\psi{(2S)}}({e^{+}}{e^{-}}){{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$
mass with the fit models used to determine the $\psi{(2S)}$ control mode
yields.

## References

  * [1] G. Hiller and F. Krüger, _More model-independent analysis of $b\rightarrow s$ processes_, Phys. Rev. D69 (2004) 074020, arXiv:hep-ph/0310219
  * [2] M. Bordone, G. Isidori, and A. Pattori, _On the Standard Model predictions for $R_{K}$ and $R_{K^{*}}$_, Eur. Phys. J. C76 (2016) 440, arXiv:1605.07633
  * [3] G. Isidori, S. Nabeebaccus, and R. Zwicky, _QED corrections in ${\kern 1.79993pt\overline{\kern-1.79993ptB}}\rightarrow{\kern 1.79993pt\overline{\kern-1.79993ptK}}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-}$ at the double-differential level_, JHEP 12 (2020) 104, arXiv:2009.00929
  * [4] C. Bobeth, G. Hiller, and G. Piranishvili, _Angular distributions of $\bar{B}\rightarrow\bar{K}\ell^{+}\ell^{-}$ decays_, JHEP 12 (2007) 040, arXiv:0709.4174
  * [5] LHCb collaboration, R. Aaij et al., _Test of lepton universality with ${{{B}^{0}}\\!\rightarrow{{K}^{*0}}\ell^{+}\ell^{-}}$ decays_, JHEP 08 (2017) 055, arXiv:1705.05802
  * [6] LHCb collaboration, R. Aaij et al., _Test of lepton universality in beauty-quark decays_ , Nature Phys. 18 (2022) 277, arXiv:2103.11769
  * [7] LHCb collaboration, R. Aaij et al., _Test of lepton universality using ${{{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow p{{K}^{-}}\ell^{+}\ell^{-}}$ decays_, JHEP 05 (2020) 040, arXiv:1912.08139
  * [8] LHCb collaboration, R. Aaij et al., _Angular analysis of the $B^{+}\rightarrow K^{\ast+}\mu^{+}\mu^{-}$ decay_, Phys. Rev. Lett. 126 (2021) 161802, arXiv:2012.13241
  * [9] LHCb collaboration, R. Aaij et al., _Measurement of $C\\!P$-averaged observables in the ${{{B}^{0}}\\!\rightarrow{{K}^{*0}}{\mu^{+}\mu^{-}}}$ decay_, Phys. Rev. Lett. 125 (2020) 011802, arXiv:2003.04831
  * [10] LHCb collaboration, R. Aaij et al., _Angular analysis of the ${{{B}^{0}}\\!\rightarrow{{K}^{*0}}{\mu^{+}\mu^{-}}}$ decay using $3\text{\,fb}^{-1}$ of integrated luminosity_, JHEP 02 (2016) 104, arXiv:1512.04442
  * [11] LHCb collaboration, R. Aaij et al., _Angular analysis of the rare decay ${{B}^{0}_{s}}\rightarrow\phi{\mu^{+}}{\mu^{-}}$_, JHEP 11 (2021) 043, arXiv:2107.13428
  * [12] ATLAS collaboration, M. Aaboud et al., _Angular analysis of $B^{0}_{d}\rightarrow K^{*}\mu^{+}\mu^{-}$ decays in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector_, JHEP 10 (2018) 047, arXiv:1805.04000
  * [13] BaBar collaboration, B. Aubert et al., _Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays $B\rightarrow K\ell^{+}\ell^{-}$ and $B\rightarrow K^{*}\ell^{+}\ell^{-}$_, Phys. Rev. D73 (2006) 092001, arXiv:hep-ex/0604007
  * [14] BaBar collaboration, J. P. Lees et al., _Measurement of angular asymmetries in the decays $B\rightarrow K^{*}\ell^{+}\ell^{-}$_, Phys. Rev. D93 (2016) 052015, arXiv:1508.07960
  * [15] Belle collaboration, J.-T. Wei et al., _Measurement of the differential branching Fraction and forward-backward Asymmetry for $B\rightarrow K^{(*)}\ell^{+}\ell^{-}$_, Phys. Rev. Lett. 103 (2009) 171801, arXiv:0904.0770
  * [16] Belle collaboration, S. Wehle et al., _Lepton-flavor-dependent angular analysis of $B\rightarrow K^{\ast}\ell^{+}\ell^{-}$_, Phys. Rev. Lett. 118 (2017) 111801, arXiv:1612.05014
  * [17] CDF collaboration, T. Aaltonen et al., _Measurements of the angular distributions in the decays $B\rightarrow K^{(*)}\mu^{+}\mu^{-}$ at CDF_, Phys. Rev. Lett. 108 (2012) 081807, arXiv:1108.0695
  * [18] CMS collaboration, V. Khachatryan et al., _Angular analysis of the decay $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ from pp collisions at $\sqrt{s}=8$ TeV_, Phys. Lett. B753 (2016) 424, arXiv:1507.08126
  * [19] CMS collaboration, A. M. Sirunyan et al., _Measurement of angular parameters from the decay $\mathrm{B}^{0}\rightarrow\mathrm{K}^{*0}\mu^{+}\mu^{-}$ in proton-proton collisions at $\sqrt{s}=$ 8 TeV_, Phys. Lett. B781 (2018) 517, arXiv:1710.02846
  * [20] LHCb collaboration, R. Aaij et al., _Measurements of the S-wave fraction in ${{{B}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}{\mu^{+}\mu^{-}}}$ decays and the ${{{B}^{0}}\\!\rightarrow{{K}^{*}}(892)^{0}{\mu^{+}\mu^{-}}}$ differential branching fraction_, JHEP 11 (2016) 047, Erratum ibid. 04 (2017) 142, arXiv:1606.04731
  * [21] LHCb collaboration, R. Aaij et al., _Branching fraction measurements of the rare $B^{0}_{s}\rightarrow\phi\mu^{+}\mu^{-}$ and $B^{0}_{s}\rightarrow f_{2}^{\prime}(1525)\mu^{+}\mu^{-}$ decays_, Phys. Rev. Lett. 127 (2021) 151801, arXiv:2105.14007
  * [22] LHCb collaboration, R. Aaij et al., _Differential branching fractions and isospin asymmetries of ${{B}\\!\rightarrow K^{(*)}{\mu^{+}\mu^{-}}}$ decays_, JHEP 06 (2014) 133, arXiv:1403.8044
  * [23] LHCb collaboration, R. Aaij et al., _Differential branching fraction and angular analysis of ${{{\mathchar 28931\relax}^{0}_{b}}\\!\rightarrow{\mathchar 28931\relax}{\mu^{+}\mu^{-}}}$ decays_, JHEP 06 (2015) 115, Erratum ibid. 09 (2018) 145, arXiv:1503.07138
  * [24] S. Descotes-Genon, L. Hofer, J. Matias, and J. Virto, _Global analysis of $b\rightarrow s\ell\ell$ anomalies_, JHEP 06 (2016) 092, arXiv:1510.04239
  * [25] S. Jäger and J. Martin Camalich, _Reassessing the discovery potential of the $B\rightarrow K^{*}\ell^{+}\ell^{-}$ decays in the large-recoil region: SM challenges and BSM opportunities_, Phys. Rev. D93 (2016) 014028, arXiv:1412.3183
  * [26] J. Lyon and R. Zwicky, _Resonances gone topsy turvy - the charm of QCD or new physics in $b\rightarrow s\ell^{+}\ell^{-}$?_, arXiv:1406.0566
  * [27] A. Khodjamirian, T. Mannel, and Y. M. Wang, _$B\rightarrow K\ell^{+}\ell^{-}$ decay at large hadronic recoil_, JHEP 02 (2013) 010, arXiv:1211.0234
  * [28] A. Khodjamirian, T. Mannel, A. A. Pivovarov, and Y.-M. Wang, _Charm-loop effect in $B\rightarrow K^{(*)}\ell^{+}\ell^{-}$ and $B\rightarrow K^{*}\gamma$_, JHEP 09 (2010) 089, arXiv:1006.4945
  * [29] S. Descotes-Genon, L. Hofer, J. Matias, and J. Virto, _On the impact of power corrections in the prediction of $B\rightarrow K^{*}\mu^{+}\mu^{-}$ observables_, JHEP 12 (2014) 125, arXiv:1407.8526
  * [30] R. R. Horgan, Z. Liu, S. Meinel, and M. Wingate, _Calculation of $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ and $B_{s}^{0}\rightarrow\phi\mu^{+}\mu^{-}$ observables using form factors from lattice QCD_, Phys. Rev. Lett. 112 (2014) 212003, arXiv:1310.3887
  * [31] F. Beaujean, C. Bobeth, and D. van Dyk, _Comprehensive Bayesian analysis of rare (semi)leptonic and radiative $B$ decays_, Eur. Phys. J. C74 (2014) 2897, Erratum ibid. C74 (2014) 3179, arXiv:1310.2478
  * [32] C. Hambrock, G. Hiller, S. Schacht, and R. Zwicky, _$B\rightarrow K^{\star}$ form factors from flavor data to QCD and back_, Phys. Rev. D89 (2014) 074014, arXiv:1308.4379
  * [33] W. Altmannshofer and D. M. Straub, _New physics in $B\rightarrow K^{*}\mu\mu$?_, Eur. Phys. J. C73 (2013) 2646, arXiv:1308.1501
  * [34] C. Bobeth, M. Chrzaszcz, D. van Dyk, and J. Virto, _Long-distance effects in $B\rightarrow K^{*}\ell\ell$ from analyticity_, Eur. Phys. J. C78 (2018) 451, arXiv:1707.07305
  * [35] M. Ciuchini et al., _Lessons from the $B^{0,+}\rightarrow K^{*0,+}\mu^{+}\mu^{-}$ angular analyses_, Phys. Rev. D103 (2021) 015030, arXiv:2011.01212
  * [36] K. Kowalska, D. Kumar, and E. M. Sessolo, _Implications for new physics in $b\rightarrow s\mu\mu$ transitions after recent measurements by Belle and LHCb_, Eur. Phys. J. C79 (2019) 840, arXiv:1903.10932
  * [37] M. Algueró et al., _Emerging patterns of new physics with and without lepton flavour universal contributions_ , Eur. Phys. J. C79 (2019) 714, Addendum ibid. C80 (2020) 511, arXiv:1903.09578
  * [38] T. Hurth, F. Mahmoudi, and S. Neshatpour, _Implications of the new LHCb angular analysis of $B\rightarrow K^{*}\mu^{+}\mu^{-}$ : Hadronic effects or new physics?_, Phys. Rev. D102 (2020) 055001, arXiv:2006.04213
  * [39] M. Ciuchini et al., _New physics in $b\rightarrow s\ell^{+}\ell^{-}$ confronts new data on lepton universality_, Eur. Phys. J. C79 (2019) 719, arXiv:1903.09632
  * [40] J. Aebischer et al., _$B$ -decay discrepancies after Moriond 2019_, Eur. Phys. J. C80 (2020) 252, arXiv:1903.10434
  * [41] A. K. Alok, A. Dighe, S. Gangal, and D. Kumar, _Continuing search for new physics in $b\rightarrow s\mu\mu$ decays: two operators at a time_, JHEP 06 (2019) 089, arXiv:1903.09617
  * [42] W. Altmannshofer and P. Stangl, _New physics in rare B decays after Moriond 2021_ , Eur. Phys. J. C 81 (2021) 952, arXiv:2103.13370
  * [43] L.-S. Geng et al., _Implications of new evidence for lepton-universality violation in $brightarrows\ell^{+}\ell^{-}$ decays_, Phys. Rev. D104 (2021) 035029, arXiv:2103.12738
  * [44] C. Cornella et al., _Reading the footprints of the B-meson flavor anomalies_ , JHEP 08 (2021) 050, arXiv:2103.16558
  * [45] M. Algueró et al., _$b\rightarrow s\ell\ell$ global fits after Moriond 2021 results_, in 55th Rencontres de Moriond on QCD and High Energy Interactions, 2021, arXiv:2104.08921
  * [46] T. Hurth, F. Mahmoudi, D. M. Santos, and S. Neshatpour, _More indications for lepton nonuniversality in $b\rightarrow s\ell^{+}\ell^{-}$_, Phys. Lett. B 824 (2022) 136838, arXiv:2104.10058
  * [47] W. Altmannshofer, S. Gori, M. Pospelov, and I. Yavin, _Quark flavor transitions in $L_{\mu}-L_{\tau}$ models_, Phys. Rev. D89 (2014) 095033, arXiv:1403.1269
  * [48] A. Crivellin, G. D’Ambrosio, and J. Heeck, _Explaining $h\rightarrow\mu^{\pm}\tau^{\mp}$, $B\rightarrow K^{*}\mu^{+}\mu^{-}$ and $B\rightarrow K\mu^{+}\mu^{-}/B\rightarrow Ke^{+}e^{-}$ in a two-Higgs-doublet model with gauged $L_{\mu}-L_{\tau}$_, Phys. Rev. Lett. 114 (2015) 151801, arXiv:1501.00993
  * [49] A. Celis, J. Fuentes-Martin, M. Jung, and H. Serodio, _Family nonuniversal Z’ models with protected flavor-changing interactions_ , Phys. Rev. D92 (2015) 015007, arXiv:1505.03079
  * [50] A. Falkowski, M. Nardecchia, and R. Ziegler, _Lepton flavor non-universality in B-meson decays from a U(2) flavor model_ , JHEP 11 (2015) 173, arXiv:1509.01249
  * [51] B. C. Allanach, J. M. Butterworth, and T. Corbett, _Collider constraints on Z ${}^{{}^{\prime}}$ models for neutral current B-anomalies_, JHEP 08 (2019) 106, arXiv:1904.10954
  * [52] B. C. Allanach and J. Davighi, _Naturalising the third family hypercharge model for neutral current $B$-anomalies_, Eur. Phys. J. C79 (2019) 908, arXiv:1905.10327
  * [53] J. Kawamura, S. Raby, and A. Trautner, _Complete vectorlike fourth family and new U(1)’ for muon anomalies_ , Phys. Rev. D100 (2019) 055030, arXiv:1906.11297
  * [54] S. Dwivedi, D. Kumar Ghosh, A. Falkowski, and N. Ghosh, _Associated $Z^{\prime}$ production in the flavorful $U(1)$ scenario for $R_{K^{(*)}}$_, Eur. Phys. J. C80 (2020) 263, arXiv:1908.03031
  * [55] Z.-L. Han, R. Ding, S.-J. Lin, and B. Zhu, _Gauged $U(1)_{L_{\mu}-L_{\tau}}$ scotogenic model in light of $R_{K^{(*)}}$ anomaly and AMS-02 positron excess_, Eur. Phys. J. C79 (2019) 1007, arXiv:1908.07192
  * [56] B. Capdevila, A. Crivellin, C. A. Manzari, and M. Montull, _Explaining $b\rightarrow s\ell^{+}\ell^{-}$ and the Cabibbo angle anomaly with a vector triplet_, Phys. Rev. D103 (2021) 015032, arXiv:2005.13542
  * [57] W. Altmannshofer, J. Davighi, and M. Nardecchia, _Gauging the accidental symmetries of the standard model, and implications for the flavor anomalies_ , Phys. Rev. D101 (2020) 015004, arXiv:1909.02021
  * [58] S.-L. Chen et al., _Signatures of a flavor changing $Z^{\prime}$ boson in $B_{q}\rightarrow\gamma Z^{\prime}$_, Nucl. Phys. B962 (2021) 115237, arXiv:2006.03383
  * [59] A. Carvunis, D. Guadagnoli, M. Reboud, and P. Stangl, _Composite dark matter and a horizontal symmetry_ , JHEP 02 (2021) 056, arXiv:2007.11931
  * [60] A. Karozas, G. K. Leontaris, I. Tavellaris, and N. D. Vlachos, _On the LHC signatures of $SU(5)\times U(1)^{\prime}$ F-theory motivated models_, Eur. Phys. J. C81 (2021) 35, arXiv:2007.05936
  * [61] D. Borah, L. Mukherjee, and S. Nandi, _Low scale U(1) X gauge symmetry as an origin of dark matter, neutrino mass and flavour anomalies_, JHEP 12 (2020) 052, arXiv:2007.13778
  * [62] B. C. Allanach, _$U(1)_{B_{3}-L_{2}}$ explanation of the neutral current $B$$-$anomalies_, Eur. Phys. J. C81 (2021) 56, Erratum ibid. C81 (2021) 321, arXiv:2009.02197
  * [63] J.-H. Sheng, _The analysis of $b\rightarrow s\ell^{+}\ell^{-}$ in the family non-universal $Z^{\prime}$ model_, Int. J. Theor. Phys. 60 (2021) 26
  * [64] G. Hiller and M. Schmaltz, _$R_{K}$ and future $b\rightarrow s\ell\ell$ physics beyond the standard model opportunities_, Phys. Rev. D90 (2014) 054014, arXiv:1408.1627
  * [65] L. Di Luzio, A. Greljo, and M. Nardecchia, _Gauge leptoquark as the origin of B-physics anomalies_ , Phys. Rev. D96 (2017) 115011, arXiv:1708.08450
  * [66] A. Greljo and B. A. Stefanek, _Third family quark–lepton unification at the TeV scale_ , Phys. Lett. B782 (2018) 131, arXiv:1802.04274
  * [67] B. Gripaios, M. Nardecchia, and S. A. Renner, _Composite leptoquarks and anomalies in $B$-meson decays_, JHEP 05 (2015) 006, arXiv:1412.1791
  * [68] I. de Medeiros Varzielas and G. Hiller, _Clues for flavor from rare lepton and quark decays_ , JHEP 06 (2015) 072, arXiv:1503.01084
  * [69] R. Barbieri, C. W. Murphy, and F. Senia, _B-decay anomalies in a composite leptoquark model_ , Eur. Phys. J. C77 (2017) 8, arXiv:1611.04930
  * [70] M. Bordone, C. Cornella, J. Fuentes-Martín, and G. Isidori, _Low-energy signatures of the $\mathrm{PS}^{3}$ model: from $B$-physics anomalies to LFV_, JHEP 10 (2018) 148, arXiv:1805.09328
  * [71] B. Fornal, S. A. Gadam, and B. Grinstein, _Left-right SU(4) vector leptoquark model for flavor anomalies_ , Phys. Rev. D99 (2019) 055025, arXiv:1812.01603
  * [72] S. Balaji and M. A. Schmidt, _Unified SU(4) theory for the $R_{D^{(*)}}$ and $R_{K^{(*)}}$ anomalies_, Phys. Rev. D101 (2020) 015026, arXiv:1911.08873
  * [73] C. Cornella, J. Fuentes-Martin, and G. Isidori, _Revisiting the vector leptoquark explanation of the B-physics anomalies_ , JHEP 07 (2019) 168, arXiv:1903.11517
  * [74] A. Datta, D. Sachdeva, and J. Waite, _Unified explanation of $b\rightarrow s\mu^{+}\mu^{-}$ anomalies, neutrino masses, and $B\rightarrow\pi K$ puzzle_, Phys. Rev. D100 (2019) 055015, arXiv:1905.04046
  * [75] O. Popov, M. A. Schmidt, and G. White, _$R_{2}$ as a single leptoquark solution to $R_{D^{(*)}}$ and $R_{K^{(*)}}$_, Phys. Rev. D100 (2019) 035028, arXiv:1905.06339
  * [76] I. Bigaran, J. Gargalionis, and R. R. Volkas, _A near-minimal leptoquark model for reconciling flavour anomalies and generating radiative neutrino masses_ , JHEP 10 (2019) 106, arXiv:1906.01870
  * [77] J. Bernigaud, I. de Medeiros Varzielas, and J. Talbert, _Finite family groups for fermionic and leptoquark mixing patterns_ , JHEP 01 (2020) 194, arXiv:1906.11270
  * [78] L. Da Rold and F. Lamagna, _A vector leptoquark for the B-physics anomalies from a composite GUT_ , JHEP 12 (2019) 112, arXiv:1906.11666
  * [79] J. Fuentes-Martín, M. Reig, and A. Vicente, _Strong $CP$ problem with low-energy emergent QCD: The 4321 case_, Phys. Rev. D100 (2019) 115028, arXiv:1907.02550
  * [80] C. Hati, J. Kriewald, J. Orloff, and A. M. Teixeira, _A nonunitary interpretation for a single vector leptoquark combined explanation to the $B$-decay anomalies_, JHEP 12 (2019) 006, arXiv:1907.05511
  * [81] A. Datta, J. L. Feng, S. Kamali, and J. Kumar, _Resolving the $(g-2)_{\mu}$ and $B$ anomalies with leptoquarks and a dark Higgs boson_, Phys. Rev. D101 (2020) 035010, arXiv:1908.08625
  * [82] A. Crivellin, D. Müller, and F. Saturnino, _Flavor phenomenology of the leptoquark singlet-triplet model_ , JHEP 06 (2020) 020, arXiv:1912.04224
  * [83] C. Borschensky, B. Fuks, A. Kulesza, and D. Schwartländer, _Scalar leptoquark pair production at hadron colliders_ , Phys. Rev. D101 (2020) 115017, arXiv:2002.08971
  * [84] S. Saad, _Combined explanations of $(g-2)_{\mu}$, $R_{D^{(*)}}$, $R_{K^{(*)}}$ anomalies in a two-loop radiative neutrino mass model_, Phys. Rev. D102 (2020) 015019, arXiv:2005.04352
  * [85] J. Fuentes-Martín and P. Stangl, _Third-family quark-lepton unification with a fundamental composite Higgs_ , Phys. Lett. B811 (2020) 135953, arXiv:2004.11376
  * [86] P. S. Bhupal Dev, R. Mohanta, S. Patra, and S. Sahoo, _Unified explanation of flavor anomalies, radiative neutrino masses, and ANITA anomalous events in a vector leptoquark model_ , Phys. Rev. D102 (2020) 095012, arXiv:2004.09464
  * [87] B. Fornal, _Gravitational wave signatures of lepton universality violation_ , Phys. Rev. D103 (2021) 015018, arXiv:2006.08802
  * [88] J. Davighi, M. Kirk, and M. Nardecchia, _Anomalies and accidental symmetries: charging the scalar leptoquark under L μ $-$ Lτ_, JHEP 12 (2020) 111, arXiv:2007.15016
  * [89] K. S. Babu, P. S. B. Dev, S. Jana, and A. Thapa, _Unified framework for $B$-anomalies, muon $g-2$ and neutrino masses_, JHEP 03 (2021) 179, arXiv:2009.01771
  * [90] A. Angelescu et al., _Single leptoquark solutions to the B-physics anomalies_ , Phys. Rev. D104 (2021) 055017, arXiv:2103.12504
  * [91] S. Trifinopoulos, _B -physics anomalies: The bridge between R -parity violating supersymmetry and flavored dark matter_ , Phys. Rev. D100 (2019) 115022, arXiv:1904.12940
  * [92] Q.-Y. Hu and L.-L. Huang, _Explaining $b\rightarrow s\ell^{+}\ell^{-}$ data by sneutrinos in the $R$ -parity violating MSSM_, Phys. Rev. D101 (2020) 035030, arXiv:1912.03676
  * [93] Q.-Y. Hu, Y.-D. Yang, and M.-D. Zheng, _Revisiting the $B$-physics anomalies in $R$-parity violating MSSM_, Eur. Phys. J. C80 (2020) 365, arXiv:2002.09875
  * [94] A. Shaw, _Looking for $B\rightarrow X_{s}\ell^{+}\ell^{-}$ in a nonminimal universal extra dimensional model_, Phys. Rev. D99 (2019) 115030, arXiv:1903.10302
  * [95] B. Barman, D. Borah, L. Mukherjee, and S. Nandi, _Correlating the anomalous results in $b\rightarrow s$ decays with inert Higgs doublet dark matter and muon $(g-2)$_, Phys. Rev. D100 (2019) 115010, arXiv:1808.06639
  * [96] P. Arnan, A. Crivellin, M. Fedele, and F. Mescia, _Generic loop effects of new scalars and fermions in $b\rightarrow s\ell^{+}\ell^{-}$, $(g-2)_{\mu}$ and a vector-like $4^{\rm th}$ generation_, JHEP 06 (2019) 118, arXiv:1904.05890
  * [97] L. Delle Rose, S. Khalil, S. J. D. King, and S. Moretti, _$R_{K}$ and $R_{K^{*}}$ in an aligned 2HDM with right-handed neutrinos_, Phys. Rev. D101 (2020) 115009, arXiv:1903.11146
  * [98] A. Ordell, R. Pasechnik, H. Serôdio, and F. Nottensteiner, _Classification of anomaly-free 2HDMs with a gauged U(1)’ symmetry_ , Phys. Rev. D100 (2019) 115038, arXiv:1909.05548
  * [99] C. Marzo, L. Marzola, and M. Raidal, _Common explanation to the $R_{K^{(*)}}$, $R_{D^{(*)}}$ and $\epsilon^{\prime}/\epsilon$ anomalies in a 3HDM+$\nu_{R}$ and connections to neutrino physics_, Phys. Rev. D100 (2019) 055031, arXiv:1901.08290
  * [100] BaBar collaboration, J. P. Lees et al., _Measurement of branching fractions and rate asymmetries in the rare decays $B\rightarrow K^{(*)}l^{+}l^{-}$_, Phys. Rev. D86 (2012) 032012, arXiv:1204.3933
  * [101] Belle collaboration, A. Abdesselam et al., _Test of lepton-flavor universality in ${B\rightarrow K^{\ast}\ell^{+}\ell^{-}}$ decays at Belle_, Phys. Rev. Lett. 126 (2021) 161801, arXiv:1904.02440
  * [102] Belle collaboration, S. Choudhury et al., _Test of lepton flavor universality and search for lepton flavor violation in $B\rightarrow K\ell\ell$ decays_, JHEP 03 (2021) 105, arXiv:1908.01848
  * [103] Particle Data Group, P. A. Zyla et al., _Review of particle physics_ , Prog. Theor. Exp. Phys. 2020 (2020) 083C01
  * [104] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [105] LHCb collaboration, R. Aaij et al., _LHCb detector performance_ , Int. J. Mod. Phys. A30 (2015) 1530022, arXiv:1412.6352
  * [106] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [107] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 (2006) 026, arXiv:hep-ph/0603175
  * [108] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [109] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [110] Geant4 collaboration, J. Allison et al., _Geant4 developments and applications_ , IEEE Trans. Nucl. Sci. 53 (2006) 270
  * [111] Geant4 collaboration, S. Agostinelli et al., _Geant4: A simulation toolkit_ , Nucl. Instrum. Meth. A506 (2003) 250
  * [112] M. Clemencic et al., _The LHCb simulation application, Gauss: Design, evolution and experience_, J. Phys. Conf. Ser. 331 (2011) 032023
  * [113] N. Davidson, T. Przedzinski, and Z. Was, _PHOTOS interface in C++: Technical and physics documentation_ , Comp. Phys. Comm. 199 (2016) 86, arXiv:1011.0937
  * [114] BaBar collaboration, B. Aubert et al., _Measurement of branching fractions and charge asymmetries for exclusive $B$ decays to charmonium_, Phys. Rev. Lett. 94 (2005) 141801, arXiv:hep-ex/0412062
  * [115] Belle collaboration, K. Abe et al., _Measurements of branching fractions and decay amplitudes in $B\rightarrow J/\psi K^{*}$ decays_, Phys. Lett. B538 (2002) 11, arXiv:hep-ex/0205021
  * [116] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
  * [117] 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
  * [118] See Supplemental Material at [URL will be inserted by publisher] for further details.
  * [119] S. S. Wilks, _The large-sample distribution of the likelihood ratio for testing composite hypotheses_ , Ann. Math. Stat. 9 (1938) 60
  * [120] D. M. Straub, _flavio: a Python package for flavour and precision phenomenology in the Standard Model and beyond_ , arXiv:1810.08132

LHCb collaboration

R. Aaij32, A.S.W. Abdelmotteleb56, C. Abellán Beteta50, F. Abudinén56, T.
Ackernley60, B. Adeva46, M. Adinolfi54, H. Afsharnia9, C. Agapopoulou13, C.A.
Aidala87, S. Aiola25, Z. Ajaltouni9, S. Akar65, J. Albrecht15, F. Alessio48,
M. Alexander59, A. Alfonso Albero45, Z. Aliouche62, G. Alkhazov38, P. Alvarez
Cartelle55, S. Amato2, J.L. Amey54, Y. Amhis11, L. An48, L. Anderlini22, N.
Andersson50, A. Andreianov38, M. Andreotti21, F. Archilli17, A. Artamonov44,
M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B. Audurier12, S.
Bachmann17, M. Bachmayer49, J.J. Back56, P. Baladron Rodriguez46, V.
Balagura12, W. Baldini21, J. Baptista Leite1, M. Barbetti22,h, R.J. Barlow62,
S. Barsuk11, W. Barter61, M. Bartolini55, F. Baryshnikov83, J.M. Basels14, S.
Bashir34, G. Bassi29, B. Batsukh68, A. Battig15, A. Bay49, A. Beck56, M.
Becker15, F. Bedeschi29, I. Bediaga1, A. Beiter68, V. Belavin42, S. Belin27,
V. Bellee50, K. Belous44, I. Belov40, I. Belyaev41, G. Bencivenni23, E. Ben-
Haim13, A. Berezhnoy40, R. Bernet50, D. Berninghoff17, H.C. Bernstein68, C.
Bertella62, A. Bertolin28, C. Betancourt50, F. Betti48, Ia. Bezshyiko50, S.
Bhasin54, J. Bhom35, L. Bian73, M.S. Bieker15, N.V. Biesuz21, S. Bifani53, P.
Billoir13, A. Biolchini32, M. Birch61, F.C.R. Bishop55, A. Bitadze62, A.
Bizzeti22,l, M. Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49, S. Blusk68, D.
Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T. Boettcher65, A.
Boldyrev82, A. Bondar43, N. Bondar38,48, S. Borghi62, M. Borisyak42, M.
Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60,48, A. Boyer48, C.
Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, J. Brodzicka35, A.
Brossa Gonzalo56, D. Brundu27, A. Buonaura50, L. Buonincontri28, A.T. Burke62,
C. Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,g, L. Calefice15,13, S.
Cali23, R. Calladine53, M. Calvi26,k, M. Calvo Gomez85, P. Camargo
Magalhaes54, P. Campana23, A.F. Campoverde Quezada6, S. Capelli26,k, L.
Capriotti20,e, A. Carbone20,e, G. Carboni31,q, R. Cardinale24,i, A. Cardini27,
I. Carli4, P. Carniti26,k, L. Carus14, K. Carvalho Akiba32, A. Casais Vidal46,
R. Caspary17, G. Casse60, M. Cattaneo48, G. Cavallero48, S. Celani49, J.
Cerasoli10, D. Cervenkov63, A.J. Chadwick60, M.G. Chapman54, M. Charles13, Ph.
Charpentier48, G. Chatzikonstantinidis53, C.A. Chavez Barajas60, M.
Chefdeville8, C. Chen3, S. Chen4, A. Chernov35, V. Chobanova46, S. Cholak49,
M. Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23, M.F. Cicala56,
X. Cid Vidal46, G. Ciezarek48, P.E.L. Clarke58, M. Clemencic48, H.V. Cliff55,
J. Closier48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10, E.
Cogneras9, L. Cojocariu37, P. Collins48, T. Colombo48, L. Congedo19,d, A.
Contu27, N. Cooke53, G. Coombs59, I. Corredoira 46, G. Corti48, C.M. Costa
Sobral56, B. Couturier48, D.C. Craik64, J. Crkovská67, M. Cruz Torres1, R.
Currie58, C.L. Da Silva67, S. Dadabaev83, L. Dai71, E. Dall’Occo15, J.
Dalseno46, C. D’Ambrosio48, A. Danilina41, P. d’Argent48, A. Dashkina83, J.E.
Davies62, A. Davis62, O. De Aguiar Francisco62, K. De Bruyn79, S. De Capua62,
M. De Cian49, E. De Lucia23, J.M. De Miranda1, L. De Paula2, M. De Serio19,d,
D. De Simone50, P. De Simone23, F. De Vellis15, J.A. de Vries80, C.T. Dean67,
F. Debernardis19,d, D. Decamp8, V. Dedu10, L. Del Buono13, B. Delaney55, H.-P.
Dembinski15, A. Dendek34, V. Denysenko50, D. Derkach82, O. Deschamps9, F.
Desse11, F. Dettori27,f, B. Dey77, A. Di Cicco23, P. Di Nezza23, S. Didenko83,
L. Dieste Maronas46, H. Dijkstra48, V. Dobishuk52, C. Dong3, A.M. Donohoe18,
F. Dordei27, A.C. dos Reis1, L. Douglas59, A. Dovbnya51, A.G. Downes8, M.W.
Dudek35, L. Dufour48, V. Duk78, P. Durante48, J.M. Durham67, D. Dutta62, A.
Dziurda35, A. Dzyuba38, S. Easo57, U. Egede69, V. Egorychev41, S.
Eidelman43,v,†, S. Eisenhardt58, S. Ek-In49, L. Eklund86, S. Ely68, A. Ene37,
E. Epple67, S. Escher14, J. Eschle50, S. Esen50, T. Evans48, L.N. Falcao1, Y.
Fan6, B. Fang73, S. Farry60, D. Fazzini26,k, M. Féo48, A. Fernandez Prieto46,
A.D. Fernez66, F. Ferrari20,e, L. Ferreira Lopes49, F. Ferreira Rodrigues2, S.
Ferreres Sole32, M. Ferrillo50, M. Ferro-Luzzi48, S. Filippov39, R.A. Fini19,
M. Fiorini21,g, M. Firlej34, K.M. Fischer63, D.S. Fitzgerald87, C.
Fitzpatrick62, T. Fiutowski34, A. Fkiaras48, F. Fleuret12, M. Fontana13, F.
Fontanelli24,i, R. Forty48, D. Foulds-Holt55, V. Franco Lima60, M. Franco
Sevilla66, M. Frank48, E. Franzoso21, G. Frau17, C. Frei48, D.A. Friday59, J.
Fu6, Q. Fuehring15, E. Gabriel32, G. Galati19,d, A. Gallas Torreira46, D.
Galli20,e, S. Gambetta58,48, Y. Gan3, M. Gandelman2, P. Gandini25, Y. Gao5, M.
Garau27, L.M. Garcia Martin56, P. Garcia Moreno45, J. García Pardiñas26,k, B.
Garcia Plana46, F.A. Garcia Rosales12, L. Garrido45, C. Gaspar48, R.E.
Geertsema32, D. Gerick17, L.L. Gerken15, E. Gersabeck62, M. Gersabeck62, T.
Gershon56, D. Gerstel10, L. Giambastiani28, V. Gibson55, H.K. Giemza36, A.L.
Gilman63, M. Giovannetti23,q, A. Gioventù46, P. Gironella Gironell45, C.
Giugliano21,g, K. Gizdov58, E.L. Gkougkousis48, V.V. Gligorov13, C. Göbel70,
E. Golobardes85, D. Golubkov41, A. Golutvin61,83, A. Gomes1,a, S. Gomez
Fernandez45, F. Goncalves Abrantes63, M. Goncerz35, G. Gong3, P. Gorbounov41,
I.V. Gorelov40, C. Gotti26, E. Govorkova48, J.P. Grabowski17, T. Grammatico13,
L.A. Granado Cardoso48, E. Graugés45, E. Graverini49, G. Graziani22, A.
Grecu37, L.M. Greeven32, N.A. Grieser4, L. Grillo62, S. Gromov83, B.R. Gruberg
Cazon63, C. Gu3, M. Guarise21, M. Guittiere11, P. A. Günther17, E. Gushchin39,
A. Guth14, Y. Guz44, T. Gys48, T. Hadavizadeh69, G. Haefeli49, C. Haen48, J.
Haimberger48, T. Halewood-leagas60, P.M. Hamilton66, J.P. Hammerich60, Q.
Han7, X. Han17, T.H. Hancock63, E.B. Hansen62, S. Hansmann-Menzemer17, N.
Harnew63, T. Harrison60, C. Hasse48, M. Hatch48, J. He6,b, M. Hecker61, K.
Heijhoff32, K. Heinicke15, R.D.L. Henderson69,56, A.M. Hennequin48, K.
Hennessy60, L. Henry48, J. Heuel14, A. Hicheur2, D. Hill49, M. Hilton62, S.E.
Hollitt15, R. Hou7, Y. Hou8, J. Hu17, J. Hu72, W. Hu7, X. Hu3, W. Huang6, X.
Huang73, W. Hulsbergen32, R.J. Hunter56, M. Hushchyn82, D. Hutchcroft60, D.
Hynds32, P. Ibis15, M. Idzik34, D. Ilin38, P. Ilten65, A. Inglessi38, A.
Ishteev83, K. Ivshin38, R. Jacobsson48, H. Jage14, S. Jakobsen48, E. Jans32,
B.K. Jashal47, A. Jawahery66, V. Jevtic15, X. Jiang4, M. John63, D. Johnson64,
C.R. Jones55, T.P. Jones56, B. Jost48, N. Jurik48, S.H. Kalavan Kadavath34, S.
Kandybei51, Y. Kang3, M. Karacson48, M. Karpov82, J.W. Kautz65, F. Keizer48,
D.M. Keller68, M. Kenzie56, T. Ketel33, B. Khanji15, A. Kharisova84, S.
Kholodenko44, T. Kirn14, V.S. Kirsebom49, O. Kitouni64, S. Klaver32, N.
Kleijne29, K. Klimaszewski36, M.R. Kmiec36, S. Koliiev52, A. Kondybayeva83, A.
Konoplyannikov41, P. Kopciewicz34, R. Kopecna17, P. Koppenburg32, M.
Korolev40, I. Kostiuk32,52, O. Kot52, S. Kotriakhova21,38, P. Kravchenko38, L.
Kravchuk39, R.D. Krawczyk48, M. Kreps56, F. Kress61, S. Kretzschmar14, P.
Krokovny43,v, W. Krupa34, W. Krzemien36, J. Kubat17, M. Kucharczyk35, V.
Kudryavtsev43,v, H.S. Kuindersma32,33, G.J. Kunde67, T. Kvaratskheliya41, D.
Lacarrere48, G. Lafferty62, A. Lai27, A. Lampis27, D. Lancierini50, J.J.
Lane62, R. Lane54, G. Lanfranchi23, C. Langenbruch14, J. Langer15, O.
Lantwin83, T. Latham56, F. Lazzari29,r, R. Le Gac10, S.H. Lee87, R. Lefèvre9,
A. Leflat40, S. Legotin83, O. Leroy10, T. Lesiak35, B. Leverington17, H. Li72,
P. Li17, S. Li7, Y. Li4, Y. Li4, Z. Li68, X. Liang68, T. Lin61, R. Lindner48,
V. Lisovskyi15, R. Litvinov27, G. Liu72, H. Liu6, Q. Liu6, S. Liu4, A. Lobo
Salvia45, A. Loi27, J. Lomba Castro46, I. Longstaff59, J.H. Lopes2, S. Lopez
Solino46, G.H. Lovell55, Y. Lu4, C. Lucarelli22,h, D. Lucchesi28,m, S.
Luchuk39, M. Lucio Martinez32, V. Lukashenko32,52, Y. Luo3, A. Lupato62, E.
Luppi21,g, O. Lupton56, A. Lusiani29,n, X. Lyu6, L. Ma4, R. Ma6, S.
Maccolini20,e, F. Machefert11, F. Maciuc37, V. Macko49, P. Mackowiak15, S.
Maddrell-Mander54, O. Madejczyk34, L.R. Madhan Mohan54, O. Maev38, A.
Maevskiy82, M.W. Majewski34, J.J. Malczewski35, S. Malde63, B. Malecki48, A.
Malinin81, T. Maltsev43,v, H. Malygina17, G. Manca27,f, G. Mancinelli10, D.
Manuzzi20,e, D. Marangotto25,j, J. Maratas9,t, J.F. Marchand8, U. Marconi20,
S. Mariani22,h, C. Marin Benito48, M. Marinangeli49, J. Marks17, A.M.
Marshall54, P.J. Marshall60, G. Martelli78, G. Martellotti30, L.
Martinazzoli48,k, M. Martinelli26,k, D. Martinez Santos46, F. Martinez
Vidal47, A. Massafferri1, M. Materok14, R. Matev48, A. Mathad50, V.
Matiunin41, C. Matteuzzi26, K.R. Mattioli87, A. Mauri32, E. Maurice12, J.
Mauricio45, M. Mazurek48, M. McCann61, L. Mcconnell18, T.H. Mcgrath62, N.T.
Mchugh59, A. McNab62, R. McNulty18, J.V. Mead60, B. Meadows65, G. Meier15, D.
Melnychuk36, S. Meloni26,k, M. Merk32,80, A. Merli25,j, L. Meyer Garcia2, M.
Mikhasenko75,c, D.A. Milanes74, E. Millard56, M. Milovanovic48, M.-N. Minard8,
A. Minotti26,k, L. Minzoni21,g, S.E. Mitchell58, B. Mitreska62, D.S. Mitzel15,
A. Mödden 15, R.A. Mohammed63, R.D. Moise61, S. Mokhnenko82, T. Mombächer46,
I.A. Monroy74, S. Monteil9, M. Morandin28, G. Morello23, M.J. Morello29,n, J.
Moron34, A.B. Morris75, A.G. Morris56, R. Mountain68, H. Mu3, F. Muheim58,48,
M. Mulder79, D. Müller48, K. Müller50, C.H. Murphy63, D. Murray62, R. Murta61,
P. Muzzetto27, P. Naik54, T. Nakada49, R. Nandakumar57, T. Nanut48, I.
Nasteva2, M. Needham58, N. Neri25,j, S. Neubert75, N. Neufeld48, R.
Newcombe61, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S. Nolte64, C.
Normand8, C. Nunez87, A. Oblakowska-Mucha34, V. Obraztsov44, T. Oeser14, D.P.
O’Hanlon54, S. Okamura21, R. Oldeman27,f, F. Oliva58, M.E. Olivares68, C.J.G.
Onderwater79, R.H. O’Neil58, J.M. Otalora Goicochea2, T. Ovsiannikova41, P.
Owen50, A. Oyanguren47, K.O. Padeken75, B. Pagare56, P.R. Pais48, T. Pajero63,
A. Palano19, M. Palutan23, Y. Pan62, G. Panshin84, A. Papanestis57, M.
Pappagallo19,d, L.L. Pappalardo21,g, C. Pappenheimer65, W. Parker66, C.
Parkes62, B. Passalacqua21, G. Passaleva22, A. Pastore19, M. Patel61, C.
Patrignani20,e, C.J. Pawley80, A. Pearce48,57, A. Pellegrino32, M. Pepe
Altarelli48, S. Perazzini20, D. Pereima41, A. Pereiro Castro46, P. Perret9, M.
Petric59,48, K. Petridis54, A. Petrolini24,i, A. Petrov81, S. Petrucci58, M.
Petruzzo25, T.T.H. Pham68, A. Philippov42, R. Piandani6, L. Pica29,n, M.
Piccini78, B. Pietrzyk8, G. Pietrzyk49, M. Pili63, D. Pinci30, F. Pisani48, M.
Pizzichemi26,48,k, Resmi P.K10, V. Placinta37, J. Plews53, M. Plo Casasus46,
F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10, N. Polukhina83,u,
I. Polyakov68, E. Polycarpo2, S. Ponce48, D. Popov6,48, S. Popov42, S.
Poslavskii44, K. Prasanth35, L. Promberger48, C. Prouve46, V. Pugatch52, V.
Puill11, G. Punzi29,o, H. Qi3, W. Qian6, N. Qin3, R. Quagliani49, N.V. Raab18,
R.I. Rabadan Trejo6, B. Rachwal34, J.H. Rademacker54, M. Rama29, M. Ramos
Pernas56, M.S. Rangel2, F. Ratnikov42,82, G. Raven33, M. Reboud8, F. Redi49,
F. Reiss62, C. Remon Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, A.M.
Ricci27, S. Ricciardi57, K. Rinnert60, P. Robbe11, G. Robertson58, A.B.
Rodrigues49, E. Rodrigues60, J.A. Rodriguez Lopez74, E.R.R. Rodriguez
Rodriguez46, A. Rollings63, P. Roloff48, V. Romanovskiy44, M. Romero Lamas46,
A. Romero Vidal46, J.D. Roth87, M. Rotondo23, M.S. Rudolph68, T. Ruf48, R.A.
Ruiz Fernandez46, J. Ruiz Vidal47, A. Ryzhikov82, J. Ryzka34, J.J. Saborido
Silva46, N. Sagidova38, N. Sahoo56, B. Saitta27,f, M. Salomoni48, C. Sanchez
Gras32, R. Santacesaria30, C. Santamarina Rios46, M. Santimaria23, E.
Santovetti31,q, D. Saranin83, G. Sarpis14, M. Sarpis75, A. Sarti30, C.
Satriano30,p, A. Satta31, M. Saur15, D. Savrina41,40, H. Sazak9, L.G.
Scantlebury Smead63, A. Scarabotto13, S. Schael14, S. Scherl60, M. Schiller59,
H. Schindler48, M. Schmelling16, B. Schmidt48, S. Schmitt14, O. Schneider49,
A. Schopper48, M. Schubiger32, S. Schulte49, M.H. Schune11, R. Schwemmer48, B.
Sciascia23,48, S. Sellam46, A. Semennikov41, M. Senghi Soares33, A. Sergi24,i,
N. Serra50, L. Sestini28, A. Seuthe15, Y. Shang5, D.M. Shangase87, M.
Shapkin44, I. Shchemerov83, L. Shchutska49, T. Shears60, L. Shekhtman43,v, Z.
Shen5, S. Sheng4, V. Shevchenko81, E.B. Shields26,k, Y. Shimizu11, E.
Shmanin83, J.D. Shupperd68, B.G. Siddi21, R. Silva Coutinho50, G. Simi28, S.
Simone19,d, N. Skidmore62, T. Skwarnicki68, M.W. Slater53, I. Slazyk21,g, J.C.
Smallwood63, J.G. Smeaton55, A. Smetkina41, E. Smith50, M. Smith61, A.
Snoch32, L. Soares Lavra9, M.D. Sokoloff65, F.J.P. Soler59, A. Solovev38, I.
Solovyev38, F.L. Souza De Almeida2, B. Souza De Paula2, B. Spaan15, E. Spadaro
Norella25,j, P. Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, S.
Stanislaus63, O. Steinkamp50,83, O. Stenyakin44, H. Stevens15, S.
Stone68,48,†, D. Strekalina83, F. Suljik63, J. Sun27, L. Sun73, Y. Sun66, P.
Svihra62, P.N. Swallow53, K. Swientek34, A. Szabelski36, T. Szumlak34, M.
Szymanski48, S. Taneja62, A.R. Tanner54, M.D. Tat63, A. Terentev83, F.
Teubert48, E. Thomas48, D.J.D. Thompson53, K.A. Thomson60, H. Tilquin61, V.
Tisserand9, S. T’Jampens8, M. Tobin4, L. Tomassetti21,g, X. Tong5, D. Torres
Machado1, D.Y. Tou13, E. Trifonova83, S.M. Trilov54, C. Trippl49, G. Tuci6, A.
Tully49, N. Tuning32,48, A. Ukleja36,48, D.J. Unverzagt17, E. Ursov83, A.
Usachov32, A. Ustyuzhanin42,82, U. Uwer17, A. Vagner84, V. Vagnoni20, A.
Valassi48, G. Valenti20, N. Valls Canudas85, M. van Beuzekom32, M. Van Dijk49,
H. Van Hecke67, E. van Herwijnen83, M. van Veghel79, R. Vazquez Gomez45, P.
Vazquez Regueiro46, C. Vázquez Sierra48, S. Vecchi21, J.J. Velthuis54, M.
Veltri22,s, A. Venkateswaran68, M. Veronesi32, M. Vesterinen56, D. Vieira65,
M. Vieites Diaz49, H. Viemann76, X. Vilasis-Cardona85, E. Vilella Figueras60,
A. Villa20, P. Vincent13, F.C. Volle11, D. Vom Bruch10, A. Vorobyev38, V.
Vorobyev43,v, N. Voropaev38, K. Vos80, R. Waldi17, J. Walsh29, C. Wang17, J.
Wang5, J. Wang4, J. Wang3, J. Wang73, M. Wang3, R. Wang54, Y. Wang7, Z.
Wang50, Z. Wang3, Z. Wang6, J.A. Ward56,69, N.K. Watson53, S.G. Weber13, D.
Websdale61, C. Weisser64, B.D.C. Westhenry54, D.J. White62, M. Whitehead54,
A.R. Wiederhold56, D. Wiedner15, G. Wilkinson63, M. Wilkinson68, I.
Williams55, M. Williams64, M.R.J. Williams58, F.F. Wilson57, W. Wislicki36, M.
Witek35, L. Witola17, G. Wormser11, S.A. Wotton55, H. Wu68, K. Wyllie48, Z.
Xiang6, D. Xiao7, Y. Xie7, A. Xu5, J. Xu6, L. Xu3, M. Xu7, Q. Xu6, Z. Xu9, Z.
Xu6, D. Yang3, S. Yang6, Y. Yang6, Z. Yang5, Z. Yang66, Y. Yao68, L.E.
Yeomans60, H. Yin7, J. Yu71, X. Yuan68, O. Yushchenko44, E. Zaffaroni49, M.
Zavertyaev16,u, M. Zdybal35, O. Zenaiev48, M. Zeng3, D. Zhang7, L. Zhang3, S.
Zhang71, S. Zhang5, Y. Zhang5, Y. Zhang63, A. Zharkova83, A. Zhelezov17, Y.
Zheng6, T. Zhou5, X. Zhou6, Y. Zhou6, V. Zhovkovska11, X. Zhu3, X. Zhu7, Z.
Zhu6, V. Zhukov14,40, J.B. Zonneveld58, Q. Zou4, S. Zucchelli20,e, D.
Zuliani28, G. Zunica62.

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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77Eotvos Lorand University, Budapest, Hungary, associated to 48
78INFN Sezione di Perugia, Perugia, Italy, associated to 21
79Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
82National Research University Higher School of Economics, Moscow, Russia,
associated to 42
83National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
85DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
86Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden,
associated to 59
87University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cExcellence Cluster ORIGINS, Munich, Germany
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Firenze, Firenze, Italy
iUniversità di Genova, Genova, Italy
jUniversità degli Studi di Milano, Milano, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Modena e Reggio Emilia, Modena, Italy
mUniversità di Padova, Padova, Italy
nScuola Normale Superiore, Pisa, Italy
oUniversità di Pisa, Pisa, Italy
pUniversità della Basilicata, Potenza, Italy
qUniversità di Roma Tor Vergata, Roma, Italy
rUniversità di Siena, Siena, Italy
sUniversità di Urbino, Urbino, Italy
tMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
†Deceased