EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-283 LHCb-PAPER-2015-043

First observation of the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ in the
${\rho}^{0}$-$\omega$ region of the dimuon mass spectrum

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

A study of the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ is performed
using data collected by the LHCb detector in proton-proton collisions at a
centre-of-mass energy of 8$\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an
integrated luminosity of 2.0$\mbox{\,fb}^{-1}$. Decay candidates with muon
pairs that have an invariant mass in the range
675–875${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are considered. This region
is dominated by the ${{\rho}^{0}}$ and $\omega$ resonances. The branching
fraction in this range is measured to be

${\cal
B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})=(4.17\pm
0.12\,\mathrm{(stat)}\pm 0.40\,\mathrm{(syst)})\times 10^{-6}.$

This is the first observation of the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$. Its branching
fraction is consistent with the value expected in the Standard Model.

Published as Physics Letters B757 (2016) 558

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

##  1 Introduction

Rare charm decays may proceed via the highly suppressed
${c}\\!\rightarrow{u}{\mu^{+}}{\mu^{-}}$ flavour changing neutral current
process. In the Standard Model such processes can only occur through loop
diagrams, where in charm decays the GIM cancellation [1] is almost complete.
As a consequence, the short-distance contribution to the inclusive
${D}\\!\rightarrow X{\mu^{+}}{\mu^{-}}$ branching fraction is predicted to be
as low as $\mathcal{O}(10^{-9})$ [2], making these decays interesting for
searches for new physics beyond the Standard Model. However, taking into
account long-distance contributions through tree diagrams involving resonances
such as ${D}\\!\rightarrow XV(\rightarrow{\mu^{+}}{\mu^{-}})$, where $V$
represents a $\phi$, ${\rho}^{0}$ or $\omega$ vector meson, the total
branching fraction of these rare charm decays can reach $\mathcal{O}(10^{-6})$
[3, 2, 4]. Their sensitivity to new physics therefore is greatest in regions
of the dimuon mass spectrum away from these resonances, where the main
contributions to the branching fraction may come from short-distance
amplitudes. Angular asymmetries are sensitive to new physics both in the
vicinity of these resonances and away from them [5, 6, 7, 4, 8] and could be
as large as $\mathcal{O}(1\%)$.

This Letter focuses on the measurement of the decay111 The inclusion of charge
conjugate decays is implied.
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$. This will
provide an important reference channel for measurements of the
${c}\\!\rightarrow{u}{\mu^{+}}{\mu^{-}}$ processes
${{D}^{0}}\\!\rightarrow\pi^{+}\pi^{-}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow K^{+}K^{-}{\mu^{+}}{\mu^{-}}$: precise branching
fractions are easier to obtain if they are compared with a normalisation mode
that has similar features. When restricted to the dimuon mass range 675
$<m({\mu^{+}}{\mu^{-}})<$ 875${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where
the ${{\rho}^{0}}$ and $\omega$ resonances are expected to dominate, it can
also be used to normalise the decays ${{D}^{0}}\\!\rightarrow
K^{-}\pi^{+}\eta^{(^{\prime})}(\rightarrow{\mu^{+}}{\mu^{-}})$. Measuring
their branching fractions allows the coupling
$\eta^{(^{\prime})}\rightarrow\mu^{+}\mu^{-}$ to be determined. This contains
crucial information for various low energy phenomena, and is an input to the
prediction of the anomalous magnetic moment of the muon [9, 10, 11]. Focussing
on this dimuon mass range also simplifies the analysis, which does not have to
account for the variation of the selection efficiency as a function of
$m({\mu^{+}}{\mu^{-}})$. From previous measurements the most stringent 90%
confidence level upper limits on the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ are set by the
E791 experiment [12]: $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) $<$ 35.9
$\times$ 10-5 in the full ${K}^{-}$ ${\pi}^{+}$ mass region and $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) $<$ 2.4
$\times$ 10-5 in the region of the ${\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}$ resonance.

The study presented here is based on data collected by the LHCb detector in
proton-proton collisions at a centre-of-mass energy of
8$\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an integrated luminosity of
2.0$\mbox{\,fb}^{-1}$. A subsample corresponding to an integrated luminosity
of 1.6$\mbox{\,fb}^{-1}$ has been used to measure $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$). The
remainder of the data set was used to optimise the selection. The branching
fraction $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) is
measured relative to that of the normalisation decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$. The most
accurate recent measurement of this branching fraction is used, $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$) =
(8.287 $\pm$ 0.043 $\pm$ 0.200) $\times$ 10-2, obtained by the CLEO experiment
[13].

##  2 Detector and simulation

The LHCb detector [14, 15] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex, the impact parameter (IP), is
measured with a resolution of $(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm m}$,
where $p_{\rm T}$ is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.

Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are
identified by a calorimeter system consisting of scintillating-pad and
preshower detectors, an electromagnetic calorimeter and a hadronic
calorimeter. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers [16].

The online event selection is performed by a trigger [17], which consists of a
hardware stage, based on information from the calorimeter and muon systems,
followed by a software stage, which applies a full event reconstruction. In
the offline selection, requirements are made on whether the trigger decision
was due to the signal candidate or to other particles produced in the $pp$
collision. Throughout this Letter, these two non-exclusive categories of
candidates are referred to as Trigger On Signal (TOS) and Trigger Independent
of Signal (TIS) candidates.

Simulated samples of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
have been produced. In the simulation, $pp$ collisions are generated using
Pythia [18, *Sjostrand:2007gs] with a specific LHCb configuration [20]. Decays
of hadronic particles are described by EvtGen [21], in which final-state
radiation is generated using Photos [22]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [23, *Agostinelli:2002hh] as described in Ref. [25]. No
theoretical model or experimental measurement provides a reliable decay model
for ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$. This
decay mode is therefore modelled as an incoherent sum of resonant and non-
resonant contributions, such as ${{\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$
and ${{\rho}^{0}}$/$\omega\\!\rightarrow{\mu^{+}}{\mu^{-}}$, motivated by the
resonant structure observed in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}{{\pi}^{0}}$
decays [26], and by the theoretical predictions of Ref. [4]. In the case of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$, a decay
model reproducing the data was implemented using the MINT software package
[27].

##  3 Event selection

The criteria used to select the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays are
as similar as possible to allow many systematic uncertainties to cancel in the
efficiency ratio. At trigger level, only events that are TIS with respect to
the hadron hardware trigger, which has a transverse energy threshold of
3.7$\mathrm{\,Ge\kern-1.00006ptV}$, are kept. In the offline selection, the
only differences between the signal and normalisation channels are the muon
identification criteria.

The first-level software trigger selects events that contain at least one good
quality track with high $p_{\rm T}$ and $\chi^{2}_{\rm IP}$, where the latter
is defined as the difference in $\chi^{2}$ of the closest primary $pp$
interaction vertex (PV) reconstructed with and without the particle under
consideration. The offline selection requires that at least one of these
tracks originates from either the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ or the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decay
candidates. The second-level software trigger uses two dedicated selections to
reconstruct ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ or
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ candidates
originating from the PV. These combine good quality tracks that satisfy
$p_{\rm T}$ $>$ 350${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ and $p>$
3000${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. A muon
(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) or charged
hadron (${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$)
pair is required to form a good quality secondary vertex that is significantly
displaced from the PV. In events where such a pair is found, two charged
hadrons are subsequently added. The resulting four-particle candidate must
have a good quality vertex and its invariant mass must be consistent with the
known ${D}^{0}$ mass [26]. The momentum vector of this ${D}^{0}$ candidate
must be consistent with having originated from the PV.

A preselection follows the trigger selections. Four charged particles are
combined to form ${D}^{0}$ candidates. Tracks that do not correspond to actual
trajectories of charged particles are suppressed by using a neural network
optimisation procedure. To reject the combinatorial background involving
tracks from the PV, only high-$p$ and high-$p_{\rm T}$ tracks that are
significantly displaced from any PV are used. This background is further
reduced by requiring that the four decay products of the ${D}^{0}$ meson form
a good quality vertex that is significantly displaced from the PV and that
$p_{\mathrm{T}}$(${D}^{0}$) $>$ 3000${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$.
These three criteria also reject candidates formed from partially
reconstructed charm hadron decays, combined with either random tracks from the
PV or with tracks from the decay of another charmed hadron in the same event.
This type of background is further reduced by requiring the ${D}^{0}$ momentum
vector is within 14 mrad of the vector that joins the PV with the ${D}^{0}$
decay vertex, ensuring that the ${D}^{0}$ candidate originates from the PV.
Finally, the invariant mass of the ${D}^{0}$ candidate, which is reconstructed
with a resolution of about 7${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, is
required to lie within 65${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
known ${D}^{0}$ mass. In the case of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$,
$m({\mu^{+}}{\mu^{-}})$ is restricted to the range
675–875${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The two backgrounds
described above are referred to as the non-peaking background throughout this
Letter.

After the preselection, a multivariate selection based on a boosted decision
tree (BDT) [28, 29] is used to further suppress the non-peaking background.
The GradBoost algorithm is used [30]. The BDT uses the following variables:
the $p_{\rm T}$ and $\chi^{2}_{\rm IP}$ of the final state particles; the
$p_{\rm T}$ and $\chi^{2}_{\rm IP}$ of the ${D}^{0}$ candidate as well as the
$\chi^{2}$ per degree of freedom of its vertex fit; the significance of the
distance between this vertex and the PV; the largest distance of closest
approach between the tracks that form the ${D}^{0}$ candidate; the angle
between the ${D}^{0}$ momentum vector and the vector that joins the PV with
its decay vertex. The cut on the BDT response used in the selection discards
more than 80% of the non-peaking candidates and retains more than 80% of the
signal candidates that have passed the preselection.

Finally, the information from the RICH, the calorimeters and the muon systems
are combined to assign probabilities for each decay product to be a pion, a
kaon or a muon, as described in Ref. [15]. A loose requirement on the kaon
identification probability rejects about 90% of the backgrounds that consist
of ${\pi}^{+}$ ${\pi}^{-}$ $\mu^{+}$ $\mu^{-}$ or ${\pi}^{+}$ ${\pi}^{-}$
${\pi}^{+}$ ${\pi}^{-}$ combinations while preserving 98% of the signal
candidates. In the case of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays, the
muon identification criteria have an efficiency of 90% per signal muon and
reduce the rate of misidentified pions by a factor of about 150. In the
absence of muon identification,
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
with two misidentified pions would outnumber signal decays by four orders of
magnitude. After these particle identification requirements, this background
is reduced to around 50% of the signal yield and is dominated by decays
involving two pion decays in flight
(${{\pi}^{+}}\\!\rightarrow{\mu^{+}}{{\nu}_{\mu}}$). It is referred to as the
peaking background throughout this Letter.

In addition to
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
with two misidentified pions, backgrounds due to the decays of ${D}^{+}$,
${D}^{+}_{s}$, ${D}^{*+}$, $\tau$, ${\mathchar 28931\relax}^{+}_{c}$ and
$\Sigma_{c}^{0}$ are considered. These are studied using simulated events and
found to be negligible.

The selection is optimised using data and simulated samples. The BDT is
trained using simulated
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ events to
model the signal. The sample used to represent the background consists of
candidates with $m$(${K}^{+}$ ${\pi}^{-}$ $\mu^{+}$ $\mu^{-}$) $>$
1890${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, drawn from 2% of the total
data sample. Candidates on the low-mass side of the signal peak are not used
due to the presence there of peaking background decays, whose features are
very close to those of signal decays. Optimal selection criteria on the BDT
response and muon identification are found using another independent data
sample corresponding to 20% of the total dataset. The fit described in Sect. 4
is used to estimate the yields of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ signal ($S$),
peaking background ($B_{\mathrm{pk}}$) and non-peaking background
($B_{\mathrm{npk}}$) present in this sample in the region of the signal peak,
defined as 1840 $<$ $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ $<$
1890${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. The requirements on the muon
identification and BDT response are chosen to maximise
$S/\sqrt{S+B_{\mathrm{pk}}+B_{\mathrm{npk}}}$.

The two samples described above consist of events chosen randomly from the
2012 data and are not used for the subsequent analysis. The remainder of the
dataset (78%), which corresponds to an integrated luminosity of
1.6$\mbox{\,fb}^{-1}$, is used to measure $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$). The final
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ sample
obtained with this selection consists of 5411 candidates. In the case of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$, the large
value of $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$) allows
us to use a small sample (3$\mbox{\,pb}^{-1}$), drawn randomly from the total
dataset. The final
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ sample
consists of 121 922 candidates.

##  4 Determination of the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ yields

A simultaneous binned maximum likelihood fit to the
$m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ and
$m({{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}})$ distributions is performed to
measure $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$).

In each sample, the probability density function (PDF) fitted to the signal
peak is a Gaussian function with power law tails. It is defined in the
following way:

$f(m;m_{D^{0}},\sigma,\alpha_{L},n_{L},\alpha_{R},n_{R})=\left\\{\begin{array}[]{cccc}\dfrac{\left(\frac{n_{L}}{|\alpha_{L}|}\right)^{n_{L}}\times
e^{-\frac{1}{2}\alpha^{2}_{L}}}{\left(\frac{n_{L}}{|\alpha_{L}|}-|\alpha_{L}|-\frac{m-m_{D^{0}}}{\sigma}\right)^{n^{\vphantom{s}}_{L}}}&\mbox{if}&\frac{m-m_{D^{0}}}{\sigma}\leq-|\alpha_{L}|,\\\
&&&\\\ \dfrac{\left(\frac{n_{R}}{|\alpha_{R}|}\right)^{n_{R}}\times
e^{-\frac{1}{2}\alpha^{2}_{R}}}{\left(\frac{n_{R}}{|\alpha_{R}|}-|\alpha_{R}|+\frac{m-m_{D^{0}}}{\sigma}\right)^{n^{\vphantom{s}}_{R}}}&\mbox{if}&\frac{m-m_{D^{0}}}{\sigma}\geq|\alpha_{R}|,\\\
&&&\\\
exp\left(\frac{-(m-m_{D^{0}})^{2}}{2\sigma^{2}}\right)&&\mbox{otherwise},\\\
\end{array}\right.$

where $m_{D^{0}}$ and $\sigma$ are the mean and width of the peak, and
$\alpha_{L}$, $n_{L}$, $\alpha_{R}$ and $n_{R}$ parameterise the left and
right tails. This function was found to describe accurately the
$m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ and
$m({{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}})$ distributions obtained with
the simulation, which exhibit non-Gaussian tails on both sides of the peaks.
The tail on the left-hand side is dominated by final-state radiation and
interactions with matter, while the right-hand side tail is due to non-
Gaussian effects in the reconstruction.

The non-peaking background in the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ sample is
described by a first-order polynomial. In the case of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$, a second-
order polynomial is used.

Three peaking backgrounds due to misidentified
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays are
categorised by the presence of candidates involving misidentified pions that
did not decay in flight before reaching the most downstream tracking stations,
or candidates where one or two pions decayed upstream of these tracking
stations. Candidates from the first category are described by a one-
dimensional kernel density estimate [31]. This PDF is derived from the
$m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ distribution obtained using
simulated ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
decays reconstructed under the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ hypothesis.
Candidates from the remaining two categories appear as tails on the lower-mass
side of the $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ distribution and must
be accounted for to avoid biases in the non-peaking background and in the
signal yield measured by the fit. Due to the small number of such candidates
in the simulated sample, simulated
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ candidates
where no pion decays in flight are altered to reproduce the effect of such
decays, and the corresponding $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$
distribution is determined. This is achieved by modifying the momentum vectors
of either one or two of the pions present in the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ final
state according to the kinematics of
${{\pi}^{+}}\\!\rightarrow{\mu^{+}}{{\nu}_{\mu}}$ decays. The
$m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$ distributions obtained after this
modification are converted into one-dimensional kernel density estimates.

The fit model involves 5 yields: the signal yield, $N_{\mathrm{sig}}$, the
yield of normalisation decays,
$N_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}$, the
peaking and non-peaking background yields, $N_{\mathrm{pk}}$ and
$N_{\mathrm{npk}}$, and the yield of background candidates in the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ sample,
$N_{\mathrm{npk}}^{K\pi\pi\pi}$. They are all free parameters in the fit. It
also involves 15 parameters to define the shapes of the PDFs. The parameters
describing the widths and upper-mass tails are free parameters in the fit but
are common between the PDFs for the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ peaks. The
lower-mass tail parameters are determined separately. Those used for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ candidates
are allowed to vary in the fit. This is not possible for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ candidates
because of the overlap between the signal and the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ peaking
background and therefore the parameters are fixed to the values obtained from
the simulated sample. In total, there are 15 free parameters in the fit.

Table 1:  Summary of the results of the fit described in Sect. 4. The yields measured in the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ sample and the correlations between them, the yields measured in the normalisation sample, the common width fitted to the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ yields, and the relative uncertainty on $\cal B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) are presented. Uncertainties on the fitted parameters are statistical. The variation of the uncertainty on $\cal B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) when the background yields are fixed indicates to what extent it is enhanced by the need to separate contributions in overlap and which shapes present some similarities. Parameter | Value
---|---
$N_{\mathrm{sig}}$ |  2357 $\pm$ 67
$N_{\mathrm{pk}}$ |  1047 $\pm$ 84
$N_{\mathrm{npk}}$ |  2007 $\pm$ 116
$N_{\mathrm{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}}$ |  83 575 $\pm$ 334
$N_{\mathrm{npk}}^{K\pi\pi\pi}$ |  38 346 $\pm$ 257
$\sigma$ | 7.17 $\pm$ 0.03 ${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
$C_{N_{\mathrm{pk}},N_{\mathrm{npk}}}$ | -78%
$C_{N_{\mathrm{sig}},N_{\mathrm{pk}}}$ | 27%
$C_{N_{\mathrm{sig}},N_{\mathrm{npk}}}$ | -48%
$\sigma_{{\cal B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})}$ | 2.9%
$\sigma_{{\cal B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})}$, if $N_{\mathrm{pk}}$ fixed | 2.8%
$\sigma_{{\cal B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})}$, if $N_{\mathrm{pk}}$ and $N_{\mathrm{npk}}$ fixed | 2.4%

The relative yields of the three peaking background categories described above
are fixed to values obtained by a fit to a large control sample. It consists
of ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ candidates
that are in the TOS category with respect to the muon hardware trigger, in
contrast to the signal and normalisation samples that are in the TIS category
with respect to the hadron trigger. All of the other selection requirements
are the same as those described in Sect. 3. This TOS signal control sample
consists of 28 835 candidates and contains approximately six times more
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays than
the nominal TIS sample.

The fit results are summarized in Table 1 and the observed mass distributions
are shown in Fig. 1, with fit projections overlaid. The main difficulties in
this procedure are the similarities in the shape of the signal, peaking
background and non-peaking background, and the overlap between their
distributions in $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$. However, their
impact on the measurement presented in this Letter is limited, as can also be
seen in Table 1.

Figure 1:  Mass distributions of (a)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ and (b)
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ candidates.
The data are shown as points (black) and the total PDF (blue solid line) is
overlaid. In (a), the two corresponding components of the fit model are the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
(red solid line) and the non-peaking background (violet dashed line). In (b),
the components are the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ (long-dashed
green line), the peaking background due to misidentified
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
(red solid line), and the non-peaking background (violet dashed line). Figure
2:  Distributions of the BDT response of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ ( circles) and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
(triangles) in data (full markers) and simulation (open markers). In data, the
background contributions are removed using the sPlot technique. The lower plot
shows the ratio between the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
distributions in data (full squares) and simulation (open squares).

##  5 Branching fraction measurement

The branching fraction of the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ is obtained by
combining the quantities presented in Table 2 with the branching fraction of
the ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decay
according to

${\cal
B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})=\frac{N_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}}{N_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}}\times\frac{\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}}{\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}}\times{\cal
B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}),$ (1)

where $N_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}$,
$N_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}$,
$\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}$
and
$\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}$
are the yields and selection efficiencies for the signal and normalisation
decays. The branching fraction of the signal decay for dimuon invariant masses
in the range 675–875${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is measured to
be ${\cal
B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})=\mathrm{(4.17\pm
0.12)\times 10^{-6}}$, where the uncertainty is statistical.

Table 2: Measured efficiencies and yields for the decay ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ in the dimuon mass range 675–875${\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}$, and for the decay ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$. The uncertainties are statistical. In the case of efficiencies, it stems from the finite size of the simulated samples. | ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ | ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
---|---|---
Efficiency [$\mathrm{10^{-5}}$] |  $8.8\pm 0.2$ |  $8.2\pm 0.1$
Yields | $2357\pm 67$ |  $83\,575\pm 334$

###  5.1 Systematic uncertainties

The systematic uncertainties on $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) are
summarised in Table 3. Those related to reconstruction and selection
efficiencies are minimized thanks to the efficiency ratio in Eq. 1 and to the
similarities between
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays.
This is illustrated in Fig. 2, which shows the distributions of the BDT
response for the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays,
both in data and simulated samples. In data, the background contributions are
removed using the sPlot technique [32]. Also shown in this figure are the
ratios between the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
distributions. The BDT response, which combines all the offline selection
variables (with the exception of muon identification criteria), is very
similar for both kinds of decay and the differences are well described by the
simulation. In cases where selection criteria depend on the nature of the
decay products, data-driven methods are used, as described below.

The uncertainty on the charged hadron reconstruction inefficiency is dominated
by the uncertainty on the probability to undergo a nuclear interaction in the
detector. This inefficiency is evaluated using simulated events. The
corresponding uncertainty is derived from the 10% uncertainty on the modelling
of the detector material [33].

Table 3: Systematic uncertainties on $\cal B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$). Source | Uncertainty [%]
---|---
Track reconstruction | 3.2
Offline selection | 2.0
Simulated decay models | 2.5
Hardware trigger | 4.4
Software trigger | 4.3
Muon identification | 3.2
Kaon identification | 1.0
Size of simulated sample | 2.9
$\sigma_{\mathrm{syst}}(\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}/\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}})$ | 8.8
Signal shape parameters | 0.8
Peaking background tails | 1.5
Signal PDF | 0.6
Non-peaking background shape | 2.1
$\sigma_{\mathrm{syst}}(N_{{{K}^{-}}{{\pi}^{+}}({\mu^{+}}{\mu^{-}})_{{{\rho}^{0}}-\omega}}/N_{{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}})$ | 2.8
$\cal B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$) | 2.5
Quadratic sum | 9.6

The selection efficiencies based on the kinematical and geometrical
requirements are derived from simulation. A systematic uncertainty to take
into account imperfect track reconstruction modelling is estimated by smearing
track properties to reproduce those observed in data. Similarly, a systematic
uncertainty on the efficiency of the BDT selection is assigned as the
difference between the efficiency obtained in data and simulation.

The uncertainties in the decay models are estimated separately for the signal
and normalisation channels. For the signal, this is carried out by reweighting
simulated ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$
decays to reproduce the distributions of $m({{K}^{-}}{{\pi}^{+}})$ and
$m({\mu^{+}}{\mu^{-}})$ observed in data, with the difference in efficiency
relative to the default being assigned as the systematic uncertainty. For
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$, the
sensitivity to the decay model is studied by comparing the default efficiency
with that obtained in an extreme case in which the decay model provided by the
MINT package is replaced by an incoherent sum of the resonances involved in
the decay, as given in Ref. [26].

To avoid dependence on the modelling of the hardware trigger in simulation,
its efficiency is determined in data. The efficiency to be TIS with respect to
hadron hardware trigger is determined as the fraction of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays that
fulfil this requirement among
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ candidates
that are TOS with respect to the muon hardware trigger. It is measured in 12
different regions defined in the ($\mbox{$p_{\rm T}$}(D^{0})$,
$N_{\mathrm{t}}$) plane, where $N_{\mathrm{t}}$ is the track multiplicity of
the event. The overall hardware trigger efficiency for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays is the
average of these 12 efficiencies weighted according to the distributions of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ candidates
observed in data. The efficiency of the normalisation mode is obtained by
weighting the same 12 efficiencies according to the distributions of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
candidates. This procedure assumes that the probability for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays to
fulfil the TIS requirement is not enhanced by the requirement to also be in
the TOS category and that this TIS efficiency is the same in every region for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays. No
difference is found in simulation between the
$\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}}/\varepsilon_{{{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}}$
ratio obtained with this method and the ratio of true efficiencies, obtained
by directly counting the number of simulated
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
that fulfil the hadron trigger TIS requirement. To determine the systematic
uncertainty associated with the hardware trigger efficiency, the uncertainty
on this comparison is combined with the statistical uncertainties on the 12
measurements performed in data in ($\mbox{$p_{\rm T}$}(D^{0})$,
$N_{\mathrm{t}}$) regions.

A similar approach is employed in the case of the first level of the software
trigger. A sample of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ candidates
is selected from data that satisfied the trigger requirements independently of
these candidates. The fraction of
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ decays
where at least one of the decay products also satisfies the requirements of
this trigger is measured using this sample. This efficiency is measured in
regions of $\mbox{$p_{\rm T}$}({{D}^{0}})$ and weighted according to
distributions of this variable in simulated
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ events.
The variation in the efficiency ratio when these distributions are corrected
to match the data is used to evaluate the corresponding systematic
uncertainty.

The efficiency of the second-level software trigger for the signal decay is
calculated relative to that of the normalisation decay. This ratio is measured
using ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays
in data and simulation and consistent results are obtained. The uncertainty on
this comparison is therefore assigned as the systematic uncertainty on this
trigger efficiency.

The efficiency of the muon identification criteria is determined in data using
a large and pure sample of
$B\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{\mu^{+}}{\mu^{-}})X$ decays. Efficiencies measured in
several regions of $p_{\mathrm{T}}(\mu)$, $\eta$($\mu$) and $N_{\mathrm{t}}$
are weighted according to the distribution observed for the muon candidates
from ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays.
Several definitions of these domains are considered, with varying binnings.
The different efficiencies obtained this way, as well as the efficiencies
obtained in simulated samples, are compared to evaluate the corresponding
systematic uncertainty. The same approach is used to evaluate the efficiency
of the kaon identification requirement. In this case, the calibration kaons
are provided by
${{D}^{*+}}\\!\rightarrow{{D}^{0}}(\rightarrow{{K}^{-}}{{\pi}^{+}}){{\pi}^{+}}$
decays in data.

In the fit outlined in Sect. 4, the parameters of the function that describe
the lower-mass tail of the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ peak are fixed
to values obtained from simulation. The corresponding systematic uncertainty
is determined by repeating the fit using the values obtained by a fit to the
signal TOS control sample. A similar difference is observed when the
corresponding test is performed for
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$
candidates.

The systematic uncertainty related to the description of the peaking
background is determined by the change observed in $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) when the
components due to the decay of one or two pions in flight are neglected, and
when their yields relative to the rest of the peaking background are enhanced
by twice their uncertainty.

Two other systematic uncertainties have been evaluated. To estimate the impact
of the signal PDF employed, the fit is repeated using the Cruijff function
[34] instead. Potential effects arising from non-peaking backgrounds are
assessed by repeating the fits with the non-peaking backgrounds assumed to be
linear in $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$. The values of the
systematic uncertainties associated with the choice of fit model and its
parameters were also further validated using pseudoexperiments.

The impact on the fit of the similarities between the shapes of the signal and
background components was further controlled in two ways. First, fixing the
background yields decreases the relative uncertainty on $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) from 2.9%
to 2.4%. This variation is far lower than the total systematic uncertainty due
to the yield determination (2.8%). Moreover, another study is performed based
on pseudoexperiments, generated with realistic values of the yields and PDFs
shape parameters. The fit proved able to return unbiased measurements of the
generated value of $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) and an
accurate estimation of the statistical uncertainty, consistent with the
uncertainty obtained in data.

As can be seen in Table 3, the systematic uncertainties are dominated by the
uncertainty on the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ to
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$ efficiency
ratio, which is larger than the 2.9% statistical uncertainty on $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$). As
expected, this systematic uncertainty is primarily due to the different final
state particles of the two decays. The trigger efficiencies, and the muon
identification and track reconstruction efficiencies, are responsible for
about 90% of this uncertainty. The uncertainties due to the yield
determination and the knowledge of $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}{{\pi}^{-}}$)
represent secondary contributions.

Figure 3:  Background subtracted distribution of (a) the ${K}^{-}$ ${\pi}^{+}$
invariant mass and (b) the $\mu^{+}$ $\mu^{-}$ invariant mass, measured in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays using
the sPlot technique.

##  6 Conclusions

The decay ${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ is
studied using proton-proton collision data corresponding to an integrated
luminosity of 2.0$\mbox{\,fb}^{-1}$ collected in 2012 by the LHCb detector at
a centre-of-mass energy of 8$\mathrm{\,Te\kern-1.00006ptV}$. The branching
fraction of the decay
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ in the dimuon
mass range 675–875${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ is measured to be

${\cal
B}({{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})=(4.17\pm
0.12\,\text{(stat)}\pm 0.40\,\text{(syst)})\times 10^{-6}.$

This branching fraction can be compared to the Standard Model value calculated
in Ref. [4], $\cal
B$(${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$) $=$
6.7$\times$10-6, in the full dimuon mass range. This is the first observation
of this decay. The branching fraction is measured with an overall precision of
10% and is one order of magnitude lower than the previous most stringent upper
limit. Precise measurements of the
${{D}^{0}}\\!\rightarrow\pi^{+}\pi^{-}{\mu^{+}}{\mu^{-}}$ and
${{D}^{0}}\\!\rightarrow K^{+}K^{-}{\mu^{+}}{\mu^{-}}$ decays are now possible
in all regions of the dimuon invariant mass since they can be compared with a
normalisation mode that has similar features and a precisely known branching
fraction. This will allow more stringent constraints on new physics to be
obtained using data already collected by the LHCb detector, and the
sensitivity of future experiments to angular asymmetries to be assessed.

The distributions of the ${K}^{-}$ ${\pi}^{+}$ and $\mu^{+}$ $\mu^{-}$
invariant masses in
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}}$ decays are
shown in Fig. 3 , where the background contribution is removed using the sPlot
technique [32], taking the $m({{K}^{-}}{{\pi}^{+}}{\mu^{+}}{\mu^{-}})$
invariant mass as the discriminating variable. An amplitude analysis would be
required for a full understanding of the decay dynamics. The distributions in
Fig. 3 suggest the presence of additional contributions, including the
$\omega$ resonance, beyond the ${\kern
1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}$ ${\rho}^{0}$ intermediate
state that, according to Ref. [4], should strongly dominate the decay
amplitude.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). 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 (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. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from 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 (Russia), GVA, XuntaGal and GENCAT (Spain), The
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

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LHCb collaboration

R. Aaij39, C. Abellán Beteta41, B. Adeva38, M. Adinolfi47, A. Affolder53, Z.
Ajaltouni5, S. Akar6, J. Albrecht10, F. Alessio39, M. Alexander52, S. Ali42,
G. Alkhazov31, P. Alvarez Cartelle54, A.A. Alves Jr58, S. Amato2, S. Amerio23,
Y. Amhis7, L. An3, L. Anderlini18, J. Anderson41, G. Andreassi40, M.
Andreotti17,f, J.E. Andrews59, R.B. Appleby55, O. Aquines Gutierrez11, F.
Archilli39, P. d’Argent12, A. Artamonov36, M. Artuso60, E. Aslanides6, G.
Auriemma26,m, M. Baalouch5, S. Bachmann12, J.J. Back49, A. Badalov37, C.
Baesso61, W. Baldini17,39, R.J. Barlow55, C. Barschel39, S. Barsuk7, W.
Barter39, V. Batozskaya29, V. Battista40, A. Bay40, L. Beaucourt4, J.
Beddow52, F. Bedeschi24, I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,j,
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Berezhnoy33, R. Bernet41, A. Bertolin23, M.-O. Bettler39, M. van Beuzekom42,
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Bizzeti18,h, T. Blake49, F. Blanc40, J. Blouw11, S. Blusk60, V. Bocci26, A.
Bondar35, N. Bondar31,39, W. Bonivento16, S. Borghi55, M. Borsato7, T.J.V.
Bowcock53, E. Bowen41, C. Bozzi17, S. Braun12, M. Britsch11, T. Britton60, J.
Brodzicka55, N.H. Brook47, E. Buchanan47, C. Burr55, A. Bursche41, J.
Buytaert39, S. Cadeddu16, R. Calabrese17,f, M. Calvi21,j, M. Calvo Gomez37,o,
P. Campana19, D. Campora Perez39, L. Capriotti55, A. Carbone15,d, G.
Carboni25,k, R. Cardinale20,i, A. Cardini16, P. Carniti21,j, L. Carson51, K.
Carvalho Akiba2,39, G. Casse53, L. Cassina21,j, L. Castillo Garcia40, M.
Cattaneo39, Ch. Cauet10, G. Cavallero20, R. Cenci24,s, M. Charles8, Ph.
Charpentier39, M. Chefdeville4, S. Chen55, S.-F. Cheung56, N. Chiapolini41, M.
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H.V. Cliff48, J. Closier39, V. Coco39, J. Cogan6, E. Cogneras5, V. Cogoni16,e,
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Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M. Gersabeck55, T.
Gershon49, Ph. Ghez4, S. Gianì40, V. Gibson48, O.G. Girard40, L. Giubega30,
V.V. Gligorov39, C. Göbel61, D. Golubkov32, A. Golutvin54,39, A. Gomes1,a, C.
Gotti21,j, M. Grabalosa Gándara5, R. Graciani Diaz37, L.A. Granado Cardoso39,
E. Graugés37, E. Graverini41, G. Graziani18, A. Grecu30, E. Greening56, S.
Gregson48, P. Griffith46, L. Grillo12, O. Grünberg64, B. Gui60, E. Gushchin34,
Yu. Guz36,39, T. Gys39, T. Hadavizadeh56, C. Hadjivasiliou60, G. Haefeli40, C.
Haen39, S.C. Haines48, S. Hall54, B. Hamilton59, X. Han12, S. Hansmann-
Menzemer12, N. Harnew56, S.T. Harnew47, J. Harrison55, J. He39, T. Head40, V.
Heijne42, A. Heister9, K. Hennessy53, P. Henrard5, L. Henry8, E. van
Herwijnen39, M. Heß64, A. Hicheur2, D. Hill56, M. Hoballah5, C. Hombach55, W.
Hulsbergen42, T. Humair54, N. Hussain56, D. Hutchcroft53, D. Hynds52, M.
Idzik28, P. Ilten57, R. Jacobsson39, A. Jaeger12, J. Jalocha56, E. Jans42, A.
Jawahery59, F. Jing3, M. John56, D. Johnson39, C.R. Jones48, C. Joram39, B.
Jost39, N. Jurik60, S. Kandybei44, W. Kanso6, M. Karacson39, T.M. Karbach39,†,
S. Karodia52, M. Kecke12, M. Kelsey60, I.R. Kenyon46, M. Kenzie39, T. Ketel43,
E. Khairullin66, B. Khanji21,39,j, C. Khurewathanakul40, T. Kirn9, S.
Klaver55, K. Klimaszewski29, O. Kochebina7, M. Kolpin12, I. Komarov40, R.F.
Koopman43, P. Koppenburg42,39, M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M.
Kreps49, G. Krocker12, P. Krokovny35, F. Kruse10, W. Krzemien29, W.
Kucewicz27,n, M. Kucharczyk27, V. Kudryavtsev35, A. K. Kuonen40, K. Kurek29,
T. Kvaratskheliya32, D. Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51,
G. Lanfranchi19, C. Langenbruch49, B. Langhans39, T. Latham49, C. Lazzeroni46,
R. Le Gac6, J. van Leerdam42, J.-P. Lees4, R. Lefèvre5, A. Leflat33,39, J.
Lefrançois7, E. Lemos Cid38, O. Leroy6, T. Lesiak27, B. Leverington12, Y. Li7,
T. Likhomanenko66,65, M. Liles53, R. Lindner39, C. Linn39, F. Lionetto41, B.
Liu16, X. Liu3, D. Loh49, I. Longstaff52, J.H. Lopes2, D. Lucchesi23,q, M.
Lucio Martinez38, H. Luo51, A. Lupato23, E. Luppi17,f, O. Lupton56, A.
Lusiani24, F. Machefert7, F. Maciuc30, O. Maev31, K. Maguire55, S. Malde56, A.
Malinin65, G. Manca7, G. Mancinelli6, P. Manning60, A. Mapelli39, J. Maratas5,
J.F. Marchand4, U. Marconi15, C. Marin Benito37, P. Marino24,39,s, J. Marks12,
G. Martellotti26, M. Martin6, M. Martinelli40, D. Martinez Santos38, F.
Martinez Vidal67, D. Martins Tostes2, A. Massafferri1, R. Matev39, A.
Mathad49, Z. Mathe39, C. Matteuzzi21, A. Mauri41, B. Maurin40, A. Mazurov46,
M. McCann54, J. McCarthy46, A. McNab55, R. McNulty13, B. Meadows58, F.
Meier10, M. Meissner12, D. Melnychuk29, M. Merk42, E Michielin23, D.A.
Milanes63, M.-N. Minard4, D.S. Mitzel12, J. Molina Rodriguez61, I.A. Monroy63,
S. Monteil5, M. Morandin23, P. Morawski28, A. Mordà6, M.J. Morello24,s, J.
Moron28, A.B. Morris51, R. Mountain60, F. Muheim51, D. Müller55, J. Müller10,
K. Müller41, V. Müller10, M. Mussini15, B. Muster40, P. Naik47, T. Nakada40,
R. Nandakumar50, A. Nandi56, I. Nasteva2, M. Needham51, N. Neri22, S.
Neubert12, N. Neufeld39, M. Neuner12, A.D. Nguyen40, T.D. Nguyen40, C. Nguyen-
Mau40,p, V. Niess5, R. Niet10, N. Nikitin33, T. Nikodem12, A. Novoselov36,
D.P. O’Hanlon49, A. Oblakowska-Mucha28, V. Obraztsov36, S. Ogilvy52, O.
Okhrimenko45, R. Oldeman16,e, C.J.G. Onderwater68, B. Osorio Rodrigues1, J.M.
Otalora Goicochea2, A. Otto39, P. Owen54, A. Oyanguren67, A. Palano14,c, F.
Palombo22,t, M. Palutan19, J. Panman39, A. Papanestis50, M. Pappagallo52, L.L.
Pappalardo17,f, C. Pappenheimer58, W. Parker59, C. Parkes55, G. Passaleva18,
G.D. Patel53, M. Patel54, C. Patrignani20,i, A. Pearce55,50, A. Pellegrino42,
G. Penso26,l, M. Pepe Altarelli39, S. Perazzini15,d, P. Perret5, L.
Pescatore46, K. Petridis47, A. Petrolini20,i, M. Petruzzo22, E. Picatoste
Olloqui37, B. Pietrzyk4, T. Pilař49, D. Pinci26, A. Pistone20, A. Piucci12, S.
Playfer51, M. Plo Casasus38, T. Poikela39, F. Polci8, A. Poluektov49,35, I.
Polyakov32, E. Polycarpo2, A. Popov36, D. Popov11,39, B. Popovici30, C.
Potterat2, E. Price47, J.D. Price53, J. Prisciandaro38, A. Pritchard53, C.
Prouve47, V. Pugatch45, A. Puig Navarro40, G. Punzi24,r, W. Qian4, R.
Quagliani7,47, B. Rachwal27, J.H. Rademacker47, M. Rama24, M.S. Rangel2, I.
Raniuk44, N. Rauschmayr39, G. Raven43, F. Redi54, S. Reichert55, M.M. Reid49,
A.C. dos Reis1, S. Ricciardi50, S. Richards47, M. Rihl39, K. Rinnert53,39, V.
Rives Molina37, P. Robbe7,39, A.B. Rodrigues1, E. Rodrigues55, J.A. Rodriguez
Lopez63, P. Rodriguez Perez55, S. Roiser39, V. Romanovsky36, A. Romero
Vidal38, J. W. Ronayne13, M. Rotondo23, J. Rouvinet40, T. Ruf39, P. Ruiz
Valls67, J.J. Saborido Silva38, N. Sagidova31, P. Sail52, B. Saitta16,e, V.
Salustino Guimaraes2, C. Sanchez Mayordomo67, B. Sanmartin Sedes38, R.
Santacesaria26, C. Santamarina Rios38, M. Santimaria19, E. Santovetti25,k, A.
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Schmelzer10, B. Schmidt39, O. Schneider40, A. Schopper39, M. Schubiger40,
M.-H. Schune7, R. Schwemmer39, B. Sciascia19, A. Sciubba26,l, A. Semennikov32,
N. Serra41, J. Serrano6, L. Sestini23, P. Seyfert21, M. Shapkin36, I.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
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
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN 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
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
63Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
64Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
65National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
66Yandex School of Data Analysis, Moscow, Russia, associated to 32
67Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
68Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

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