EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-101 LHCb-PAPER-2017-009 June 2, 2017

Improved limit on the branching fraction of the rare decay
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$

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

A search for the decay ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ is performed, based on a data sample of proton-
proton collisions corresponding to an integrated luminosity of
$3\,\mbox{\,fb}^{-1}$, collected by the LHCb experiment at centre-of-mass
energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$. The observed yield is
consistent with the background-only hypothesis, yielding a limit on the
branching fraction of ${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})<0.8~{}(1.0)\times 10^{-9}$ at $90\%~{}(95\%)$
confidence level. This result improves the previous upper limit on the
branching fraction by an order of magnitude.

Published in Eur. Phys. J. C

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

##  1 Introduction

In the Standard Model (SM), the unobserved
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ decay
proceeds only through a Flavour-Changing Neutral Current (FCNC) transition,
which cannot occur at tree level. It is further suppressed by the small amount
of $C\\!P$ violation in kaon decays, since the S-wave component of the decay
is forbidden when $C\\!P$ is conserved. In the SM, the decay amplitude is
expected to be dominated by long distance contributions, which can be
constrained using the observed decays ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\\!\rightarrow\gamma\gamma$ and ${{K}^{0}_{\mathrm{\scriptscriptstyle
L}}}\\!\rightarrow{{\pi}^{0}}\gamma\gamma$, leading to the prediction for the
branching fraction ${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})=(5.0\pm 1.5)\times 10^{-12}$ [1, 2]. The
predicted branching fraction for the ${K}^{0}_{\mathrm{\scriptscriptstyle L}}$
decay is $(6.85\pm 0.32)\times 10^{-9}$ [3], in excellent agreement with the
experimental world average ${\mathcal{B}}({{K}^{0}_{\mathrm{\scriptscriptstyle
L}}}\\!\rightarrow{\mu^{+}\mu^{-}})=(6.84\pm 0.11)\times 10^{-9}$ [4]. The
prediction for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ is currently being updated with a dispersive
treatment, which leads to sizeable corrections in other
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ leptonic decays [5].

Due to its suppression in the SM, the ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ decay is sensitive to possible contributions
from dynamics beyond the SM, notably from light scalars with $C\\!P$-violating
Yukawa couplings[1]. Contributions up to one order of magnitude above the SM
branching fraction expectation naturally arise in many models and are
compatible with the present bounds from other FCNC processes [2]. An upper
limit on ${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})$ close to $10^{-11}$ could be translated into
model-independent bounds on the $C\\!P$-violating phase of the
$s\\!\rightarrow d{\ell^{+}}{\ell^{-}}$ amplitude. This would be very useful
to discriminate between scenarios beyond the SM if other modes, such as
${{K}^{+}}\\!\rightarrow{{\pi}^{+}}{\nu}{\overline{\nu}}$, indicate a non-SM
enhancement.

The current experimental limit,
${\mathcal{B}}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})<9\times 10^{-9}$ at $90\%$ confidence level
(CL), was obtained using $pp$ collision data corresponding to
$1.0\,\mbox{\,fb}^{-1}$ of integrated luminosity at a centre-of-mass energy
$\sqrt{s}=7~{}\mathrm{\,Te\kern-1.00006ptV}$, collected with the LHCb detector
in 2011 [6]. This result improved the previous upper limit [7] but is still
three orders of magnitude above the predicted SM level.

In this paper, an update of the search for the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ decay is
reported. Its branching fraction is measured using the known
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decay as
normalisation. The analysis is performed on a data sample corresponding to
$2\,\mbox{\,fb}^{-1}$ of integrated luminosity at
$\sqrt{s}=8~{}\mathrm{\,Te\kern-1.00006ptV}$, collected in 2012, and the
result is combined with that from the previous LHCb analysis [6]. Besides the
gain in statistical precision due to the larger data sample, the sensitivity
is noticeably increased with respect to the previous result due to a higher
trigger efficiency, as well as other improvements to the analysis that are
discussed in the following sections.

An overview on how ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ decays are detected and triggered in LHCb is
given in Sect. 2, while the strategy for this measurement is outlined in Sect.
3. Details of background suppression and the resulting sensitivity are given
in Sects. 4 and 5, respectively. The final result, taking into account the
systematic uncertainties discussed in Sect. 6, is given in Sect. 7.

##  2 ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ decays in LHCb

The LHCb detector [8, 9] 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 locator (VELO) surrounding the
$pp$ interaction region, a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from $0.5\%$ at low
momentum to $1.0\%$ at $200\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The
minimum distance of a track to a primary vertex (PV), the impact parameter
(IP), is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$})\,{\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
(RICH). Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by five stations
which alternate layers of iron and multiwire proportional chambers

The online event selection is performed by a trigger [10], which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a two-step software stage, which applies a full event
reconstruction. Candidates are subsequently classified as TOS, if the event is
triggered on the signal candidate, or TIS, if triggered by other activities in
the detector, independently of signal. Only candidates that are classified as
TOS at each trigger stage are used to search for
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ decays.

The trigger selection constitutes the main limitation to the efficiency for
detecting ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ decays. A muon is only
selected at the hardware stage when it is detected in all muon stations,
implying a momentum larger than about
$5\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and a $p_{\mathrm{T}}$ above
$1.76\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. These thresholds have an
efficiency of order $1\%$ for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ decays.

In the first step of the software trigger, all charged particles with
$\mbox{$p_{\mathrm{T}}$}>500\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ are
reconstructed. At this stage most signal decays are triggered either by
requiring a reconstructed track loosely identified as a muon [10, 11], with
$\text{IP}>0.1\,\mathrm{\,mm}$ and
$\mbox{$p_{\mathrm{T}}$}>1.0\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, or by
finding two oppositely charged muon candidates forming a detached secondary
vertex (SV). Since these two categories, hereafter referred to as TOSμ and
TOSμμ, induce different kinematic biases on the signal and background
candidates, the analysis steps described below are performed independently on
each category. The two categories are made mutually exclusive by applying the
TOSμμ selection only to candidates not already selected by TOSμ.

In the second software trigger stage, an offline-quality event reconstruction
is performed. Signal candidates are selected requiring a dimuon with
$\mbox{$p_{\mathrm{T}}$}>600\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ detached
from the primary vertex, with both tracks having
$\mbox{$p_{\mathrm{T}}$}>300\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. In the
2011 data taking, the dimuon mass was required to be larger than
$1\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ in the second software trigger
stage. This excluded the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ region,
making the use of TIS candidates necessary. Due to the trigger reoptimisation,
no mass requirements were applied during 2012 and a lower $p_{\mathrm{T}}$
threshold for reconstructed tracks was used. According to simulation, these
changes improve the trigger efficiency over the previous analysis [6] by about
a factor $2.5$.

Due to its large and well-known branching fraction and its similar topology,
the ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decay
is taken as the normalisation mode. A large sample of candidates is obtained
from an unbiased trigger, which does not apply any selection requirement.

Despite the low trigger efficiency, the study detailed in this paper profits
from the unprecedented number of ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$
produced at the LHC, $\mathcal{O}(10^{13})$ per $\mbox{\,fb}^{-1}$ of
integrated luminosity within the LHCb acceptance, and from the fact that about
$40\%$ of these ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ decays occur inside
the VELO region. For such decays, the ${K}^{0}_{\mathrm{\scriptscriptstyle
S}}$ invariant mass is reconstructed with a resolution of about
$4\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

The analysis makes use of large samples of simulated collisions containing a
signal decay, or background decays which can be reconstructed as the signal,
and contaminate the $\mu\mu$ invariant mass distribution, such as
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ or
${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\mu^{-}\bar{\nu}_{\mu}$.111The inclusion of charge-
conjugate processes is implied throughout. In the simulation, $pp$ collisions
are generated using Pythia [12, *Sjostrand:2007gs] with a specific LHCb
configuration [14]. Decays of hadronic particles are described by EvtGen [15],
in which final-state radiation is generated using Photos [16]. The interaction
of the generated particles with the detector, and its response, are
implemented using the Geant4 toolkit [17, *Agostinelli:2002hh] as described in
Ref. [19].

##  3 Selection and search strategy

Common offline preselection criteria are applied to
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ and
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$
candidates to cancel many systematic effects in the ratio. Candidates are
required to decay in the VELO region, where the best
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass resolution is achieved. The two
reconstructed tracks must have momentum smaller than
$100\,{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and quality requirements are set
on the track and secondary vertex fits. The SV must be well detached from the
PV by requiring the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ decay time to be
larger than $8.95\,$ps, $10\%$ of the ${K}^{0}_{\mathrm{\scriptscriptstyle
S}}$ mean lifetime. The ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ IP must be
less than $0.4\,\mathrm{\,mm}$, while the two charged tracks are required to
be incompatible with originating from any PV.

Decays of $\mathchar 28931\relax$ baryons to ${p}{{\pi}^{-}}$ are suppressed
by removing candidates close to the expected ellipses in the Armenteros-
Podolanski (AP) plane [20]. In this plane the $p_{\mathrm{T}}$ of the final-
state particles under the pion mass hypothesis is plotted versus the
longitudinal momentum asymmetry, defined as
$\alpha=(p_{L}^{+}-p_{L}^{-})/(p_{L}^{+}+p_{L}^{-})$, where $p_{L}^{\pm}$ is
the longitudinal momentum of the charged tracks. Both $p_{\mathrm{T}}$ and
$p_{L}$ are considered with respect to the direction of the mother particle.
The ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ decays are symmetrically
distributed on the AP plane while $\mathchar 28931\relax$ decays produce two
ellipses at low $p_{\mathrm{T}}$ and $|\alpha|\sim 0.7$. A kaon veto, based on
the response of the RICH detector, is used to suppress
${{K}^{*0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}$ decays and other possible final
states including a charged kaon.

The preselection reduces the combinatorial background, arising from candidates
formed from secondary hadronic collisions in the detector material or from
spurious reconstructed SV. The purity of the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ sample
used for normalisation, whose mass distribution is shown in Fig. 1, is
estimated from a fit to the mass spectrum to be $99.8\%$. The fraction of
events with more than one candidate is less than $0.1\%$ for signal and $4\%$
for the normalisation channel, and all candidates are retained. Additional
discrimination against backgrounds for the signal mode is achieved through the
use of two multivariate discriminants. The first is designed to further
suppress combinatorial background, and the second to reduce the number of
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decays in
which both pions are misidentified as muons.

After requirements on the output of these discriminants have been applied, the
number of signal candidates is obtained by fitting the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ mass
spectrum. The mass sidebands provide a data-driven estimation of the residual
background by extrapolation into the signal region. The number of candidates
is converted into a branching fraction using the yield of the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$
normalisation mode, and the estimated relative efficiency. Events in the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass region are scrutinised only
after fixing the analysis strategy.

##  4 Backgrounds

The ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$
sample contains two main sources of background. Combinatorial background
candidates are expected to exhibit a smooth mass distribution, and can
therefore be estimated from the sidebands. The other relevant source of
background is due to ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays where both pions pass the loose muon
identification requirements after the trigger stage. This can be due either to
${{\pi}^{+}}\\!\rightarrow{\mu^{+}}{{\nu}_{\mu}}$ decays or to random
association of muon detector hits with the pion trajectory. In such cases the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass, reconstructed with a wrong
mass hypothesis for the final-state particles, is underestimated by
$39\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ on average, as shown in Fig. 1.
Despite the excellent mass resolution, the right-hand tail of the
reconstructed mass distribution under the dimuon hypothesis extends into the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ signal mass range and, given the
large branching fraction of the ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ mode, constitutes a nonnegligible background.
Two multivariate discriminants, based on a Boosted Decision Tree (BDT)
algorithm [21, 22], are applied on the preselected candidates to improve the
signal discrimination with respect to these backgrounds.

Figure 1: Reconstructed mass for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays in trigger-unbiased events, computed
assuming the muon (dashed red line) or pion (solid blue line) mass for the
final-state tracks. Candidates satisfy the selection criteria described in the
text.

The first discriminant, named hereafter $\text{BDT}_{\rm cb}$, aims to reduce
the combinatorial background, exploiting the different decay topologies,
kinematic spectra and reconstruction qualities of signal and combinatorial
candidates. It is optimised separately for each trigger category. A set of ten
input variables is used in $\text{BDT}_{\rm cb}$: the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ $p_{\mathrm{T}}$ and IP, the minimum
IP of the two charged tracks, the angle between the positively charged final-
state particle and the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ flight
direction in the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ rest frame, the
$\chi^{2}$ of the SV fit, the distance of closest approach between the two
tracks, an SV isolation variable, defined as the difference in vertex-fit
$\chi^{2}$ when the next nearest track is included in the vertex fit, and the
SV absolute position coordinates. The SV position is particularly important,
since a large fraction of the background is found to originate from
interactions in the detector material. This set of variables does not
distinguish between ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ and ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays as it does not contain quantities
related to muon identification and ignores the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ candidate invariant mass
distribution.

The signal training sample for $\text{BDT}_{\rm cb}$ is composed of
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ simulated
candidates passing the trigger and preselection criteria. A signal training
sample consisting of ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays in data is also used as a cross-check,
as explained in Sect. 6. The background training sample is made from
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ data
candidates surviving the trigger and preselection requirements with
reconstructed mass in the range
$[520,600]\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Since candidates in the
same mass region are also used to estimate the residual background, the
training is performed using a k-fold cross-validation technique [23] to avoid
any possible effect of overtraining.

A loose requirement on the $\text{BDT}_{\rm cb}$ output is applied to suppress
the combinatorial background. The cut is chosen to remove 99% of the
background training candidates. The corresponding signal efficiency is about
$56\%$ and $66\%$ for the TOSμ and TOSμμ trigger categories, respectively. To
exploit further the information provided by the discriminant, the candidates
surviving this requirement are allocated to ten bins according to their
$\text{BDT}_{\rm cb}$ value, with bounds defined in order to have
approximately equal population of signal training candidates in each bin.

The background from misidentified ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays is further reduced with the second
multivariate discriminant, called $\text{BDT}_{\mu}$. Its input includes the
position, time and number of detector hits around the extrapolated track
position to each muon detector station, a global match $\chi^{2}$ between the
muon hit positions and the track extrapolation, and other variables related to
the tracking and the response of the RICH and calorimeter detectors.

To train the $\text{BDT}_{\mu}$ discriminant, highly pure samples of $1.2$
million pions and $0.68$ million muons are obtained from TIS-triggered
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ and
$B^{+}\rightarrow J/\psi K^{+}$ decays, respectively. In the latter case, a
probe muon from the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ is required
to be TIS at all trigger stages, while stringent muon identification
requirements are set on the other muon, reaching an estimated purity for muons
above $99.9\%$. Before using it in the $\text{BDT}_{\mu}$ training, the muon
sample is weighted to have the same two-dimensional distribution in $p$ and
$p_{\mathrm{T}}$ as the pion sample, as well as the same distribution of
number of tracks in the event. This is to prevent the $\text{BDT}_{\mu}$ from
discriminating pions and muons using these variables, which are included in
the input because of their strong correlation with the identification
variables. Weighting also allows optimisation of the discrimination power for
the kinematic spectrum relevant to this search.

The level of misidentification of the discriminant for a pion from
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decay is
found to be $0.4\%$ for $90\%$ muon efficiency. This reduces the level of
double misidentification background, for a given efficiency, by about a factor
of four with respect to the discriminant used in the previous publication [6],
which was not tuned specifically for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ searches.

The $\text{BDT}_{\mu}$ discriminant is trained using half of the
$B^{+}\rightarrow J/\psi K^{+}$ sample, while the other half is used to
evaluate the muon identification efficiency as a function of ($p$,
$p_{\mathrm{T}}$). These values are used to compute the efficiency of a
$\text{BDT}_{\mu}$ requirement on the candidate
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ decays
after selection and trigger requirements, in each bin of the $\text{BDT}_{\rm
cb}$ discriminant. The muon spectra assumed in this calculation are obtained
from simulated decays, weighted to better reproduce the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ $p_{\mathrm{T}}$ spectrum observed
in ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$
candidates.

The $\text{BDT}_{\mu}$ requirement on the signal candidates is optimised by
maximising the figure of merit [24] $\epsilon_{\mu{\rm{ID}}}/(\sqrt{N_{\rm
bg}}+a/2)$, with $a=3$, where $\epsilon_{\mu{\rm{ID}}}$ is the signal
efficiency and $N_{\rm bg}$ the expected background yield. The latter is
estimated from a fit to the mass distribution, after removing candidates in
the range $[492,504]\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass, and extrapolating the result
into the signal region. This optimisation is performed independently for the
two trigger categories, with no significant difference found as a function of
the $\text{BDT}_{\rm cb}$ bin. The optimal threshold corresponds to a signal
efficiency of $\epsilon_{\mu{\rm{ID}}}\sim 98\%$ in both cases.

Other possible sources of background have been explored and found to give
negligible contribution to this search. The irreducible background due to
${{K}^{0}_{\mathrm{\scriptscriptstyle L}}}\\!\rightarrow{\mu^{+}\mu^{-}}$
decays and from ${K}^{0}_{\mathrm{\scriptscriptstyle
S}}$–${K}^{0}_{\mathrm{\scriptscriptstyle L}}$ interference is evaluated from
the known ${{K}^{0}_{\mathrm{\scriptscriptstyle L}}}\rightarrow\mu^{+}\mu^{-}$
branching fraction and lifetime, and by studying the decay-time dependence of
the selection efficiency for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays in data. The yield from this background
becomes comparable to the signal for a branching fraction lower than $2\times
10^{-11}$, which is well below the sensitivity of this search.

Semileptonic ${{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{0}}\\!\rightarrow{{\pi}^{+}}{\mu^{-}}{{\overline{\nu}}_{\mu}}$
decays with pion misidentification provide another possible source of
background. Simulated events, where the pion is forced to decay to $\mu\nu$
within the detector, are used to determine the efficiency of the offline
selection requirements. No event survives the trigger selection. Under the
very conservative hypothesis that the trigger efficiency is the same as in
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ decays,
the expected yields from both ${K}^{0}_{\mathrm{\scriptscriptstyle L}}$ and
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ semileptonic decays are negligible.

Decays including a dimuon from resonances, like
$\omega\\!\rightarrow{{\pi}^{0}}{\mu^{+}\mu^{-}}$ and
$\eta\\!\rightarrow{\mu^{+}\mu^{-}}\gamma$, do not produce peaking structures
in the mass distribution, and are accounted for in the combinatorial
background.

##  5 Search sensitivity

The observed number of ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ candidates is converted into a branching
fraction using the normalisation mode and its precisely known branching
fraction ${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-})=0.6920\pm 0.0005$ [4]. The computation is made
in every $\text{BDT}_{\rm cb}$ bin $i$ and trigger category $j$ as follows

${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})={\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-})\cdot\frac{\epsilon^{\pi\pi}}{\epsilon^{\mu\mu}_{ij}}\cdot\frac{N^{\mu\mu}_{ij}}{N^{\pi\pi}}\equiv\alpha_{ij}N^{\mu\mu}_{ij},$
(1)

where $N^{\mu\mu}_{ij}$ and $N^{\pi\pi}$ denote the background-subtracted
yields for the signal and normalisation modes, respectively. The total
selection efficiencies $\epsilon$ can be factorised as

$\frac{\epsilon^{\pi\pi}}{\epsilon^{\mu\mu}_{ij}}=\frac{\epsilon^{\pi\pi}_{\rm{sel}}}{\epsilon^{\mu\mu}_{\rm{sel}}}\times\frac{\epsilon^{\pi\pi}_{{\rm{trig}}}}{\epsilon^{\mu\mu}_{{\rm{trig}};j}}\times\frac{1}{\epsilon^{\mu\mu}_{{\text{BDT}};ij}}\times\frac{1}{\epsilon_{\mu{\rm{ID}};ij}}.$
(2)

The first factor refers to the offline selection requirements, which are
applied identically to both modes and cancel to first order in the ratio; the
residual difference is mainly due to the different interaction cross-sections
for pions and muons with the detector material, and is estimated from
simulation. The second factor is the ratio of trigger efficiencies; the
efficiency for the signal is determined from simulation, with its systematic
uncertainty estimated from data-driven checks, while that for the
normalisation mode is the efficiency of the random trigger used to select
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$,
$(9.38\pm 1.01)\times 10^{-8}$. The third factor reflects the fraction of
candidates in each $\text{BDT}_{\rm cb}$ bin, and is also determined from
simulation. Finally, the efficiency of the $\text{BDT}_{\mu}$ requirement is
obtained from the $B^{+}\rightarrow J/\psi K^{+}$ calibration sample described
in Sect. 4, for each $\text{BDT}_{\rm cb}$ bin and trigger category.

To account for the difference between the kaon $p_{\mathrm{T}}$ spectra
observed in the ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays in data and simulation, all efficiencies
obtained from simulation are computed in six roughly equally populated
$p_{\mathrm{T}}$ bins. A weighted average of the efficiencies is then
performed, where the weights are determined from the yields in each bin
observed in data for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ candidates.

The resulting values for the single candidate sensitivity $\alpha_{ij}$ are
reported in Table 1. The quoted uncertainties are statistical only. They are
separated between the uncertainty on $\epsilon^{\mu\mu}_{{\text{BDT}};ij}$,
due to the limited statistics of simulated data and uncorrelated among
$\text{BDT}_{\rm cb}$ bins, and all the other statistical uncertainties, which
are conservatively considered as fully correlated among bins within the same
trigger category. Table 1 also presents the number of candidates after the
inspection of the signal region. The separation between signal and background
is presented in Sect. 7.

Table 1: Values of the single candidate sensitivity $\alpha_{ij}$ and the number of candidates $N^{K}_{ij}$ compatible with the ${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass (reconstructed mass in the range $[492,504]\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$), for each $\text{BDT}_{\rm cb}$ bin $i$ and trigger category $j$. Only statistical uncertainties are given. The first uncertainty is uncorrelated, while the second is fully correlated among the $\text{BDT}_{\rm cb}$ bins of the same trigger category.  Bin $i$ | $\alpha_{i\text{TOS}_{\mu}}(\times 10^{-10})$ | $\alpha_{i\text{TOS}_{\mu\mu}}(\times 10^{-9})$ | $N^{K}_{i\text{TOS}_{\mu}}$ | $N^{K}_{i\text{TOS}_{\mu\mu}}$
---|---|---|---|---
1 | $7.48\pm 0.84\pm 0.16$ | $5.30\pm 0.72\pm 0.12$ | 49 | 13
2 | $7.72\pm 0.87\pm 0.17$ | $4.71\pm 0.63\pm 0.10$ | 28 | 9
3 | $7.85\pm 0.89\pm 0.18$ | $4.88\pm 0.65\pm 0.11$ | 9 | 14
4 | $7.93\pm 0.89\pm 0.19$ | $4.66\pm 0.62\pm 0.10$ | 18 | 10
5 | $7.53\pm 0.85\pm 0.18$ | $4.65\pm 0.61\pm 0.10$ | 6 | 3
6 | $7.78\pm 0.88\pm 0.19$ | $4.95\pm 0.66\pm 0.11$ | 2 | 2
7 | $7.56\pm 0.85\pm 0.19$ | $4.60\pm 0.61\pm 0.10$ | 3 | 1
8 | $7.90\pm 0.89\pm 0.19$ | $5.00\pm 0.67\pm 0.11$ | 2 | 1
9 | $7.81\pm 0.88\pm 0.18$ | $4.72\pm 0.63\pm 0.11$ | 1 | 1
10 | $7.75\pm 0.87\pm 0.17$ | $4.66\pm 0.62\pm 0.11$ | 0 | 0

##  6 Systematic uncertainties

Several systematic effects, summarised in Table 2, contribute to the
uncertainty on the normalisation factors. Tracking efficiencies are not
perfectly reproduced in simulated events. Corrections based on a
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$
data control sample are determined as a function of the muon $p$ and $\eta$.
The average effect of these corrections on the ratio $\epsilon^{\pi\pi}_{\rm
sel}/\epsilon^{\mu\mu}_{\rm sel}$ and its standard deviation, added in
quadrature, leads to a systematic uncertainty of $0.4\%$.

The distributions of all variables relevant to the selection are compared in
data and simulation for ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays. The largest differences are found in
the kaon $p_{\mathrm{T}}$ and its decay vertex radial position. The effect on
$\epsilon^{\pi\pi}_{\rm sel}/\epsilon^{\mu\mu}_{\rm sel}$ of applying a two-
dimensional weight to account for these discrepancies is taken as a systematic
uncertainty, and amounts to a relative $1.9\%$ and $1.8\%$ for the TOSμ and
TOSμμ trigger categories, respectively.

The difference between data and simulation in the kaon $p_{\mathrm{T}}$
spectrum could also affect the other factors in the computation of
$\alpha_{ij}$. An additional uncertainty is assigned by repeating the whole
calculation with a finer binning in $p_{\mathrm{T}}$. Due to the limited size
of the data samples, this is possible only in the TOSμ category. The average
relative change in $\alpha_{ij}$, $4.3\%$, is assigned as an uncertainty for
the TOSμμ category.

A specific cross-check is performed to validate the efficiencies predicted by
the simulation for the $\text{BDT}_{\rm cb}$ requirements. An alternative
discriminant is made using a signal training sample consisting of trigger-
unbiased ${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$
decays, selected with additional kinematic criteria which mimic the effect of
the muon trigger selections. The distributions of this alternative
discriminant in data and simulation are found to agree within the statistical
uncertainty, and no systematic uncertainty is assigned.

The uncertainty due to the simulation of TOS selections in the first two
trigger stages is assessed by comparing the trigger efficiency in simulation
and data, using a control sample of
${{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ decays. The resulting relative differences, $8.1\%$ for TOSμ
and $11.5\%$ for TOSμμ, are assigned as systematic uncertainties. No
uncertainty is considered for the selection in the last trigger stage, which
is based on the same offline kinematic variables used in the selection, for
which a systematic uncertainty is already assigned.

The uncertainty on $\epsilon_{\mu{\rm{ID}};ij}$ is estimated from half the
difference between the values obtained with and without the weighting of the
${{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ sample used in the determination of the muon identification
efficiency. This results in an uncertainty of 0.2% and 0.3% for the TOSμ and
TOSμμ categories, respectively, which is comparable to the statistical
uncertainties on these efficiencies due to the limited size of the
${{B}^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ samples.

Systematic uncertainties on the signal yields $N^{\mu\mu}_{ij}$ are related to
the assumed models for the reconstructed ${K}^{0}_{\mathrm{\scriptscriptstyle
S}}$ mass distribution, determined from simulation. Possible discrepancies
from the shape in data are estimated by comparing the shape of the invariant
mass distribution in data and simulation for
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\pi^{+}\pi^{-}$ decays,
leading to a relative $0.8\%$ systematic uncertainty on the signal yield. The
final fit for the determination of the branching fraction is performed with
two different background models, as discussed in Sect. 7. This leads to a
relative variation on the branching fraction of 0.9%, which is assigned as a
systematic uncertainty.

Table 2: Relevant systematic uncertainties on the branching fraction. They are separated, using horizontal lines, into relative uncertainties on (i) $\alpha_{ij}$, (ii) on the signal yield from the signal model used in the mass fit, and (iii) on the branching fraction, obtained combining the two categories, from the background model. Source | TOSμ | TOSμμ
---|---|---
Tracking | $0.4\%$ | $0.4\%$
Selection | $1.9\%$ | $1.8\%$
Trigger | $8.1\%$ | $11.5\%$
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ $p_{\mathrm{T}}$ spectrum | $4.3\%$ | $4.3\%$
Muon identification | $0.2\%$ | $0.3\%$
Signal mass shape | $0.8\%$ | $0.8\%$
Background shape | $0.9\%$

##  7 Results

The $\mu^{+}\mu^{-}$ mass distribution of the signal candidates is fitted in
the range $[470,600]\,{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ to determine
the signal and background yield in each trigger category and $\text{BDT}_{\rm
cb}$ bin. The model chosen for the signal is a Hypatia distribution [25], the
parameters of which are determined from simulation and fixed in the fit to
data. In the background model, a power law function describes the tail of the
double-misidentification background from ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ decays, affecting the mass region below the
${K}^{0}_{\mathrm{\scriptscriptstyle S}}$ mass, while the combinatorial
background mass distribution is described by an exponential function. The
background model is validated on simulation, and its parameters are left free
in the fit to data to account for possible discrepancies. An alternative
combinatorial background shape, based on a linear function, is used instead of
the exponential function to determine a systematic uncertainty due to the
choice of the background shape. The normalisation channel candidates within
the mass region $[460,\,530]\,$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are
counted, leading to $N({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-})=70\,318\pm 265$. The $\mu^{+}\mu^{-}$ invariant
mass distributions for the two highest $\text{BDT}_{\rm cb}$ bins, which
exhibit the best signal-to-background ratio and therefore the best sensitivity
for a discovery, are shown in Fig. 2.

A simultaneous maximum likelihood fit to the dimuon mass in all
$\text{BDT}_{\rm cb}$ bins is performed, using the values of $\alpha_{ij}$
given in Table 1, to determine the branching fraction. The quoted systematic
uncertainties are included in the likelihood computation as nuisance
parameters with Gaussian uncertainties. A posterior probability is obtained by
multiplying the likelihood by a prior density computed from the result based
on the 2011 data sample. Limits are obtained by integrating $90\%~{}(95\%)$ of
the area of the posterior probability distribution provided by the fit, as
shown in Fig. 3. Due to the much larger sensitivity achieved with the 2012
data, the inclusion of the 2011 data result does not have a significant effect
on the final limit, and a uniform prior would have provided very similar
results.

In conclusion, a search for the ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-}$ decay based on a data sample corresponding to
an integrated luminosity of $3\,\mbox{\,fb}^{-1}$ of proton-proton collisions,
collected by the LHCb experiment at centre-of-mass energies $\sqrt{s}=7$ and
8$\mathrm{\,Te\kern-1.00006ptV}$, allows upper limits to be set on the
branching fraction

${\cal B}({{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\mu^{+}\mu^{-})<0.8~{}(1.0)\times
10^{-9}~{}\text{at}~{}90\%~{}(95\%)~{}\text{CL}.$

This result supersedes the previous upper limit published by LHCb [6], and
represents a factor 11 improvement.

(a)  (b)  (c)  (d)

Figure 2: Fits to the reconstructed kaon mass distributions, for the two most
sensitive $\text{BDT}_{\rm cb}$ bins in the two trigger categories, TOSμ and
TOSμμ. The fitted model is shown as the solid blue line, while the
combinatorial background and ${{K}^{0}_{\mathrm{\scriptscriptstyle
S}}}\rightarrow\pi^{+}\pi^{-}$ double misidentification are overlaid with
dotted red and dashed green lines, respectively. For each fit, the pulls are
shown on the lower smaller plots.

Figure 3: Confidence level of exclusion for each value of the
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}\rightarrow\mu^{+}\mu^{-}$ branching
fraction. The regions corresponding to $90\%$ and $95\%$ CL are emphasised in
green (dark shading) and yellow (light shading), respectively.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing
resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany),
INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),
RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF
(Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities
behind the multiple open source software packages on which we depend.
Individual groups or members have received support from AvH Foundation
(Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne
(France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain),
Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of
1851 and the Leverhulme Trust (United Kingdom).

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Placinta30, S. Playfer52, M. Plo Casasus39, T. Poikela40, F. Polci8, M. Poli
Lener19, A. Poluektov50,36, I. Polyakov61, E. Polycarpo2, G.J. Pomery48, S.
Ponce40, A. Popov37, D. Popov11,40, B. Popovici30, S. Poslavskii37, C.
Potterat2, E. Price48, J. Prisciandaro39, C. Prouve48, V. Pugatch46, A. Puig
Navarro42, G. Punzi24,p, W. Qian50, R. Quagliani7,48, B. Rachwal28, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F.
Ratnikov35, G. Raven44, F. Redi55, S. Reichert10, A.C. dos Reis1, C. Remon
Alepuz69, V. Renaudin7, S. Ricciardi51, S. Richards48, M. Rihl40, K.
Rinnert54, V. Rives Molina38, P. Robbe7, A.B. Rodrigues1, E. Rodrigues59, J.A.
Rodriguez Lopez66, P. Rodriguez Perez56,†, A. Rogozhnikov35, S. Roiser40, A.
Rollings57, V. Romanovskiy37, A. Romero Vidal39, J.W. Ronayne13, M. Rotondo19,
M.S. Rudolph61, T. Ruf40, P. Ruiz Valls69, J.J. Saborido Silva39, E.
Sadykhov32, N. Sagidova31, B. Saitta16,f, V. Salustino Guimaraes1, C. Sanchez
Mayordomo69, B. Sanmartin Sedes39, R. Santacesaria26, C. Santamarina Rios39,
M. Santimaria19, E. Santovetti25,j, A. Sarti19,k, C. Satriano26,s, A. Satta25,
D.M. Saunders48, D. Savrina32,33, S. Schael9, M. Schellenberg10, M.
Schiller53, H. Schindler40, M. Schlupp10, M. Schmelling11, T. Schmelzer10, B.
Schmidt40, O. Schneider41, A. Schopper40, H.F. Schreiner59, K. Schubert10, M.
Schubiger41, M.-H. Schune7, R. Schwemmer40, B. Sciascia19, A. Sciubba26,k, A.
Semennikov32, A. Sergi47, N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert21,
M. Shapkin37, I. Shapoval45, Y. Shcheglov31, T. Shears54, L. Shekhtman36,w, V.
Shevchenko68, B.G. Siddi17,40, R. Silva Coutinho42, L. Silva de Oliveira2, G.
Simi23,o, S. Simone14,d, M. Sirendi49, N. Skidmore48, T. Skwarnicki61, E.
Smith55, I.T. Smith52, J. Smith49, M. Smith55, l. Soares Lavra1, M.D.
Sokoloff59, F.J.P. Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, S.
Sridharan40, F. Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55,
O. Steinkamp42, S. Stemmle12, O. Stenyakin37, H. Stevens10, S. Stoica30, S.
Stone61, B. Storaci42, S. Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U.
Straumann42, L. Sun64, W. Sutcliffe55, K. Swientek28, V. Syropoulos44, M.
Szczekowski29, T. Szumlak28, S. T’Jampens4, A. Tayduganov6, T. Tekampe10, G.
Tellarini17,g, F. Teubert40, E. Thomas40, J. van Tilburg43, M.J. Tilley55, V.
Tisserand4, M. Tobin41, S. Tolk49, L. Tomassetti17,g, D. Tonelli24, F.
Toriello61, R. Tourinho Jadallah Aoude1, E. Tournefier4, S. Tourneur41, K.
Trabelsi41, M. Traill53, M.T. Tran41, M. Tresch42, A. Trisovic40, A.
Tsaregorodtsev6, P. Tsopelas43, A. Tully49, N. Tuning43,40, A. Ukleja29, A.
Ustyuzhanin35, U. Uwer12, C. Vacca16,f, V. Vagnoni15,40, A. Valassi40, S.
Valat40, G. Valenti15, R. Vazquez Gomez19, P. Vazquez Regueiro39, S. Vecchi17,
M. van Veghel43, J.J. Velthuis48, M. Veltri18,r, G. Veneziano57, A.
Venkateswaran61, T.A. Verlage9, M. Vernet5, M. Vesterinen12, J.V. Viana
Barbosa40, B. Viaud7, D. Vieira63, M. Vieites Diaz39, H. Viemann67, X.
Vilasis-Cardona38,m, M. Vitti49, V. Volkov33, A. Vollhardt42, B. Voneki40, A.
Vorobyev31, V. Vorobyev36,w, C. Voß9, J.A. de Vries43, C. Vázquez Sierra39, R.
Waldi67, C. Wallace50, R. Wallace13, J. Walsh24, J. Wang61, D.R. Ward49, H.M.
Wark54, N.K. Watson47, D. Websdale55, A. Weiden42, M. Whitehead40, J. Wicht50,
G. Wilkinson57,40, M. Wilkinson61, M. Williams56, M.P. Williams47, M.
Williams58, T. Williams47, F.F. Wilson51, J. Wimberley60, M. Winn7, J.
Wishahi10, W. Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton49, K.
Wraight53, K. Wyllie40, Y. Xie65, Z. Xu4, Z. Yang3, Z. Yang60, Y. Yao61, H.
Yin65, J. Yu65, X. Yuan61, O. Yushchenko37, K.A. Zarebski47, M.
Zavertyaev11,c, L. Zhang3, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V.
Zhukov33, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Universita & INFN, Milano-Bicocca, Milano, Italy
22Sezione di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
70Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

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


# Masked Face Recognition Challenge: The InsightFace Track Report

Jiankang Deng
Imperial College London
<EMAIL_ADDRESS>Jia Guo
InsightFace
<EMAIL_ADDRESS>Xiang An
InsightFace
<EMAIL_ADDRESS>Zheng Zhu
Tsinghua University
<EMAIL_ADDRESS>Stefanos Zafeiriou
Imperial College London
<EMAIL_ADDRESS>
###### Abstract

During the COVID-19 coronavirus epidemic, almost everyone wears a facial mask,
which poses a huge challenge to deep face recognition. In this workshop, we
organize Masked Face Recognition (MFR) challenge
111https://ibug.doc.ic.ac.uk/resources/masked-face-recognition-challenge-
workshop-iccv-21/ and focus on bench-marking deep face recognition methods
under the existence of facial masks. In the MFR challenge, there are two main
tracks: the InsightFace track and the WebFace260M track [38]. For the
InsightFace track, we manually collect a large-scale masked face test set with
7K identities. In addition, we also collect a children test set including 14K
identities and a multi-racial test set containing 242K identities. By using
these three test sets, we build up an online model testing system, which can
give a comprehensive evaluation of face recognition models. To avoid data
privacy problems, no test image is released to the public. As the challenge is
still under-going, we will keep on updating the top-ranked solutions as well
as this report on the arxiv.

##  1 Introduction

Recently, great progress has been achieved in face recognition with large-
scale training data [14, 24, 1, 39], sophisticated network structures [26, 16]
and advanced loss designs [28, 29, 26, 25, 8, 20, 31, 30, 4, 3, 18, 6].
However, existing face recognition systems are presented with mostly non-
occluded faces, which include primary facial features such as the eyes, nose,
and mouth. During the COVID-19 coronavirus epidemic, almost everyone wears a
facial mask, which poses a huge challenge to existing face recognition
systems. Traditional face recognition systems may not effectively recognize
the masked faces, but removing the mask for authentication will increase the
risk of virus infection.

To cope with the above-mentioned challenging scenarios arising from wearing
facial masks, it is crucial to improve the existing face recognition
approaches222https://pages.nist.gov/frvt/html/frvt_facemask.html. Generally,
there are two kinds of methods to overcome masked face recognition: (1)
recovering unmasked faces for feature extraction and (2) producing direct
occlusion-robust face feature embedding from masked face images.

Based on Generative Adversarial Network (GAN) [13], there are many identity-
preserved masked face restoration methods [9, 11]. In [9], masked face images
are first segmented and then impainted with fine facial details while
retaining the global coherency of face structure. Ge _et al_. [11] propose
identity-preserved inpainting to facilitate occluded face recognition. The
core idea is integrating GAN with an optimized pre-trained CNN model which
serves as the third player to compete with the generator by enabling the
inpainted faces to be close to their identity centers.

Since occlusion recovery methods [9, 11] are more complicated to set up the
online evaluation toolkit, we focus on occlusion-robust face feature embedding
in this challenge. In [36], a new partial face recognition approach is
proposed by using local texture set matching to recognize persons of interest
from their partial faces. In [15], a masked-aware face feature embedding is
proposed by extracting deep features from the unmasked regions (mostly eyes
and forehead regions). In [22], masked face augmentation and extra mask-usage
classification loss is proposed to train mask robust facial feature embedding.
In [19, 35], visual attention mechanism is employed to enhance feature
learning from non-occluded face regions.

Even though there are some existing explorations for occluded (masked) face
recognition, there is yet no publicly available large-scale masked face
recognition benchmark due to the sudden outbreak of the epidemic. In this
report, we make a significant step further and propose a new comprehensive
benchmark for masked face recognition as well as non-masked face recognition.
To this end, we have collected a real-world masked test set, children test
set, multi-racial test set (_i.e_. African, Caucasian, South Asian and East
Asian [37, 12, 34, 33]). We define different sub-tracks with fixed training
data, and each sub-track has strict constraints on computational complexity
and model size. Therefore, the performance comparison between different models
can be fair.

By using the proposed test data, we organized the InsightFace track in Masked
Face Recognition Challenge (ICCV 2021). This report presents the details of
this track, including the training data, the test set, evaluation protocols,
baseline solutions, performance analysis of the top-ranked submissions
received as part of the competition, and effective strategies for masked face
recognition. The report of another WebFace260M track is available in [38].

##  2 Datasets of InsightFace Track

###  2.1 Training Dataset

As given in Tab. 1, we employ two existing datasets (_i.e_. MS1M [14] and
Glint360K [1]) as the training data.

MS1M: The MS1M training dataset is cleaned from the MS-Celeb-1M [14] dataset.
All face images are pre-processed to the size of $112\times 112$ by the five
facial landmarks predicted by RetinaFace [5]. Then, a semi-automatic
refinement is conducted by employing the pre-trained ArcFace [4] model and
ethnicity-specific annotators [7]. Finally, the refined MS1M dataset contains
5.1M images of 93K identities.

Glint360K: The Glint360K training dataset is cleaned from the MS-Celeb-1M [14]
and Celeb-500k [2] datasets. All face images are downloaded from the Internet
and pre-processed to the size of $112\times 112$ by the five facial landmarks
predicted by RetinaFace [5]. Then, an automatic refinement is conducted by
employing the pre-trained ArcFace [4] model for intra-class and inter-class
cleaning. Finally, the released Glint360K dataset contains 17M images of 360K
individuals, which is one of the largest and cleanest training datasets [39]
in academia.

Dataset | # Identities | # Images
---|---|---
MS1M | 93K | 5.1M
Glint360K | 360K | 17M
Table 1: Statistics of the training data of the masked face recognition
challenge (the InsightFace track).

The training data (_i.e_. MS1M and Glint360K) are fixed to facilitate
performance reproduction and fair comparison. Detailed requirements:

  * •

No external dataset is allowed and no pre-trained model is allowed.

  * •

All participants must use the predefined training dataset for a particular
challenge track. Data augmentation for the facial mask is allowed but the
augmentation method needs to be reproducible.

| # Identities | # Images | # Positive Pairs | # Negative Pairs
---|---|---|---|---
Masked Test Set | 6,964 | 20,892 | 13,928 | 96,983,824
Children Test Set | 14,344 | 157,280 | 1,773,428 | 24,735,067,692
Multi-racial Test Set | 242,143 | 1,624,305 | 4,689,037 | 2,638,360,419,683
African | 43,874 | 298,010 | 870,091 | 88,808,791,999
Caucasian | 103,293 | 697,245 | 2,024,609 | 486,147,868,171
South Asian | 35,086 | 237,080 | 688,259 | 56,206,001,061
East Asian | 59,890 | 391,970 | 1,106,078 | 153,638,982,852
Table 2: Statistics of the test sets of the masked face recognition challenge
(the InsightFace track).

(a) Masked Test Set

(b) Children Test Set

(c) Multi-racial Test Set

Figure 1: Exemplar blurred face images of Masked Test Set, Children Test Set
and Multi-racial Test Set (_i.e_. African, Caucasian, South Asian, East
Asian). To ensure data privacy, we intentionally decrease the quality of the
exemplar facial images. On our test server, all of the test images are still
in high quality.

###  2.2 Test Dataset

As shown in Tab. 2 and Fig. 1, we manually collected the following three test
sets for the comprehensive evaluation of different algorithms. Unlike existing
face recognition test sets (_e.g_. LFW [17], CFP-FP [27], AgeDB [23], and
IJB-C [21]), our test sets are not collected from celebrities, thus we can
naturally avoid the identity-overlapping problem. The pre-processing step for
the test set is the same as that on the training data. All of the faces are
normalized into $112\times 112$ by using RetinaFace [5]. We also employ a
semi-automatic method to strictly ensure that (1) most of the test sets are
noise-free and (2) there is no identity overlap between our training data and
the test set.

Masked Test Set: The masked test set contains 6,964 masked facial images and
13,928 non-masked facial images of 6,964 identities. In total, there are
13,928 positive pairs and 96,983,824 negative pairs for the verification
evaluation.

Children Test Set: The children test set contains 157,280 images of 14,344
identities aging between 2 and 16. There are totally 1,773,428 positive pairs
and 24,735,067,692 negative pairs for the verification evaluation.

Multi-racial Test Set: Participants will also have their algorithms tested on
the multi-racial test set for fairly evaluating the performance on different
demographic groups. The multi-racial test set consists of four demographic
groups 333Here, we refer to the NIST standard:
https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8280.pdf: African,
Caucasian, South Asian and East Asian [37, 12, 34, 33]. In total, there are
1.6M images of 242K identities.

##  3 Evaluation Protocols of InsightFace Track

The test is aimed to determine whether, and to what degree, face recognition
performance differs when they process photographs of masked faces, child
faces, and individuals from various demographic groups (_e.g_. African,
Caucasian, South Asian and East Asian). All pairs between the gallery and
probe sets will be used for evaluation. We employ the 1:1 face verification as
the evaluation metric.

Masked Test Set: We report True Positive Rate (TPR) @ False Positive Rate
(FPR) = 1e-4 given 13,928 positive pairs and 96,983,824 negative pairs.

Children Test Set: We report True Positive Rate (TPR) @ False Positive Rate
(FPR) = 1e-4 given 1,773,428 positive pairs and 24,735,067,692 negative pairs.

Multi-racial Test Set: We assess accuracy by demographic groups (_e.g_.
African, Caucasian, South Asian and East Asian) and report True Positive Rate
(TPR) @ False Positive Rate (FPR) = 1e-6. The number of positive pairs for
each demographic group is of the order of million and the number of negative
pairs for each demographic group is of the order of billion.

InsightFace Track Ranking Rules: To protect data privacy and ensure fairness
in the competition, we withhold all images as well as labels of the test data.
Participants can submit their models in the ONNX format to our evaluation
server and get their results from the leader-board after the online evaluation
(usually several hours). Participants are only allowed to use the training
data we provided for a particular challenge track. On the widely used V100
GPU, we set an upper bound of inference time ($<10$ ms/image for the MS1M sub-
track and $<20$ ms/image for the Glint360 sub-track) to control the model
complexity and the submitted model size should be smaller than 1GB in the
format of float32. On our online test server, we employ cosine similarity for
the verification test. The feature dimension of the MS1M sub-track should be
smaller than $512$ and the feature dimension of the Glint360K sub-track should
be smaller than $1024$. All challenge submissions are ordered in terms of
weighted TPRs across two test sets (_i.e_. Masked Test Set and Multi-racial
Test Set) by the formula of 0.25 * TPR@Masked + 0.75 * TPR@MR-All.

Figure 2: Masked face augmentation through texture blending in the UV space. Demo images and the pipeline are from the JDAI-CV toolkit [32]. layer name | R18 | R34 | R50 | R100 | output size
---|---|---|---|---|---
|  |  |  |  | 112$\times$112$\times$3
stem | 3$\times$3, 64, s=1 | 3$\times$3, 64, s=1 | 3$\times$3, 64, s=1 | 3$\times$3, 64, s=1 | 112$\times$112$\times$64
Conv1_x | $\left[\begin{array}[]{c}\text{3$\times$3, 64}\\\\[-1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$2 | $\left[\begin{array}[]{c}\text{3$\times$3, 64}\\\\[-1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$3 | $\left[\begin{array}[]{c}\text{3$\times$3, 64}\\\\[-1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$3 | $\left[\begin{array}[]{c}\text{3$\times$3, 64}\\\\[-1.00006pt] \text{3$\times$3, 64}\end{array}\right]$$\times$3 | 56$\times$56$\times$64
Conv2_x | $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\\\[-1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$2 | $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\\\[-1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$4 | $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\\\[-1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$4 | $\left[\begin{array}[]{c}\text{3$\times$3, 128}\\\\[-1.00006pt] \text{3$\times$3, 128}\end{array}\right]$$\times$13 | 28$\times$28$\times$128
Conv3_x | $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\\\[-1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$2 | $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\\\[-1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$6 | $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\\\[-1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$14 | $\left[\begin{array}[]{c}\text{3$\times$3, 256}\\\\[-1.00006pt] \text{3$\times$3, 256}\end{array}\right]$$\times$30 | 14$\times$14$\times$256
Conv4_x | $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\\\[-1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$2 | $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\\\[-1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$3 | $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\\\[-1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$3 | $\left[\begin{array}[]{c}\text{3$\times$3, 512}\\\\[-1.00006pt] \text{3$\times$3, 512}\end{array}\right]$$\times$3 | 7$\times$7$\times$512
FC |  |  |  |  | 1$\times$1$\times$512
Flops (G) | 2.62 | 4.48 | 6.33 | 12.12 |
# Params (M) | 24.03 | 34.14 | 43.59 | 65.16 |
Table 3: The network configuration, computation complexity and model size of baseline models. Convolutional building blocks are shown in brackets with the numbers of blocks stacked. Down-sampling is performed by the second conv in conv1_1, conv2_1, conv3_1, and conv4_1 with a stride of 2. Data | Backbone | Loss | LFW | CFP-FP | AgeDB | IJB-C (1e-4) | IJB-C (1e-5)
---|---|---|---|---|---|---|---
MS1M | R18 | ArcFace | 99.77 | 97.73 | 97.77 | 94.66 | 92.07
MS1M | R34 | ArcFace | 99.80 | 98.67 | 98.10 | 95.90 | 94.10
MS1M | R50 | ArcFace | 99.83 | 98.96 | 98.35 | 96.46 | 94.79
MS1M | R100 | ArcFace | 99.85 | 99.06 | 98.48 | 96.81 | 95.31
Glint360K | R18 | ArcFace | 99.77 | 97.73 | 97.72 | 95.33 | 93.16
Glint360K | R34 | ArcFace | 99.82 | 98.78 | 98.33 | 96.56 | 95.16
Glint360K | R50 | ArcFace | 99.83 | 99.20 | 98.38 | 96.97 | 95.61
Glint360K | R100 | ArcFace | 99.82 | 99.29 | 98.48 | 97.32 | 95.88
Table 4: Baseline performance on the public test benchmarks (_e.g_. LFW, CFP-
FP, AgeDB and IJB-C).

##  4 Baseline Solutions of InsightFace Track

Training details of baseline models are released before the challenge to
facilitate participation. We re-implement a simple online masked face
augmentation function [32], customize the ResNet [16] for the baseline models
and employ ArcFace [4] as our loss function, which is one of the top-
performing methods for deep face recognition.

###  4.1 Masked Face Augmentation

As shown in Fig. 2, we follow the JDAI-CV toolkit [32]
444https://github.com/JDAI-CV/FaceX-
Zoo/tree/main/addition_module/face_mask_adding/FMA-3D to implement our online
masked face generation function
555https://github.com/deepinsight/insightface/tree/master/recognition/_tools_.
After 3D face reconstruction [10] on the input 2D face image, we obtain the UV
texture map, the face geometry and the camera pose. Then, we randomly select
one facial mask from the collected mask dataset and project it into the UV
space. Based on a simple texture blending, we can easily get the masked facial
UV texture. Finally, we combine the masked facial UV texture and the face
geometry, and render the masked face into a 2D face image.

###  4.2 Implementation Details

During training, we follow ArcFace [4] to set the feature scale to $64$ and
choose the angular margin at $0.5$. As shown in Tab. 3, we customize the
ResNet [16] as our baseline models (_i.e_. R18, R34, R50 and R100). More
specifically, we only employ the basic residual block instead of the
bottleneck residual block following ArcFace [4]. The baseline models are
implemented by PyTorch with parallel acceleration on both features and
centres666https://github.com/deepinsight/insightface/tree/master/recognition/arcface_torch.
We set batch size as $1,024$ and train models on eight NVIDIA V100(32GB) GPUs.
The learning rate starts with $0.1$, drops by $0.1$ at 10, 16, 22 epochs, and
the whole training procedure finishes at 24 epochs. We set the momentum to
$0.9$ and the weight decay to $5e-4$. During testing, we only keep the feature
embedding network without the fully connected layer and extract the $512$-$D$
features for each normalized face crop. We use the cosine similarity metric
for each feature pair.

###  4.3 Baseline Performance

As shown in Tab. 4, we first test our baseline models on public benchmarks,
including LFW [17], CFP-FP [27], AgeDB [23], and IJB-C [21]. By increasing the
computation complexity from R18 to R100, the performance rises steadily across
all test sets. After changing the training data from MS1M to Glint360K,
TPR@FPR=1e-4 on IJB-C significantly increases from $96.81\%$ to $97.32\%$ for
R100. On CFP-FP, R100 trained on Glint360K outperforms the counterpart model
trained on MS1M by $0.23\%$, indicating that frontal-to-profile face
verification can benefit from more training data. By contrast, the
verification accuracy on LFW and AgeDB is almost the same, which indicates
that LFW and AgeDB are saturated to distinguish high performing models.

In Tab. 5, we report the performance on the challenge benchmarks. As we can
see from these results, the verification accuracy benefits from more training
data (from MS1M to Glint360K) and heavier backbone structures (from R18 to
R100) across all testing scenarios (_i.e_. masked, children and multi-racial
test sets). Compared to the performance gaps on public test datasets (_i.e_.
LFW [17], CFP-FP [27], AgeDB [23], and IJB-C [21]), the performance gaps on
the proposed masked test set, children test set and multi-racial test set are
more obvious. In addition, we also conduct experiments with masked face
augmentation. When $10\%$ of training data wear facial masks during training,
the verification accuracy on the masked test set significantly increases from
$69.091\%$ to $77.325\%$ by using MS1M, and increases from $75.567\%$ to
$83.710\%$ by using Glint360K. However, masked face augmentation is slightly
harmful for non-masked face verification, as the TPR on the MR-All dataset
drops by $0.484\%$ for the MS1M sub-track and decreases by $0.644\%$ for the
Glint360K sub-track. We leave the balance of masked face augmentation for the
challenge participants.

Data | Backbone | Loss | Mask | Children | African | Caucasian | South Asian | East Asian | MR-All | Size(MB) | Time (ms)
---|---|---|---|---|---|---|---|---|---|---|---
MS1M | R18 | ArcFace | 47.853 | 41.047 | 62.613 | 75.125 | 70.213 | 43.859 | 68.326 | 91.658 | 1.856
MS1M | R34 | ArcFace | 58.723 | 55.834 | 71.644 | 83.291 | 80.084 | 53.712 | 77.365 | 130.245 | 3.054
MS1M | R50 | ArcFace | 63.850 | 60.457 | 75.488 | 86.115 | 84.305 | 57.352 | 80.533 | 166.305 | 4.262
MS1M | R100 | ArcFace | 69.091 | 66.864 | 81.083 | 89.040 | 88.082 | 62.193 | 84.312 | 248.590 | 7.031
MS1M+MA-0.1 | R100 | ArcFace | 77.325 | 67.053 | 80.247 | 88.706 | 87.583 | 61.410 | 83.828 | 248.590 | 7.032
Glint360K | R18 | ArcFace | 53.317 | 48.113 | 68.230 | 80.575 | 75.852 | 47.831 | 72.074 | 91.658 | 2.013
Glint360K | R34 | ArcFace | 65.106 | 65.454 | 79.907 | 88.620 | 86.815 | 60.604 | 83.015 | 130.245 | 3.044
Glint360K | R50 | ArcFace | 70.233 | 69.952 | 85.272 | 91.617 | 90.541 | 66.813 | 87.077 | 166.305 | 4.340
Glint360K | R100 | ArcFace | 75.567 | 75.202 | 89.488 | 94.285 | 93.434 | 72.528 | 90.659 | 248.590 | 7.038
Glint360K+MA-0.1 | R100 | ArcFace | 83.710 | 75.894 | 88.919 | 94.038 | 92.882 | 71.137 | 90.015 | 248.590 | 7.036

Table 5: The baseline performance of the masked face recognition challenge
(the InsightFace track). “MR-All” denotes the verification accuracy on all
multi-racial images. Inference time is evaluated on Tesla V100 GPU using
onnxruntime-gpu==1.6. “MA-0.1” means masked face augmentation with a specific
probability of $10\%$.

Rank | Participant | Mask | Children | African | Caucasian | South Asian | East Asian | MR-All | Size(MB) | Time (ms) | Feat Dim
---|---|---|---|---|---|---|---|---|---|---|---
1 | agir | 84.169 | 75.003 | 88.322 | 93.396 | 93.349 | 72.623 | 90.452 | 317.665 | 9.764 | 512
2 | Rhapsody | 83.831 | 64.152 | 86.516 | 93.459 | 92.461 | 72.616 | 90.098 | 327.618 | 9.083 | 512
3 | paradox | 84.183 | 75.105 | 88.436 | 93.374 | 92.398 | 71.127 | 89.710 | 357.488 | 9.520 | 512
4 | mayidong | 84.312 | 73.936 | 86.258 | 92.227 | 91.244 | 70.042 | 88.897 | 295.954 | 9.762 | 512
5 | jerrysunnn | 82.201 | 57.467 | 85.395 | 92.124 | 91.270 | 71.501 | 89.252 | 327.624 | 9.036 | 512
6 | mind_ft | 84.528 | 68.303 | 86.820 | 92.251 | 88.326 | 68.595 | 88.355 | 250.145 | 9.318 | 512
7 | upupup | 82.352 | 53.794 | 85.069 | 92.061 | 91.044 | 71.159 | 89.000 | 327.618 | 9.071 | 512
8 | hammer_hk | 81.706 | 58.097 | 84.853 | 91.917 | 91.163 | 70.783 | 88.894 | 327.618 | 9.078 | 512
9 | unitykd0701 | 83.522 | 71.915 | 84.158 | 91.172 | 89.093 | 68.684 | 87.239 | 322.265 | 9.656 | 512
10 | kisstea | 83.831 | 71.050 | 83.828 | 90.866 | 90.054 | 67.108 | 87.046 | 288.849 | 9.079 | 512
11 | Hello | 79.308 | 67.126 | 86.012 | 92.168 | 92.603 | 68.694 | 88.529 | 250.145 | 9.253 | 512
12 | JulieXU | 82.209 | 70.465 | 83.823 | 90.734 | 89.889 | 68.194 | 87.236 | 235.505 | 7.909 | 512
13 | hjgw | 82.115 | 70.463 | 83.813 | 90.689 | 89.956 | 68.039 | 87.155 | 235.505 | 7.892 | 512
14 | xuyang1 | 76.163 | 77.104 | 87.962 | 93.256 | 92.580 | 68.774 | 89.080 | 302.869 | 9.654 | 512
15 | webill | 78.123 | 72.833 | 85.942 | 92.099 | 91.151 | 69.273 | 88.333 | 253.756 | 9.688 | 512

Table 6: Top-15 submissions of the MS1M sub-track by 16 August 2021.

Rank | Participant | Mask | Children | African | Caucasian | South Asian | East Asian | MR-All | Size(MB) | Time (ms) | Feat Dim
---|---|---|---|---|---|---|---|---|---|---|---
1 | jerrysunnn | 88.972 | 86.628 | 93.064 | 96.278 | 95.578 | 77.969 | 93.512 | 728.879 | 18.981 | 512
2 | mayidong | 86.933 | 84.545 | 93.043 | 96.529 | 95.361 | 77.554 | 93.358 | 541.023 | 17.837 | 1024
3 | derron | 87.636 | 84.679 | 92.289 | 95.564 | 95.109 | 77.512 | 92.815 | 566.625 | 19.153 | 1024
4 | mind_ft | 86.962 | 81.321 | 92.566 | 96.100 | 95.417 | 76.024 | 92.705 | 456.505 | 17.801 | 512
5 | DongWang | 83.487 | 82.619 | 92.182 | 95.655 | 94.791 | 76.392 | 92.743 | 564.831 | 17.101 | 1024
6 | helloface | 87.881 | 82.423 | 90.337 | 94.382 | 93.272 | 73.818 | 91.252 | 248.590 | 7.025 | 512
7 | didujustfart | 89.130 | 83.165 | 90.373 | 95.181 | 93.557 | 72.638 | 90.776 | 453.391 | 13.584 | 512
8 | yossi_avram | 81.469 | 82.848 | 92.974 | 96.162 | 95.739 | 76.584 | 93.005 | 248.583 | 7.472 | 512
9 | tinytan | 84.657 | 81.438 | 91.139 | 95.183 | 94.238 | 75.369 | 91.823 | 497.807 | 14.875 | 1024
10 | deepcam | 84.391 | 82.781 | 90.871 | 94.573 | 94.176 | 75.821 | 91.834 | 284.102 | 11.276 | 512
11 | sgglink | 84.966 | 78.323 | 90.067 | 94.738 | 93.251 | 73.284 | 91.162 | 605.258 | 19.071 | 512
12 | suanying | 77.642 | 82.362 | 92.874 | 96.305 | 95.484 | 77.582 | 93.477 | 456.505 | 17.813 | 512
13 | dingweichao | 82.223 | 79.652 | 90.042 | 94.772 | 93.438 | 73.479 | 91.263 | 453.391 | 13.559 | 512
14 | HYL_Dave | 78.116 | 79.770 | 91.670 | 95.575 | 94.690 | 74.872 | 92.098 | 453.391 | 13.602 | 512
15 | EvilGeniusFeng | 76.249 | 80.140 | 91.042 | 94.860 | 94.300 | 75.468 | 92.011 | 250.390 | 9.363 | 512

Table 7: Top-15 submissions of the Glint360K sub-track by 16 August 2021.

##  5 Leader-board Results of InsightFace Track

The masked face recognition competition (InsightFace track) is conducted as
part of the Masked Face Recognition Challenge &
Workshop777https://ibug.doc.ic.ac.uk/resources/masked-face-recognition-
challenge-workshop-iccv-21/, at the International Conference on Computer
Vision 2021 (ICCV 2021). Participants can freely select different sub-tracks
to develop a face feature embedding model, which is automatically evaluated on
our test server based on the above-mentioned protocols. The competition has
been opened worldwide, to both industry and academic institutions. By 16th
August 2021, the InsightFace track has received hundred of registrations from
across the world. More specifically, the competition has received 123 valid
submissions for the MS1M sub-track and 69 valid submissions for the Glint360K
sub-track. Here, multi-submissions for one sub-track from the same participant
is only counted once.

As we postpone the leader-board submission to 1st October 2021, we can not
collect the final top-ranked solutions before the camera-ready deadline. After
the competition, we will close the test server and select the valid top-3
solutions for each track. We will collect the training code from these top-
ranked participants and re-train the models to confirm whether the performance
of each submission is valid or not. We will update the challenge report
through arxiv with detailed team information and detailed top-ranked
solutions.

By 16th August 2021, we have found the best model of the MS1M sub-track has
achieved $84.169\%$ on the masked test set, and $90.452\%$ on the MR-All test
set. As given in Tab. 6, we list the top-15 submissions from the leader-board.
Comparing with the baseline models in Tab. 5, there are around $7\%$ absolute
improvements on the masked test set and the MR-All test set. For the Glint360K
sub-track, the best model has achieved $88.972\%$ on the masked test set, and
$93.512\%$ on the MR-All test set as shown in Tab. 7. Comparing with the
baseline models in Tab. 5, there is around $6\%$ absolute improvement on the
masked test set and about $3.5\%$ absolute improvement on the MR-All test set.
Therefore, there is huge space for the training optimization to improve masked
face recognition without the accuracy drop on the non-masked face recognition.

##  6 Ethical Considerations

Face recognition has been a controversial topic recently. There have been
questions over ethical concerns about invasion of privacy, alongside how well
face recognition systems recognize darker shades of skin (known as the bias
problem). In the InsighFace track of this challenge, we employ existing
academic data as the training datasets. Most of the identities inside the
training data are well-known celebrities [14]. The pre-processed training data
are compressed into the binary record and only released to relevant
researchers to facilitate the reproducible training. Our private test data
will not be released to the public to avoid the data privacy problem and
ensure fairness for all participants. For the bias concern, we follow the most
authoritative evaluation set up by NIST-FRVT
888https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8280.pdf. We wish to
promote fairness among deep face recognition and thus set up the multi-racial
verification benchmark.

##  7 Conclusions and Future Works

In this InsightFace track report, we introduce our new benchmark for the
evaluation of masked face recognition as well as non-masked face recognition.
Based on our baseline solutions, we confirm the effectiveness of the naive
masked face augmentation. As the challenge is still under-going, we will keep
on updating the top-ranked solutions as well as this report on arxiv.

Besides the InsightFace track, there is also a parallel WebFace260M track
999https://www.face-benchmark.org/challenge.html in the Masked Face
Recognition challenge. The WebFace260M track is organized by Zheng Zhu, Guan
Huang, Jiankang Deng, Yun Ye, Junjie Huang, Xinze Chen, Jiagang Zhu, Tian
Yang, Jia Guo, Jiwen Lu, Dalong Du and Jie Zhou. Detailes can be found in the
arxiv report [38], which will be also updated in the future.

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