EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-186 LHCb-PAPER-2021-028 14 October 2021

Search for massive long-lived particles decaying semileptonically at
$\sqrt{s}$ =13 TeV

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

A search is performed for massive long-lived particles (LLP) decaying
semileptonically into a muon and two quarks. Two kinds of LLP production
processes were considered. In the first a Higgs-like boson with mass from 30
to 200$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ is produced by gluon fusion and
decays into two LLPs. The analysis covers LLP mass values from
10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ up to about one half the Higgs-like
boson mass. The second LLP production mode is directly from quark
interactions, with LLP masses from 10 to
90$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The LLP lifetimes considered range
from 5 to 200 ps. This study uses LHCb data collected from proton-proton
collisions at $\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$, corresponding to an
integrated luminosity of 5.4$\text{\,fb}^{-1}$. No evidence of these long-
lived states has been observed, and upper limits on the production cross-
section times branching ratio have been set for each model considered.

Submitted to Eur. Phys. J. C

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

##  1 Introduction

Supersymmetry (SUSY) is one of the most popular extensions of the Standard
Model (SM), which solves the hierarchy problem, unifies the gauge couplings at
the Planck scale and proposes dark matter candidates. The minimal
supersymmetric extension of the Standard Model (MSSM) is the simplest
phenomenologically viable realization of SUSY [1, 2]. The present study
addresses a subset of models featuring massive long-lived particles (LLP) with
a measurable flight distance [3, 4]. Searches for LLPs have been performed by
the Tevatron and LHC experiments [5, 6, 7, 8, 9, 10, 11, 12], often using the
Hidden Valley framework [4] as a benchmark model. In particular, the
production of LLPs from the decay of a SM-like Higgs boson has been studied in
several searches at LHC assuming LLP decays to light-flavour jets [7, 13, 14,
15, 12], $b$-quark jets [16] and light leptons [17, 18, 19]. Additional
information on searches for LLPs at collider experiments can be found in Refs.
[20] and [21].

This analysis focuses on LLPs decaying semileptonically into SM particles. It
uses proton-proton ($pp$) collision data at a centre-of-mass energy $\sqrt{s}$
=13 TeV collected by the LHCb experiment at LHC, corresponding to a total
integrated luminosity of 5.4$\text{\,fb}^{-1}$. It extends the analysis of
Ref. [14] on data collected at $\sqrt{s}=7$ and 8 TeV. A reinterpretation of
the LHCb results in terms of sterile neutrinos searches can be found in Ref.
[22].

The theoretical model chosen as benchmark is the minimal SUper GRAvity
(mSUGRA) with R-parity violation (RPV) [23], in which the neutralino can decay
into a muon and two quarks:
$\tilde{\chi}^{0}_{1}\rightarrow\mu^{+}q_{i}q_{j}(\mu^{-}\bar{q_{i}}\bar{q_{j}})$.
Neutralinos can be produced by a variety of processes. In this paper the
analysis has been performed assuming the two simple mechanisms depicted in
Fig. 1.

(a)(b)

Figure 1:  LLP production processes considered in this paper, where the
$\tilde{\chi}^{0}_{1}$ represents the LLP: (a) di-LLP production via a scalar
particle $h^{0}$; (b) non-resonant, direct LLP production from quark
interactions, where $X$ is a stable particle, with mass identical to the LLP.
The LLP decays into a muon and two quarks:
$\tilde{\chi}^{0}_{1}\rightarrow\mu^{+}q_{i}q_{j}(\mu^{-}\bar{q_{i}}\bar{q_{j}})$.

In the first process, a Higgs-like particle, $h^{0}$, is produced by gluon
fusion and decays into two LLPs. The analysis covers $h^{0}$ masses from 30 to
200$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, LLP lifetimes from 5 to 200 ps and
LLP mass values from 10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ up to about one
half the $h^{0}$ mass. The second mode is a direct LLP production from quark
interactions. The LLP lifetime range considered is from 5 to 200 ps and the
mass range from 10 to 90$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The LLP
lifetime range begins at 5 ps, well above the typical b-hadron lifetime, and
extends up to 200 ps, where most of the vertices are still within the LHCb
vertex locator (VELO). The mass range avoids the region of the SM b-quark
states, but also takes into account the forward acceptance of the LHCb
detector within which the decay products of relatively light LPPs can be
efficiently detected.

The LLP signature is a displaced vertex made of charged particles tracks
accompanied by an isolated muon with high transverse momentum with respect to
the proton beam direction, $p_{\mathrm{T}}$. This study benefits from the
excellent vertex reconstruction provided by the VELO, and by the low
$p_{\mathrm{T}}$ threshold of the muon trigger, compared to the other LHC
experiments. In addition, the LHCb experiment is probing a rapidity region
only partially accessible by other LHC experiments. These properties allow the
LHCb experiment to be complementary to similar analyses performed by the two
central detectors at LHC and even explore regions of the theoretical parameter
space where these experiments are limited by their low efficiency to
reconstruct highly boosted LLPs.

##  2 Detector description and simulation

The LHCb detector [24, 25] 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 the VELO which is a silicon-strip detector surrounding
the $pp$ interaction region [26], 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 [27, 28]
placed downstream of the magnet. The tracking system provides a measurement of
the momentum, $p$, of charged particles with a relative uncertainty that
varies from 0.5% at low momentum to 1.0% at
200$\text{\,Ge\kern-1.00006ptV\\!/}c$. The minimum distance of a track to a
primary $pp$ collision vertex (PV), the impact parameter, is measured with a
resolution of $(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$
is in $\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons
are distinguished using information from two ring-imaging Cherenkov detectors
[29]. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
(ECAL) and a hadronic calorimeter (HCAL). Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers
[30]. The online event selection is performed by a trigger [31], 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.

Simulation is used to model the effects of the detector acceptance and the
imposed selection requirements. In the simulation, $pp$ collisions are
generated using Pythia 8 [32, *Sjostrand:2006za] with a specific LHCb
configuration [34] and with parton density functions taken from CTEQ6L [35].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [36, *Agostinelli:2002hh]
as described in Ref. [38].

Several sets of signal events have been produced assuming the processes
illustrated in Fig. 1, where the $\tilde{\chi}^{0}_{1}$ plays the role of a
long-lived particle. For the first process considered, two
$\tilde{\chi}^{0}_{1}$ particles are obtained from the decay of the Higgs-like
boson produced by gluon fusion, $gg\rightarrow
h^{0}\rightarrow\tilde{\chi}^{0}_{1}\tilde{\chi}^{0}_{1}$. The
$\tilde{\chi}^{0}_{1}$ lifetime, $\tau_{\tilde{\chi}^{0}_{1}}$, is chosen from
5 to 200 ps. The mass value of the Higgs-like boson, $m_{h^{0}}$, is in the
range 30 to 200$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, the
$\tilde{\chi}^{0}_{1}$ mass, $m_{\tilde{\chi}^{0}_{1}}$, varies from
10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ to about half $m_{h^{0}}$. For the
second process, the LLP is produced in a non-resonant mode,
$q\bar{q}\rightarrow\tilde{\chi}^{0}_{1}X$. Here $X$ is a stable particle with
the same mass as that of the $\tilde{\chi}^{0}_{1}$ state, varying from 10 to
90$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$.

The LLP decays into a muon and two quarks; the branching ratio of
$\tilde{\chi}^{0}_{1}\rightarrow\mu^{+}q_{i}q_{j}(\mu^{-}\bar{q_{i}}\bar{q_{j}})$
is set to be equal for each quark combination ($q_{i}=u,c$ and
$q_{j}=\bar{d},\bar{s},\bar{b}$), with an equal proportion of $\mu^{+}$ and
$\mu^{-}$.

In the following, the model name is indicated by the values of $m_{h^{0}}$,
$m_{\tilde{\chi}^{0}_{1}}$ and $\tau_{\tilde{\chi}^{0}_{1}}$; h125-chi40-10ps,
for example, corresponds to
$m_{h^{0}}=125\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$,
$m_{\tilde{\chi}^{0}_{1}}=40\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$,
$\tau_{\tilde{\chi}^{0}_{1}}=10\text{\,ps}$. For the direct production, the
Higgs mass is omitted from this notation, such as for example in chi30-10ps.

The most relevant background in this analysis is from events containing heavy
quarks. The background from heavy quarks directly produced in $pp$ collisions,
as well as from ${W}$, ${Z}$, Higgs boson and top quark decays, is studied
using the simulation. The simulation of inclusive ${b}{\overline{b}}$ and
${c}{\overline{c}}$ events is not efficient to produce a large enough sample
to cover the relevant high-$p_{\mathrm{T}}$ muon kinematic region. Hence, a
dedicated sample of $20\times 10^{6}$ ($1\times 10^{6})$ simulated
${b}{\overline{b}}$ (${c}{\overline{c}}$) events has been produced with a
minimum parton $\hat{p}_{\rm T}$ of 20$\text{\,Ge\kern-1.00006ptV\\!/}c$ and
requiring a muon with $p_{\mathrm{T}}>12\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$1.5<\eta<5.0$. All the simulated background species are suppressed by the
multivariate analysis presented in the next section. Therefore a data-driven
approach is employed for the final background estimation.

##  3 Signal selection

Signal events are selected by requiring a vertex displaced from any PV in the
event and containing one isolated, high-$p_{\mathrm{T}}$ muon. Due to the
relatively high LLP mass, the muons from the LLP decay are expected to be more
isolated than muons from hadron decays. The events from $pp$ collisions are
selected online by a trigger requiring muons with
$p_{\mathrm{T}}>10\text{\,Ge\kern-1.00006ptV\\!/}c$. The offline analysis
requires that the triggering muon has an impact parameter, ${\rm IP^{\mu}}$,
with respect to any PV, larger than $0.25\text{\,mm}$ and a transverse
momentum, ${p^{\mu}_{\mathrm{T}}}$, larger than
$12\text{\,Ge\kern-1.00006ptV\\!/}c$. Primary and displaced vertices are
reconstructed offline from charged tracks [39]. Genuine PVs are identified by
a small radial distance from the beam axis, $R_{\rm xy}<0.3$ mm. Once the set
of PVs is identified, all the other vertices are candidates for the decay
position of LLPs. An LLP candidate is formed of three or more tracks including
the muon and having an invariant mass above
4.5$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. Particles interacting with the
detector material are an important source of background. Therefore a geometric
veto is used to reject candidates with vertices in regions occupied by
detector material [40]. The event preselection requires at least one PV in the
event and at least one LLP candidate.

Figure 2 compares the distributions from data and from the simulated
${b}{\overline{b}}$ events for the relevant observables, after preselection.
For illustration the shapes of simulated h125-chi40-10ps events are also
superimposed. The effect of the geometric veto is visible in the $R_{\rm xy}$
distribution, for candidates with $R_{\rm xy}$ above 5 mm. The muon-isolation
variable is defined as the sum of the energy of tracks surrounding the muon
direction, including the muon itself, in a cone of radius $R_{\eta\phi}=0.3$
in the pseudorapidity-azimuthal $(\eta,\phi)$ space, divided by the energy of
the muon track. The radius is reduced to $R_{\eta\phi}=0.2$ when the
theoretical hypothesis assumes a LLP mass of
10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, to account for the reduced aperture
of the jet of particles produced by the LLP decay. A muon-isolation value of
unity denotes a fully isolated muon. In simulation the muon from the signal is
found to be more isolated than the hadronic background.

(a)(b) (c)(d) (e)(f) (g)(h) (i)(j)

Figure 2:  Distributions from data compared to simulated ${b}{\overline{b}}$
events (blue) and the simulated signal h125-chi40-10p (red), after
preselection. From (a) to (j): muon transverse momentum; muon impact
parameter; muon isolation; the calorimetric energy, $\rm E_{calorimeters}$,
associated with the muon normalised by the muon energy, $\rm E_{muon}$; the
number of tracks used to reconstruct the LLP vertex including the muon; the
radial distance to the beam line of the reconstructed vertex; longitudinal and
radial vertex fit errors, $\sigma_{Z}$ and $\sigma_{R}$; reconstructed
transverse momentum and mass of the LLP candidate. The distributions from
simulated events are normalised to the data.

The shapes of the distributions in Fig. 2 are all consistent with a dominant
${b}{\overline{b}}$ composition of the background. This is confirmed by
comparing the yields in data and simulation: after preselection and requiring
the isolation parameter below 1.2, the total number of LLP candidates in data
is $148\times 10^{3}$. The predicted background yields from
${b}{\overline{b}}$ and ${c}{\overline{c}}$ events are $(120\pm 20)\times
10^{3}$ and $(14\pm 4)\times 10^{3}$, respectively. Small contributions are
expected from processes with $W$, $Z$ bosons plus jets, top and Standard Model
Higgs events: 260, 20, 2, and 1 candidates, respectively. The
${b}{\overline{b}}$ and ${c}{\overline{c}}$ prediction uses the cross-sections
measured by the LHCb experiment at 13 TeV [41, 42]. The acceptance of this
analysis is computed with MadGraph5-aMC@NLO [43] and the detection efficiency
is obtained from simulated events. As already stated, these background
estimations are only used for cross-checks.

A multivariate analysis (MVA) based on a boosted decision tree [44, 45] is
used to further purify the data sample. Ten MVA input variables are selected
to optimise the signal–background separation. They are:
${p^{\mu}_{\mathrm{T}}}$ and ${\rm IP^{\mu}}$, the ratio of the energies
associated with the muon measured in ECAL and HCAL normalised to the muon
energy, the LLP candidate $p_{\mathrm{T}}$, its pseudorapidity, the number of
tracks forming the LLP, the vertex uncertainties in the radial direction,
$\sigma_{R}$, and in the z direction, $\sigma_{Z}$, and the vertex $R_{\rm
xy}$ distance.

Larger vertex uncertainties are expected on the vertices of candidates from
${b}{\overline{b}}$ events compared to signal LLPs. The former are more
boosted and produce more collimated tracks, while the relatively heavier
signal LLPs decay into more divergent tracks. This effect decreases when the
mass of the LLP approaches the mass of $b$-quark hadrons. The selection based
on the energy deposit in the calorimeters is efficient to suppress the
background due to kaons or pions punching through the calorimeters and being
misidentified as muons. The muon-isolation variable and the reconstructed mass
of the long-lived particles are not included in the classifier; the
discrimination power of these two variables is subsequently exploited for the
signal determination.

The signal MVA training samples are provided by simulation. The background
training sample is obtained from data, based on the hypothesis that the
fraction of signal in the data after preselection is small. This automatically
includes all possible background sources, with the correct relative abundance.
The training is performed independently for each simulated model. The
classifier output value is then calculated for data, simulated signal and all
the background species considered. For each model, the optimal MVA cut value
is chosen by an iterative minimization procedure to give the best expected
cross-section upper limit, but keeping at least ten candidates to allow the
invariant-mass fit to work properly.

The classifier can be biased by the presence of signal in data used as
background training set. To quantify the potential bias, the MVA training is
performed adding a fraction of simulated signal events (up to 5%) to the
background set. This test demonstrates a negligible effect on the MVA
performance for all the signal models.

##  4 Determination of the signal yield

The signal yield is determined with an unbinned extended maximum-likelihood
fit to the distribution of the reconstructed LLP mass. The shape of the signal
component is taken from the simulated models, and a background component is
added. After the MVA selection, no simulated background survives, therefore a
data-driven method is adopted to determine the background shape. The data
candidates are separated into a signal region with muon isolation below 1.2
and a background region with isolation values from 1.4 to 2.0. The signal-
region selection accepts more than 80% of the signal for all the models
considered (see e.g. Fig. 2). Any potential signal yield in the background
region is considered negligible. The reconstructed mass distribution obtained
from the background candidates is used to constrain an empirical probability
density function (PDF) consisting of the sum of two negative-slope exponential
functions, one of them convolved with a Gaussian function. Shape parameters
and amplitudes are left to vary in the fit. It is possible that the mass
distribution obtained after selection of the background region does not
represent exactly the background component in the signal region. Hence a
correction is applied before performing the fit: the mass distribution
selected in the background region is weighted with weights deduced from the
comparison of the candidate mass distributions of signal and background
regions obtained from data with a relaxed MVA selection. This relaxed
selection is required to have sufficiently populated samples and to minimise
the correlation with the final distributions from which signal yields are
obtained. The consistency of this procedure is tested on ${b}{\overline{b}}$
simulated events.

Table 1:  Signal detection efficiency, in percent, after preselection, ${\varepsilon}_{presel}$, including the geometrical acceptance, and after MVA selection, ${\varepsilon}$, and numbers of fitted signal and background events in the signal region, $N_{\rm s}$ and $N_{\rm b}$, for the different signal hypotheses with resonant LLP production (masses units are $\text{\,Ge\kern-0.80005ptV\\!/}c^{2}$, lifetimes in  ps). The last column gives the value of $\chi^{2}$ per degree of freedom, ndf, from the fit. $m_{h0}$ |  m${}_{\tilde{\chi}^{0}_{1}}$ | $\tau_{khi}$ | ${\varepsilon}_{presel}$ | ${\varepsilon}$ | $N_{\rm b}$ | $N_{\rm s}$ | $\chi^{2}/\mathrm{ndf}$
---|---|---|---|---|---|---|---
30 | 10 | 10 | 0.19 | 0.03 |  $1025.7$ $\pm$ | $159.4$ |  $-89.7$ $\pm$ | $39.1$ | 2.75
41 | 10 | 10 | 0.29 | 0.01 |  $61.3$ $\pm$ | $51.7$ |  $-5.3$ $\pm$ | $5.2$ | 0.67
41 | 20 | 10 | 0.53 | 0.08 |  $73.2$ $\pm$ | $14.2$ |  $13.8$ $\pm$ | $12.8$ | 1.22
50 | 10 | 10 | 0.46 | 0.09 |  $1421.3$ $\pm$ | $84.4$ |  $-71.4$ $\pm$ | $75.1$ | 1.03
50 | 20 | 10 | 0.95 | 0.12 |  $18.3$ $\pm$ | $6.9$ |  $6.7$ $\pm$ | $6.4$ | 1.12
80 | 10 | 10 | 0.74 | 0.05 |  $127.0$ $\pm$ | $17.8$ |  $1.0$ $\pm$ | $14.5$ | 1.35
80 | 20 | 10 | 1.86 | 0.42 |  $53.9$ $\pm$ | $45.3$ |  $-5.4$ $\pm$ | $5.0$ | 1.07
80 | 30 | 10 | 2.34 | 0.72 |  $22.4$ $\pm$ | $4.2$ |  $-0.4$ $\pm$ | $4.2$ | 0.67
80 | 40 | 10 | 1.83 | 0.43 |  $12.1$ $\pm$ | $4.1$ |  $1.9$ $\pm$ | $4.5$ | 0.53
125 | 10 | 5 | 0.63 | 0.04 |  $333.7$ $\pm$ | $28.0$ |  $-10.6$ $\pm$ | $21.7$ | 0.77
125 | 10 | 10 | 0.68 | 0.06 |  $198.3$ $\pm$ | $19.2$ |  $4.7$ $\pm$ | $14.7$ | 1.72
125 | 10 | 20 | 0.73 | 0.09 |  $1680.8$ $\pm$ | $42.9$ |  $-172.2$ $\pm$ | $34.0$ | 0.96
125 | 10 | 30 | 0.64 | 0.08 |  $419.0$ $\pm$ | $45.1$ |  $-29.9$ $\pm$ | $34.8$ | 1.43
125 | 10 | 40 | 0.49 | 0.06 |  $184.7$ $\pm$ | $30.4$ |  $8.3$ $\pm$ | $28.2$ | 0.77
125 | 10 | 50 | 0.51 | 0.11 |  $667.0$ $\pm$ | $46.9$ |  $-2.0$ $\pm$ | $39.5$ | 1.20
125 | 10 | 100 | 0.32 | 0.04 |  $53.7$ $\pm$ | $12.4$ |  $10.3$ $\pm$ | $11.7$ | 1.14
125 | 10 | 200 | 0.19 | 0.03 |  $71.5$ $\pm$ | $8.4$ |  $-0.5$ $\pm$ | $4.1$ | 0.57
125 | 20 | 5 | 1.86 | 0.36 |  $56.1$ $\pm$ | $43.3$ |  $-5.8$ $\pm$ | $5.6$ | 1.27
125 | 20 | 10 | 2.28 | 0.67 |  $39.6$ $\pm$ | $36.8$ |  $-3.9$ $\pm$ | $5.4$ | 1.06
125 | 20 | 20 | 2.24 | 0.47 |  $18.1$ $\pm$ | $15.4$ |  $-0.1$ $\pm$ | $5.5$ | 0.97
125 | 20 | 30 | 2.10 | 0.35 |  $9.5$ $\pm$ | $4.0$ |  $7.5$ $\pm$ | $4.2$ | 0.93
125 | 20 | 50 | 1.73 | 0.44 |  $28.9$ $\pm$ | $9.4$ |  $8.1$ $\pm$ | $8.7$ | 1.67
125 | 20 | 80 | 1.36 | 0.21 |  $22.9$ $\pm$ | $5.8$ |  $2.1$ $\pm$ | $5.5$ | 0.24
125 | 20 | 100 | 1.18 | 0.25 |  $15.0$ $\pm$ | $14.9$ |  $-1.0$ $\pm$ | $4.1$ | 0.80
125 | 20 | 200 | 0.71 | 0.09 |  $11.0$ $\pm$ | $2.0$ |  $-3.5$ $\pm$ | $2.2$ | 0.40
125 | 30 | 5 | 2.24 | 0.68 |  $93.5$ $\pm$ | $8.8$ |  $-15.0$ $\pm$ | $5.5$ | 2.26
125 | 30 | 10 | 3.13 | 0.72 |  $7.0$ $\pm$ | $4.0$ |  $3.9$ $\pm$ | $4.0$ | 0.84
125 | 30 | 20 | 3.24 | 0.93 |  $6.6$ $\pm$ | $3.2$ |  $3.4$ $\pm$ | $3.1$ | 0.35
125 | 30 | 30 | 2.92 | 0.87 |  $14.3$ $\pm$ | $2.9$ |  $-1.6$ $\pm$ | $2.8$ | 0.84
125 | 30 | 50 | 2.51 | 1.00 |  $22.7$ $\pm$ | $22.6$ |  $-1.7$ $\pm$ | $6.2$ | 0.83
125 | 30 | 100 | 1.84 | 0.58 |  $8.8$ $\pm$ | $5.5$ |  $-2.7$ $\pm$ | $2.1$ | 0.96
125 | 30 | 200 | 1.09 | 0.45 |  $25.3$ $\pm$ | $4.8$ |  $-4.8$ $\pm$ | $4.1$ | 1.16
125 | 40 | 5 | 2.41 | 0.59 |  $9.9$ $\pm$ | $6.3$ |  $-2.5$ $\pm$ | $1.9$ | 0.77
125 | 40 | 10 | 3.44 | 0.84 |  $11.0$ $\pm$ | $1.6$ |  $-2.2$ $\pm$ | $2.1$ | 0.94
125 | 40 | 20 | 3.79 | 1.90 |  $10.5$ $\pm$ | $3.2$ |  $4.5$ $\pm$ | $2.6$ | 0.72
125 | 40 | 30 | 3.71 | 1.37 |  $6.3$ $\pm$ | $3.4$ |  $4.7$ $\pm$ | $3.4$ | 1.31
125 | 40 | 50 | 3.24 | 1.39 |  $28.6$ $\pm$ | $1.7$ |  $-10.6$ $\pm$ | $4.8$ | 0.87
125 | 40 | 100 | 2.30 | 0.64 |  $9.9$ $\pm$ | $8.3$ |  $-1.4$ $\pm$ | $2.2$ | 0.56
125 | 40 | 200 | 1.49 | 0.61 |  $9.9$ $\pm$ | $8.1$ |  $-1.5$ $\pm$ | $2.2$ | 1.28
125 | 50 | 5 | 2.25 | 0.48 |  $8.3$ $\pm$ | $1.5$ |  $-0.3$ $\pm$ | $2.4$ | 0.60
125 | 50 | 10 | 3.41 | 1.60 |  $20.9$ $\pm$ | $4.0$ |  $1.1$ $\pm$ | $1.8$ | 0.58
125 | 50 | 20 | 4.10 | 2.01 |  $16.5$ $\pm$ | $0.5$ |  $-14.9$ $\pm$ | $11.9$ | 0.57
125 | 50 | 30 | 4.13 | 2.04 |  $4.2$ $\pm$ | $2.4$ |  $3.9$ $\pm$ | $2.5$ | 0.69
125 | 50 | 50 | 3.86 | 2.30 |  $17.5$ $\pm$ | $0.5$ |  $-0.5$ $\pm$ | $0.3$ | 0.64
125 | 50 | 100 | 3.02 | 1.74 |  $15.4$ $\pm$ | $0.8$ |  $-9.3$ $\pm$ | $2.9$ | 0.95
125 | 50 | 200 | 2.00 | 0.90 |  $4.4$ $\pm$ | $1.9$ |  $3.5$ $\pm$ | $2.1$ | 0.76
125 | 60 | 5 | 1.64 | 0.48 |  $20.9$ $\pm$ | $15.8$ |  $-2.6$ $\pm$ | $3.1$ | 0.64
125 | 60 | 10 | 2.85 | 1.22 |  $9.8$ $\pm$ | $2.1$ |  $-0.8$ $\pm$ | $2.2$ | 1.10
125 | 60 | 20 | 3.98 | 2.04 |  $22.8$ $\pm$ | $4.8$ |  $1.2$ $\pm$ | $1.9$ | 0.88
125 | 60 | 30 | 4.20 | 2.39 |  $16.5$ $\pm$ | $0.3$ |  $-10.0$ $\pm$ | $0.9$ | 0.73
125 | 60 | 50 | 4.57 | 2.87 |  $20.9$ $\pm$ | $2.9$ |  $3.1$ $\pm$ | $1.4$ | 1.13
125 | 60 | 100 | 3.68 | 2.30 |  $9.9$ $\pm$ | $1.9$ |  $-1.3$ $\pm$ | $2.4$ | 1.73
125 | 60 | 200 | 2.75 | 1.90 |  $10.7$ $\pm$ | $3.8$ |  $3.3$ $\pm$ | $3.0$ | 1.58
150 | 10 | 10 | 0.62 | 0.12 |  $1514.7$ $\pm$ | $52.5$ |  $-152.0$ $\pm$ | $30.8$ | 2.01
150 | 20 | 10 | 2.19 | 0.67 |  $66.0$ $\pm$ | $13.6$ |  $-8.2$ $\pm$ | $6.0$ | 1.47
150 | 30 | 10 | 3.20 | 0.60 |  $6.9$ $\pm$ | $2.0$ |  $1.1$ $\pm$ | $1.1$ | 0.67
150 | 40 | 10 | 3.55 | 1.44 |  $15.4$ $\pm$ | $12.1$ |  $-2.1$ $\pm$ | $2.8$ | 1.35
150 | 50 | 10 | 3.79 | 1.06 |  $6.9$ $\pm$ | $2.0$ |  $1.1$ $\pm$ | $1.1$ | 0.87
150 | 60 | 10 | 3.68 | 1.79 |  $25.3$ $\pm$ | $1.5$ |  $-15.0$ $\pm$ | $1.7$ | 1.41
200 | 10 | 10 | 0.46 | 0.05 |  $433.1$ $\pm$ | $34.2$ |  $7.0$ $\pm$ | $27.6$ | 1.59
200 | 20 | 10 | 1.93 | 0.45 |  $136.2$ $\pm$ | $26.2$ |  $21.8$ $\pm$ | $24.5$ | 0.95
200 | 30 | 10 | 2.94 | 0.48 |  $8.6$ $\pm$ | $3.9$ |  $4.4$ $\pm$ | $4.2$ | 0.79
200 | 40 | 10 | 3.43 | 0.84 |  $9.3$ $\pm$ | $2.8$ |  $3.7$ $\pm$ | $2.2$ | 1.30
200 | 50 | 10 | 3.84 | 1.48 |  $12.1$ $\pm$ | $2.1$ |  $-1.8$ $\pm$ | $2.3$ | 0.50
200 | 60 | 10 | 3.97 | 1.81 |  $12.1$ $\pm$ | $2.1$ |  $-1.8$ $\pm$ | $2.5$ | 0.56
200 | 50 | 5 | 2.90 | 1.20 |  $11.8$ $\pm$ | $2.1$ |  $-0.8$ $\pm$ | $1.2$ | 0.57
200 | 50 | 20 | 3.80 | 1.79 |  $7.7$ $\pm$ | $2.7$ |  $1.3$ $\pm$ | $2.8$ | 0.70
200 | 50 | 30 | 3.45 | 0.98 |  $17.6$ $\pm$ | $1.7$ |  $-6.0$ $\pm$ | $2.7$ | 0.62
200 | 50 | 50 | 2.91 | 1.14 |  $7.7$ $\pm$ | $0.8$ |  $-3.4$ $\pm$ | $1.9$ | 1.07
200 | 50 | 100 | 1.95 | 1.04 |  $10.0$ $\pm$ | $3.0$ |  $1.0$ $\pm$ | $3.0$ | 1.07
200 | 50 | 200 | 1.17 | 0.72 |  $17.6$ $\pm$ | $3.5$ |  $-4.0$ $\pm$ | $3.6$ | 0.50
Table 2:  Signal detection efficiency, in percent, after preselection, ${\varepsilon}_{presel}$, including the geometrical acceptance, and after MVA selection, ${\varepsilon}$, and numbers of fitted signal and background events in the signal region, $N_{\rm s}$ and $N_{\rm b}$, for the different signal hypotheses for the LLP non-resonant production models (masses units are $\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, lifetimes in  ps). The last column gives the value of $\chi^{2}$ per degree of freedom, ndf, from the fit.  $m_{\tilde{\chi}^{0}_{1}}$ | $\tau_{\tilde{\chi}^{0}_{1}}$ | ${\varepsilon}_{presel}$ | ${\varepsilon}$ | $N_{\rm b}$ | $N_{\rm s}$ | $\chi^{2}/\mathrm{ndf}$
---|---|---|---|---|---|---
10 | 10 | 0.61 | 0.13 |  $2767.9$ $\pm$ | $88.2$ |  $-141.8$ $\pm$ | $69.7$ | 1.69
20 | 10 | 0.66 | 0.23 |  $43.9$ $\pm$ | $40.1$ |  $-4.2$ $\pm$ | $5.0$ | 0.67
30 | 10 | 2.29 | 0.47 |  $15.7$ $\pm$ | $5.8$ |  $3.3$ $\pm$ | $5.2$ | 0.90
40 | 10 | 2.49 | 0.52 |  $1.1$ $\pm$ | $1.4$ |  $5.9$ $\pm$ | $2.8$ | 0.96
60 | 10 | 3.81 | 1.97 |  $45.1$ $\pm$ | $5.6$ |  $-8.0$ $\pm$ | $4.3$ | 0.80
90 | 10 | 2.52 | 1.68 |  $30.8$ $\pm$ | $2.2$ |  $-9.8$ $\pm$ | $5.0$ | 1.04
30 | 5 | 1.44 | 0.21 |  $11.0$ $\pm$ | $2.5$ |  $-1.0$ $\pm$ | $2.7$ | 0.67
30 | 20 | 2.64 | 0.66 |  $13.8$ $\pm$ | $4.4$ |  $3.2$ $\pm$ | $4.2$ | 0.65
30 | 30 | 2.52 | 0.74 |  $5.6$ $\pm$ | $2.2$ |  $2.4$ $\pm$ | $2.1$ | 0.41
30 | 50 | 2.25 | 0.81 |  $16.5$ $\pm$ | $16.1$ |  $-1.8$ $\pm$ | $3.2$ | 0.69
30 | 100 | 1.68 | 0.61 |  $9.9$ $\pm$ | $7.4$ |  $-1.7$ $\pm$ | $3.1$ | 1.10
30 | 200 | 1.06 | 0.29 |  $38.0$ $\pm$ | $6.3$ |  $-0.0$ $\pm$ | $2.3$ | 0.79

(a)

LHCb

5.4$\text{\,fb}^{-1}$

(b)

LHCb

5.4$\text{\,fb}^{-1}$

(c)

LHCb

5.4$\text{\,fb}^{-1}$

(d)

LHCb

5.4$\text{\,fb}^{-1}$

(e)

LHCb

5.4$\text{\,fb}^{-1}$

(f)

LHCb

5.4$\text{\,fb}^{-1}$

Figure 3: Reconstructed invariant mass of the LLP candidates. Subfigures (a),
(c), and (e) correspond to the signal selections which assume the models
h80-chi30-10ps, h200-chi20-10ps, and the non-resonant model chi30-10ps,
respectively. Subfigures (b), (d), and (f) are the corresponding distributions
for candidates selected in the background region. The results of the fits are
superimposed.

Examples of the invariant mass of the selected LLP candidates are shown in
Fig. 3 for the signal and background regions. The invariant-mass fit is
performed simultaneously on LLP candidates from the signal and from the
background regions. In the former, the numbers of signal and background events
are free parameters of the fit. The results of the fit are shown in the
figure. The sensitivity of the fit procedure is studied by adding a small
number of simulated signal events to the data according to a given signal
model. The fitted yields are on average consistent with the numbers of added
events. The fitted signal yields, given in Tables LABEL:tab:eff-fit-h and 2
are compatible with the background-only hypothesis for all the theoretical
models.

##  5 Detection efficiency and systematic uncertainties

The signal detection efficiency is estimated from the simulated signal events.
The efficiencies after preselection and after MVA selection are shown in Table
LABEL:tab:eff-fit-h and 2, for the considered models of resonant and non-
resonant LLP productions, respectively. The values include the geometrical
acceptance. Several phenomena compete to determine the detection efficiency.
In general the efficiency after preselection increases with the LLP mass
because more particles are produced in the decay of heavier LLPs. There is a
loss of particles outside the spectrometer acceptance, especially when the
LLPs are produced from the decay of heavier states, such as the Higgs-like
particle. In addition, the lower boost of heavier LLPs results in a shorter
average flight length, which is disfavoured by the requirement of a minimum
$R_{\rm xy}$ value. With increasing LLP lifetimes a larger portion of the
decays falls into the material region and is vetoed. Finally, a drop of
sensitivity is expected for LLPs with a lifetime close to the $b$-hadron
lifetimes, where the contamination from ${b}{\overline{b}}$ events becomes
even more important, especially for low-mass LLPs. The detection efficiency is
reduced by up to one order of magnitude after the optimised MVA selection
while the background is reduced by 3–4 orders of magnitude.

A breakdown of the relative systematic uncertainties is shown in Table 3. The
uncertainties of the partonic luminosity depend upon the process considered;
they are estimated following the procedure explained in Ref. [46, 47] and vary
from 3% up to 6%, which is found for the gluon fusion process. The integrated
luminosity [48] contributes with an uncertainty of 2%. The statistical
precision of the efficiencies determined from simulation is in the range 2–4%
for the different models. Different sources of systematic uncertainty arising
from discrepancies between data and simulation have been considered. The size
of those discrepancies for the relevant observables are inferred from a
comparison of the distributions obtained from data and from
${b}{\overline{b}}$ simulated events, which describes the data quite
completely, or from other calibration processes.

The muon detection efficiency, including trigger, tracking, and muon
identification efficiencies, is studied by a tag-and-probe technique applied
to muons from $J/\psi\rightarrow{\mu^{+}\mu^{-}}$, ${\mathchar
28935\relax}(1S)\rightarrow{\mu^{+}\mu^{-}}$ and
${Z}\rightarrow{\mu^{+}\mu^{-}}$ decays. The corresponding systematic effects
due to differences between data and simulation are estimated to be between 2%
and 3.7%, depending on the theoretical model considered.

A comparison of the simulated and observed $p_{\mathrm{T}}$ distributions of
muons from ${Z}\rightarrow{\mu^{+}\mu^{-}}$ decays shows a maximum difference
of 0.2$\text{\,Ge\kern-1.00006ptV\\!/}c$ in the selected region; this
difference is propagated to the LLP analysis by shifting the muon
$p_{\mathrm{T}}$ threshold by the same amount. The corresponding systematic
uncertainty is below 1% for all models under consideration.

The muon impact-parameter distribution is also studied from ${Z}$ decays and
shows a discrepancy between data and simulation of about 10$\,\upmu\text{m}$
close to the ${p^{\mu}_{\mathrm{T}}}$ threshold. By changing the minimum ${\rm
IP^{\mu}}$ requirement by this amount, the change in the detection efficiency
is below 1% for all the models.

Uncertainties in the estimated vertex-finding efficiency are due to the per-
track efficiency, track resolution, and differences in the contribution from
background tracks due to the underlying interaction and pile-up. The loss in
the vertex-finding efficiency, in addition to detector acceptance effects,
occurs mostly because tracks that belong to the signal vertex are erroneously
assigned to another vertex. A study of vertices from
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{K}^{*0}}$ decays with
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}\mu^{-}}$ and
${{K}^{*0}}\rightarrow K^{+}\pi^{-}$, has shown that the vertex detection
efficiencies in data and simulation agree within 10%. This result, obtained
from a process with four final-state particles, is propagated to a LLP decay
into a larger number of charged tracks and a detection threshold of three
tracks. A discrepancy of at most 2% between the LLP efficiency in data and
simulation is found.

The uncertainty on the position of the beam line in the transverse plane is
less than 20$\,\upmu\text{m}$ [26]. It can affect the secondary-vertex
selection, mainly via the requirement on $R_{\rm xy}$. By altering the PV
position in simulated signal events, the effect is estimated to be below 1%.

The effect of the imperfect modelling on the observables used in the MVA
training is estimated with pseudoexperiments. As previously stated, the bias
on each input variable is determined by comparing simulated and experimental
distributions of muons and LLP candidates from $Z$ and $W$ events, as well as
from ${b}{\overline{b}}$ events. At the MVA test stage, each input variable is
modified by a scale factor randomly selected from a Gaussian distribution of
width equal to the corresponding bias. The standard deviation of the signal
efficiency distribution is taken as systematic uncertainty.

The signal and background samples are obtained through a selection on the muon
isolation parameter. By a comparison of data and muons from simulated
${b}{\overline{b}}$ events, the maximum uncertainty on this variable is
estimated to be $\pm 0.015$ in the proximity of the thresholds, with a maximal
effect on the efficiency of 1.7%.

Comparing the mass distributions of ${b}{\overline{b}}$ and
$Z\rightarrow{{b}{\overline{b}}}$ events, a maximum mass-scale discrepancy
between data and simulated events of 10% is estimated in the proximity of the
threshold, which translates into a 1.4% contribution to the detection
uncertainty.

Table 3: Contributions to the relative systematic uncertainties. The indicated
ranges cover the theoretical models considered. The contributions from the
signal and background models used in the LLP mass fit are treated separately.

Source | Contribution [$\%$]
---|---
Integrated luminosity | 2.0
Parton luminosity gluons fusion (quarks) | 6.0 (3.0)
Simulation statistics | 2.0–4.0
Muon reconstruction | 2.0–3.7
${p^{\mu}_{\mathrm{T}}}$ | 1.0
${\rm IP^{\mu}}$ | 1.0
Vertex reconstruction | 2.0
Beam line uncertainty ($R_{\rm xy}$) | 0.9
Muon isolation | 1.7
MVA | 1.7-16
Mass calibration | 1.4
Total | 7.3–18.9

Finally, the total systematic uncertainty is obtained as the sum in quadrature
of all contributions, where the different components of the detection
efficiency are assumed to be fully correlated.

The choice of the signal and background invariant-mass templates can affect
the results of the LLP mass fits. The uncertainty due to the signal model
accounts for the mass scale and the mass resolution. The mass scale and
resolution discrepancies between data and simulation are below 1% and 1.5%
respectively, as obtained from ${b}{\overline{b}}$ and
$Z\rightarrow{{b}{\overline{b}}}$ events. Pseudoexperiments are used to
estimate the effect on the cross-section calculation. For each theoretical
model, ten simulated signal events are added to the selected data after a
Gaussian smearing or after changing the mass scale. The average deviation of
the observed upper limits with respect to the one obtained from the default
signal and background distributions is below 2%.

The background shape is deduced from data selected in the poorly isolated
region after reweighting, with weights inferred from the data distributions
obtained with relaxed selection criteria. The overall uncertainty is estimated
by reducing by half the weights and running pseudoexperiments as before. The
average deviation of the observed upper limits is below 14%.

##  6 Results

The 95% confidence level (CL) upper limits, expected and observed, on the
production cross-sections times branching fraction are computed for each model
using the CLs approach [49]. Statistical and systematic uncertainties on the
signal efficiencies are included as nuisance parameters of the likelihood
function, assuming Gaussian distributions. Finally, the upper limit values are
corrected by the factors which account for the imperfect modelling of signal
and background templates.

The numerical results for all the models are given in Tables LABEL:tab:ul-hX
and 5. The figures from 4 to 7 show the measured cross-section times branching
ratio upper limits, for different theoretical models. The decrease of
sensitivity for relatively low LLP mass value is explained by the above-
mentioned effects on the detection efficiency. The upper limits for the
processes with $m_{h^{0}}=125\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ can be
compared to the prediction of the Standard Model Higgs production cross-
section from gluon fusion of about 46 pb at
$\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ [50].

##  7 Conclusion

Long-lived massive particles decaying into a muon and two quarks have been
searched for using proton-proton collision data collected by the LHCb
experiment at $\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$, corresponding to an
integrated luminosity of 5.4 $\text{\,fb}^{-1}$. The LLP lifetime range
considered is from 5 ps to 200 ps. The background is dominated by
${b}{\overline{b}}$ events and is reduced by tight selection requirements,
including a dedicated multivariate classifier. The signal yield is determined
by a fit to the LLP reconstructed mass with a signal shape inferred from the
theoretical models.

The forward acceptance of the LHCb experiment makes it complementary to other
LHC experiments, while its low trigger $p_{\mathrm{T}}$ threshold allows to
explore relatively small LLP masses. Two types of LLP productions have been
assumed. In the first a Higgs-like particle is produced by gluon fusion and
decays into two LLPs. The analysis covers Higgs-like boson masses from 30 to
200$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, and LLP mass range from 10
$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ up to about one half of the mass of the
parent boson. The second mode is a direct LLP production from quark
interactions, covering the LLP mass range from 10
$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ up to 90
$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$.

The results for all theoretical models considered are compatible with the
background-only hypothesis. The upper limits at 95% CL set on the cross-
section times branching fractions are mostly of O(0.1 pb), but the sensitivity
is limited to O(10 pb) for the lowest LLP mass value considered of
10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$.

Table 4: Upper limits at 95% CL on the production cross-section times branching ratio for signal models with a resonant production via an Higgs-like boson. Masses are given in $\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$, lifetimes in  ps, cross-sections in  pb.  $m_{h^{0}}$ |  m${}_{\tilde{\chi}^{0}_{1}}$ | $\tau_{\tilde{\chi}^{0}_{1}}$ | expected UL | $-\sigma$ | $+\sigma$ | observed UL
---|---|---|---|---|---|---
30 | 10 | 10 | $40.24$ | $16.52$ | $31.86$ | $28.34$
41 | 10 | 10 | $30.89$ | $11.41$ | $41.72$ | $22.37$
41 | 20 | 10 | $7.95$ | $2.24$ | $3.55$ | $10.07$
50 | 10 | 10 | $13.72$ | $4.39$ | $11.90$ | $17.37$
50 | 20 | 10 | $2.65$ | $0.82$ | $1.67$ | $3.46$
80 | 10 | 10 | $13.72$ | $4.36$ | $9.37$ | $14.00$
80 | 20 | 10 | $0.81$ | $0.26$ | $0.40$ | $0.64$
80 | 30 | 10 | $0.36$ | $0.10$ | $0.18$ | $0.29$
80 | 40 | 10 | $0.48$ | $0.12$ | $0.20$ | $0.56$
125 | 10 | 5 | $22.06$ | $6.37$ | $32.95$ | $21.53$
125 | 10 | 10 | $17.76$ | $0.26$ | $15.73$ | $18.08$
125 | 10 | 20 | $20.64$ | $7.89$ | $16.67$ | $12.49$
125 | 10 | 30 | $17.21$ | $5.37$ | $13.22$ | $15.40$
125 | 10 | 40 | $11.10$ | $4.01$ | $9.27$ | $20.91$
125 | 10 | 50 | $8.11$ | $2.63$ | $6.80$ | $13.42$
125 | 10 | 100 | $7.89$ | $2.74$ | $5.99$ | $16.99$
125 | 10 | 200 | $7.50$ | $1.13$ | $8.19$ | $7.82$
125 | 20 | 5 | $1.38$ | $0.45$ | $0.60$ | $0.89$
125 | 20 | 10 | $0.56$ | $0.15$ | $0.22$ | $0.47$
125 | 20 | 20 | $0.49$ | $0.13$ | $0.22$ | $0.55$
125 | 20 | 30 | $0.73$ | $0.21$ | $0.34$ | $0.87$
125 | 20 | 50 | $0.91$ | $0.21$ | $0.32$ | $1.00$
125 | 20 | 80 | $1.11$ | $0.20$ | $0.40$ | $1.11$
125 | 20 | 100 | $0.82$ | $0.22$ | $0.38$ | $0.72$
125 | 20 | 200 | $0.94$ | $0.38$ | $0.77$ | $0.98$
125 | 30 | 5 | $0.55$ | $0.15$ | $0.23$ | $0.30$
125 | 30 | 10 | $0.18$ | $0.04$ | $0.09$ | $0.25$
125 | 30 | 20 | $0.20$ | $0.05$ | $0.08$ | $0.23$
125 | 30 | 30 | $0.22$ | $0.06$ | $0.09$ | $0.19$
125 | 30 | 50 | $0.34$ | $0.07$ | $0.11$ | $0.29$
125 | 30 | 100 | $0.17$ | $0.06$ | $0.11$ | $0.17$
125 | 30 | 200 | $0.48$ | $0.15$ | $0.17$ | $0.46$
125 | 40 | 5 | $0.18$ | $0.06$ | $0.10$ | $0.15$
125 | 40 | 10 | $0.17$ | $0.05$ | $0.08$ | $0.14$
125 | 40 | 20 | $0.10$ | $0.02$ | $0.04$ | $0.11$
125 | 40 | 30 | $0.16$ | $0.04$ | $0.06$ | $0.17$
125 | 40 | 50 | $0.18$ | $0.05$ | $0.07$ | $0.14$
125 | 40 | 100 | $0.20$ | $0.06$ | $0.11$ | $0.20$
125 | 40 | 200 | $0.23$ | $0.07$ | $0.11$ | $0.20$
125 | 50 | 5 | $0.28$ | $0.08$ | $0.13$ | $0.35$
125 | 50 | 10 | $0.07$ | $0.02$ | $0.04$ | $0.07$
125 | 50 | 20 | $0.05$ | $0.02$ | $0.03$ | $0.04$
125 | 50 | 30 | $0.09$ | $0.02$ | $0.04$ | $0.10$
125 | 50 | 50 | $0.08$ | $0.02$ | $0.03$ | $0.09$
125 | 50 | 100 | $0.07$ | $0.03$ | $0.04$ | $0.05$
125 | 50 | 200 | $0.18$ | $0.04$ | $0.08$ | $0.20$
125 | 60 | 5 | $0.49$ | $0.13$ | $0.21$ | $0.49$
125 | 60 | 10 | $0.11$ | $0.03$ | $0.05$ | $0.10$
125 | 60 | 20 | $0.05$ | $0.02$ | $0.03$ | $0.06$
125 | 60 | 30 | $0.04$ | $0.01$ | $0.03$ | $0.03$
125 | 60 | 50 | $0.06$ | $0.02$ | $0.03$ | $0.06$
125 | 60 | 100 | $0.07$ | $0.02$ | $0.03$ | $0.07$
125 | 60 | 200 | $0.15$ | $0.02$ | $0.06$ | $0.14$
150 | 10 | 10 | $14.85$ | $5.52$ | $9.07$ | $9.81$
150 | 20 | 10 | $0.60$ | $0.18$ | $0.35$ | $0.41$
150 | 30 | 10 | $0.15$ | $0.05$ | $0.09$ | $0.16$
150 | 40 | 10 | $0.10$ | $0.03$ | $0.05$ | $0.09$
150 | 50 | 10 | $0.08$ | $0.03$ | $0.05$ | $0.09$
150 | 60 | 10 | $0.04$ | $0.02$ | $0.03$ | $0.04$
200 | 10 | 10 | $22.48$ | $6.43$ | $14.67$ | $28.12$
200 | 20 | 10 | $2.47$ | $0.61$ | $0.85$ | $2.71$
200 | 30 | 10 | $0.48$ | $0.12$ | $0.19$ | $0.53$
200 | 40 | 10 | $0.19$ | $0.05$ | $0.09$ | $0.22$
200 | 50 | 10 | $0.08$ | $0.03$ | $0.05$ | $0.07$
200 | 60 | 10 | $0.07$ | $0.02$ | $0.04$ | $0.06$
200 | 50 | 5 | $0.12$ | $0.04$ | $0.06$ | $0.12$
200 | 50 | 20 | $0.09$ | $0.02$ | $0.04$ | $0.09$
200 | 50 | 30 | $0.12$ | $0.04$ | $0.07$ | $0.11$
200 | 50 | 50 | $0.08$ | $0.03$ | $0.05$ | $0.07$
200 | 50 | 100 | $0.15$ | $0.04$ | $0.08$ | $0.16$
200 | 50 | 200 | $0.19$ | $0.06$ | $0.12$ | $0.20$
Table 5: Upper limits at 95% CL on the production cross-section times branching ratio for signal models with a non-resonant production. Masses are given in $\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$, lifetimes in  ps, cross-sections in  pb.  $m_{\tilde{\chi}^{0}_{1}}$ | $\tau_{\tilde{\chi}^{0}_{1}}$ | expected UL | $-\sigma$ | $+\sigma$ | observed UL
---|---|---|---|---|---
10 | 10 | $23.67$ | $6.31$ | $12.90$ | $28.84$
20 | 10 | $0.92$ | $0.24$ | $0.46$ | $0.82$
30 | 10 | $0.49$ | $0.12$ | $0.19$ | $0.50$
40 | 10 | $0.31$ | $0.09$ | $0.14$ | $0.44$
60 | 10 | $0.08$ | $0.03$ | $0.04$ | $0.06$
90 | 10 | $0.10$ | $0.03$ | $0.05$ | $0.08$
30 | 5 | $0.86$ | $0.24$ | $0.40$ | $0.90$
30 | 20 | $0.32$ | $0.08$ | $0.13$ | $0.36$
30 | 30 | $0.19$ | $0.05$ | $0.09$ | $0.20$
30 | 50 | $0.22$ | $0.06$ | $0.09$ | $0.20$
30 | 100 | $0.11$ | $0.04$ | $0.07$ | $0.13$
30 | 200 | $0.36$ | $0.12$ | $0.23$ | $0.33$

(a)(b)$\tau_{\tilde{\chi}^{0}_{1}}$=5 ps$\tau_{\tilde{\chi}^{0}_{1}}$=10 ps
(c)(d)$\tau_{\tilde{\chi}^{0}_{1}}$=20 ps$\tau_{\tilde{\chi}^{0}_{1}}$=30 ps
(e)(f)$\tau_{\tilde{\chi}^{0}_{1}}$=50 ps$\tau_{\tilde{\chi}^{0}_{1}}$=100 ps

(g)$\tau_{\tilde{\chi}^{0}_{1}}$=200 ps

Figure 4:  Expected (open dots and 1$\sigma$ and 2$\sigma$ bands) and observed
(full dots) cross-section times branching fraction upper limits (95% CL) as a
function of m${}_{\tilde{\chi}^{0}_{1}}$ for the resonant production processes
with $m_{h^{0}}=125\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$, and, from (a) to
(g), $\tau_{\tilde{\chi}^{0}_{1}}$ of 5, 10, 20, 30, 50, 100, and 200 ps.

(a)(b)$m_{\tilde{\chi}^{0}_{1}}$=20$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$m_{\tilde{\chi}^{0}_{1}}$=30$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$
(c)(d)$m_{\tilde{\chi}^{0}_{1}}$=40$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$m_{\tilde{\chi}^{0}_{1}}$=50$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$

(e)$m_{\tilde{\chi}^{0}_{1}}$=60$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$

Figure 5:  Expected (open dots and 1$\sigma$ and 2$\sigma$ bands) and observed
(full dots) cross-section times branching fraction upper limits (95% CL) as a
function of $\tau_{\tilde{\chi}^{0}_{1}}$ for the resonant production with
$m_{h^{0}}=125\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$, and, from (a) to (e),
$m_{\tilde{\chi}^{0}_{1}}$ of 20, 30, 40, 50, and
60$\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$.

(a)(b)$m_{\tilde{\chi}^{0}_{1}}$=10$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$m_{\tilde{\chi}^{0}_{1}}$=20$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$
(c)(d)$m_{\tilde{\chi}^{0}_{1}}$=30$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$m_{\tilde{\chi}^{0}_{1}}$=40$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$
(e)(f)$m_{\tilde{\chi}^{0}_{1}}$=50$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$m_{\tilde{\chi}^{0}_{1}}$=60$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$

Figure 6:  Expected (open dots and 1$\sigma$ and 2$\sigma$ bands) and observed
(full dots) cross-section times branching fraction upper limits (95% CL) as a
function of $m_{h^{0}}$ and, from from (a) to (f), $m_{\tilde{\chi}^{0}_{1}}$
of 10, 20, 30, 40, 50, and 60$\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$.

(a)(b)$m_{\tilde{\chi}^{0}_{1}}$=30$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$$\tau_{\tilde{\chi}^{0}_{1}}$=10
ps

Figure 7:  Expected (open dots and 1$\sigma$ and 2$\sigma$ bands) and observed
(full dots) cross-section times branching fraction upper limits (95% CL), (a):
as a function of $\tau_{\tilde{\chi}^{0}_{1}}$ with
$m_{\tilde{\chi}^{0}_{1}}=30\text{\,Ge\kern-0.90005ptV\\!/}c^{2}$, (b): as a
function of $m_{\tilde{\chi}^{0}_{1}}$ with
$\tau_{\tilde{\chi}^{0}_{1}}=10\text{\,ps}$. The processes are from direct,
non-resonant, LLP production.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (USA). We are indebted to the communities behind the
multiple open-source software packages on which we depend. Individual groups
or members have received support from ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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LHCb collaboration

R. Aaij32, A.S.W. Abdelmotteleb56, C. Abellán Beteta50, F.J. Abudinen
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G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, J.L. Amey54, Y. Amhis11, L.
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R.J. Barlow62, S. Barsuk11, W. Barter61, M. Bartolini24,h, F. Baryshnikov83,
J.M. Basels14, S. Bashir34, G. Bassi29, B. Batsukh68, A. Battig15, A. Bay49,
A. Beck56, M. Becker15, F. Bedeschi29, I. Bediaga1, A. Beiter68, V. Belavin42,
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A. Mödden 15, R.A. Mohammed63, R.D. Moise61, S. Mokhnenko82, T. Mombächer46,
I.A. Monroy74, S. Monteil9, M. Morandin28, G. Morello23, M.J. Morello29,m, J.
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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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77Eotvos Lorand University, Budapest, Hungary, associated to 48
78INFN Sezione di Perugia, Perugia, Italy, associated to 21
79Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
82National Research University Higher School of Economics, Moscow, Russia,
associated to 42
83National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
85DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
86Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden,
associated to 59
87University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Genova, Genova, Italy
iUniversità degli Studi di Milano, Milano, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Modena e Reggio Emilia, Modena, Italy
lUniversità di Padova, Padova, Italy
mScuola Normale Superiore, Pisa, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità della Basilicata, Potenza, Italy
pUniversità di Roma Tor Vergata, Roma, Italy
qUniversità di Siena, Siena, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
wHanoi University of Science, Hanoi, Vietnam