 CERN-EP-2017-329 LHCb-PAPER-2017-043

A search for weakly decaying $b$-flavored pentaquarks

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

Investigations of the existence of pentaquark states containing a single $b$
(anti)quark decaying weakly into four specific final states
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p$,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$, and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi(1020)p$ are reported. The
data sample corresponds to an integrated luminosity of 3.0
$\mbox{\,fb}^{-1}$ in 7 and 8 TeV $pp$ collisions acquired with the LHCb
detector. Signals are not observed and upper limits are set on the product of
the production cross section times branching fraction with respect to that of
the ${\mathchar 28931\relax}^{0}_{b}$.

Submitted to Physical Review D

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

##  1 Introduction

The observation of charmonium pentaquark states with quark content
$c\overline{c}uud$, by the LHCb [1] collaboration in ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p$ decays, raises many questions including: What is the internal
structure of these pentaquarks? Do other pentaquark states exist? Are they
molecular or tightly bound? In this analysis, we search for pentaquarks that
contain a single $b$ (anti)quark, that decay via the weak interaction. The
Skyrme model [2] has been used to predict that the heavier the constituent
quarks, the more tightly bound the pentaquark state [3, 4, 5, 6]. This
motivates our search for pentaquarks containing a $b$ (anti)quark. No existing
searches for weakly decaying pentaquarks containing a $b$ (anti)quark have
been published.

Consider the possible pentaquark states $\overline{b}duud$,
$b\overline{u}udd$, $b\overline{d}uud$ and $\overline{b}suud$. We label these
states as $P_{{{B}^{0}}p}^{+}$, $P_{{{\mathchar
28931\relax}^{0}_{b}}\pi^{-}}^{-}$, $P_{{{\mathchar
28931\relax}^{0}_{b}}\pi^{+}}^{+}$ and $P_{{{B}^{0}_{s}}p}^{+}$, respectively,
where the subscript indicates the final states the pentaquark would
predominantly decay into if it had sufficient mass to decay strongly into
those states. While there are many possible decay modes of these states, we
focus on modes containing a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
meson in the final state because these candidates generally have relatively
large efficiencies and reduced backgrounds in the LHCb experiment. The Feynman
diagrams for the decay of the $P_{{{B}^{0}}p}^{+}$ and
$P_{{{B}^{0}_{s}}p}^{+}$ states are shown in Fig. 1. The corresponding
diagrams for the decay of $P_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{-}}^{-}$
and $P_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{+}}^{+}$ are similar to that
shown in Fig. 1(a), with the decay of the state being driven by the
$b\rightarrow c\overline{c}s$ transition. We reconstruct the $\phi(1020)$
meson111Hereafter $\phi$ refers to the $\phi(1020)$ meson. in the $K^{+}K^{-}$
decay mode. We note that the $P^{+}_{{{B}^{0}}p}$ pentaquark might have some
decays inhibited by Bose statistics if its structure is based on two identical
$ud$ diquarks, i.e. $\overline{b}(ud)(ud)$. Although the
$P^{+}_{{{B}^{0}_{s}}p}$ state is expected to be produced at a smaller rate on
the grounds that ${{B}^{0}_{s}}$ production in the LHCb experiment acceptance
is only about 13% of the rate of the sum of ${{{B}^{+}}}$ and ${{B}^{0}}$
production [7], it would not have two identical diquarks, and hence none of
its decays would suffer from spin-statistics suppression.

Figure 1: Leading-order diagrams for pentaquark decay modes into (a)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$ or (b)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$ final states.

Table 1 lists all of the pentaquarks we search for along with their respective
weak decay modes.222Unless explicitly stated, mention of a particular mode
implies the use of the charge-conjugated mode as well.

Table 1: Quark content of the $b$-flavored pentaquarks and their weak decay modes explored here. We consider only the quark decay process $b\rightarrow c\overline{c}s$. The lower and upper bounds of the mass region searched are also given. (In this paper we use natural units where $\hbar=c=1$.) Mode | Quark content |  Decay mode | Search window
---|---|---|---
I | $\overline{b}duud$ | $P_{{{B}^{0}}p}^{+}~{}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$ | 4668–6220 MeV
II | $b\overline{u}udd$ | $P_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{-}}^{-}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p$ | 4668–5760 MeV
III | $b\overline{d}uud$ | $P_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{+}}^{+}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$ | 4668–5760 MeV
IV | $\overline{b}suud$ | $P_{B_{s}^{0}p}^{+}~{}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$ | 5055–6305 MeV

It is possible for these pentaquarks ($P_{B}$) to decay either strongly or
weakly depending on their masses. The threshold mass for strong decay for
$P_{{{B}^{0}}p}^{+}$ would be $m({{B}^{0}})+m(p)$, for $P_{{{\mathchar
28931\relax}^{0}_{b}}\pi^{-}}^{-}$ $m({{\mathchar
28931\relax}^{0}_{b}})+m(\pi^{-})$, for $P_{{{\mathchar
28931\relax}^{0}_{b}}\pi^{+}}^{+}$ $m({{\mathchar
28931\relax}^{0}_{b}})+m(\pi^{+}$) and for $P_{{{B}^{0}_{s}}p}^{+}$
$m(B_{s}^{0})+m(p$). Therefore, we define our signal search windows to be
below these thresholds. Note that a fifth state, the $b\overline{s}uud$
pentaquark ($P^{+}_{{{\kern
1.25995pt\overline{\kern-1.25995ptB}{}}{}^{0}_{s}}p}$) could also decay into
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$, and thus is implicitly
included in our searches. Should a signal be detected for mode IV, we would
need to examine noncharmonium modes to distinguish between the possibilities.

##  2 Detector description and data samples

The LHCb detector [8, 9] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex 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$\mathrm{\,Ge\kern-1.00006ptV}$. The minimum distance
of a track to a primary $pp$ interaction vertex (PV), the impact parameter
(IP), is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
$\mathrm{\,Ge\kern-1.00006ptV}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
(RICH). Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
calorimeter and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

The online event selection is performed by a trigger, 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. The
subsequent software trigger is composed of two stages, the first of which
performs a partial reconstruction and requires either a pair of well-
reconstructed, oppositely charged muons having an invariant mass above
2.7$\mathrm{\,Ge\kern-1.00006ptV}$, or a single well-reconstructed muon with
high $p_{\mathrm{T}}$ and large IP. The second stage of the software trigger
applies a full event reconstruction and, for this analysis, requires two
opposite-sign muons to form a good-quality vertex that is well separated from
all of the PVs, and to have an invariant mass within $\pm
120$$\mathrm{\,Me\kern-1.00006ptV}$ of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [10]. The data sample
corresponds to 1.0 $\mbox{\,fb}^{-1}$ of integrated luminosity collected
with the LHCb detector in 7 TeV $pp$ collisions and 2.0 $\mbox{\,fb}^{-1}$
in 8 TeV collisions.

Simulated events are generated in the LHCb acceptance using Pythia [11,
*Sjostrand:2007gs], with a special LHCb parameter tune [13]. Pentaquark
candidate ($P_{B}$) decays are generated uniformly in phase space. Decays of
other hadronic particles are described by EvtGen [14], in which final-state
radiation is generated using Photos [15]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [16, *Agostinelli:2002hh] as described in Ref. [18]. The
lifetime of the simulated pentaquarks is set to 1.5${\mathrm{\,ps}}$,
consistent with that of most weakly decaying $b$ hadrons [10].

##  3 Event selection and $b$-hadron reconstruction

A pentaquark candidate is reconstructed by combining a
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$
candidate with a proton, kaon, and pion (or kaon for mode IV). Our analysis
strategy consists of a preselection based on loose particle identification
(PID) and the kinematics of the decay, followed by a more sophisticated
multivariate selection (MVA) classifier based on a Boosted Decision Tree (BDT)
[19], which uses multiple input variables, accounts for the correlations and
outputs a single discriminant. In order to avoid bias, the data in the signal
search regions were not examined (blinded) until all the selection
requirements were decided.

In the preselection, the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidates are formed from two oppositely charged particles with
$p_{\mathrm{T}}$ greater than 500$\mathrm{\,Me\kern-1.00006ptV}$, identified
as muons and consistent with originating from a common vertex but inconsistent
with originating from any PV. The invariant mass of the ${\mu^{+}\mu^{-}}$
pair is required to be within $[-48,+43]~{}\\!$MeV of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [10], corresponding to a
window of about $\pm 3$ times the mass resolution. The asymmetry in the mass
window is due to the radiative tail. Pion, kaon, and proton candidates are
required to be positively identified in the RICH detector, but with loose
requirements as the MVA includes particle identification criteria. Kaon and
proton candidates are required to have momenta greater than 5 GeV and 10 GeV,
respectively, to avoid regions with suboptimal particle identification. Each
track must have an IP $\chi^{2}$ greater 9 than with respect to the closest
PV, must have $p_{\mathrm{T}}$ greater than
250$\mathrm{\,Me\kern-1.00006ptV}$, and the scalar sum of the tracks
$p_{\mathrm{T}}$ is required to be larger than
900$\mathrm{\,Me\kern-1.00006ptV}$. All of the tracks forming the pentaquark
state are required to form a good vertex and have a significant detachment
from the PV. We also require that the cosine of the angle between the vector
from the PV to the $P_{B}$ candidate vertex ($\vec{V}_{\\!\\!PV-P_{B}}$) and
the $P_{B}$ candidate momentum vector ($\vec{p}_{P_{B}}$) be greater than
$0.999$. The invariant mass of the pentaquark states is calculated by
constraining the invariant mass of the dimuon pair to the known
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass, the muon tracks to
originate from the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ vertex and
the vector sum of the momenta of the final state particles to point back to
the PV.

We measure the product of the production cross section and branching fraction
of these pentaquark states and normalize it to the analogous measurement [20]
by the LHCb collaboration for the ${{\mathchar 28931\relax}^{0}_{b}}$ baryon
in the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p$ decay. To this end, we impose the same kinematic requirements
on the $P_{B}$ candidate as applied to the ${{\mathchar 28931\relax}^{0}_{b}}$
candidates in that analysis, namely $p_{T}<20$ GeV and $2.0<y<4.5$, where
$y=\frac{1}{2}\ln\left(\frac{E+p_{z}}{E-p_{z}}\right)$ is the rapidity, $E$
the energy and $p_{z}$ the component of the momentum along the beam direction.
After these preselections, the product of trigger and reconstruction
efficiencies is around 2% for all the modes.

##  4 Selection optimization by a multivariate classifier

The MVA classifier is trained using the simulated signal samples described at
the end of Section 2 and a background sample of candidates in data with
invariant masses within 0.5$\mathrm{\,Ge\kern-1.00006ptV}$ above the strong-
decay threshold in each final state (see Fig. 2). We use $3\times 10^{6}$
$P_{{{B}^{0}}p}^{+}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-})K^{+}\pi^{-}p$ simulated events for modes I,
II and III, with the $P_{{{B}^{0}}p}^{+}$ mass set to 5750 MeV, and $3\times
10^{6}$
$P_{{{B}^{0}_{s}}p}^{+}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-})(\phi\rightarrow K^{+}K^{-})p$ simulated
events for mode IV, with the $P_{{{B}^{0}_{s}}p}^{+}$ mass set to 5835 MeV.
The dependence of the selection efficiency as a function of mass is accounted
for in Section 5.

Figure 2: Invariant mass distributions above the decay mass thresholds for the
indicated modes.

The training samples needed to model the backgrounds in the signal regions
must represent the actual backgrounds as closely as possible. Contamination in
the background samples can occur from fully reconstructed weakly decaying
$b$-hadrons that are combined with random particles. In mode I, we find
contributions from ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-}$ decays and
$B_{s}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}K^{-}$
decays where one of the kaons is misidentified as a pion; then a random
additional proton results in contamination in the background sample. In modes
II and III, along with the ${{B}^{0}}$ and $B_{s}^{0}$ contaminations, a
${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p$ decay can be paired with a random pion. In mode IV, only the
${{B}^{0}}$ and $B_{s}^{0}$ contaminations are seen. These mistaken
identification contributions in the background sample are found by looking at
the invariant mass distributions obtained by switching one or more final-state
particles to another mass hypothesis. If this produces a peak in the mass
distribution at the mass of a known particle, we apply a veto in the
background training sample eliminating all candidates within $\pm 12~{}\\!$MeV
of the peaks, approximately $\pm 1.6~{}\sigma$. No such peaks are seen in the
signal region, after switching the mass hypotheses, for any of the modes. As
an example, we show fully reconstructed decays in the background and signal
regions for mode I in Fig. 3.

The input variables used to train the classifier for modes I, II, and III are
the same. We use the difference in the logarithm of the likelihood for two
different particle hypotheses (DLL). They are the DLL($\mu-\pi$) for the two
muons, DLL($K-\pi$) and DLL($K-p$) for the kaon, DLL($p-\pi$) and DLL($p-K$)
for the proton, and DLL($\pi-K$) for the pion. Also used is the logarithm of
$\chi^{2}_{\text{IP}}$, defined as the difference in $\chi^{2}$ of a given PV
reconstructed with and without the considered $K$, $\pi$, and $p$ tracks, and
the $\chi^{2}$ of the $P_{B}$ to be consistent with originating from the PV.
Other variables are the logarithm of the cosine of the angle of
$\vec{p}_{P_{B}}$ with $\vec{V}_{\\!PV-P_{B}}$, the flight distance of
$P_{B}$, the scalar sum $p_{\mathrm{T}}$ of the $K$, $\pi$ and $p$ tracks, the
$\chi^{2}$/ndof of the fit of all the decay tracks to the $P_{B}$ vertex, and
of the two muon tracks to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
vertex with constraints that fix the dimuon invariant mass to the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass and force the $P_{B}$
candidate to point back to the PV, where ndof indicates the number of degrees
of freedom. The input variables used to train the classifier for mode IV are
similar, but with two kaons instead of a kaon and a pion.

Figure 3: For the
${P_{{{B}^{0}}p}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-}p}$ decay search (mode I), the invariant mass of
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$ combinations in
the (a) region above threshold and in the (b) signal region. The peak in the
sideband region results from ${B}^{0}$ decays.

Two important attributes of multivariate classifiers are signal efficiency and
background rejection, both of which we wish to maximize. Using the input
variables and training samples described earlier, we compared the performances
of some common classifiers, including Boosted Decision Trees (BDT), Gradient
Boosted Decision Trees, Linear Discriminant, and Likelihood Estimators [21].
We base our MVA selection on the BDT algorithm. Once the BDT classifier is
trained, it is evaluated by applying it to a separate testing sample (which is
disjoint from the data sample used to train the classifier). The classifier
assigns a response (called the BDT output) valued between –1 and 1 to the
events, with background events tending toward low values and signal events to
high values. These can be seen in Fig. 4(a) for mode I. The BDT outputs for
other modes look very similar.

Figure 4: (a) Outputs of the BDT classifier for the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$ final state. The
circles (blue) show the signal training sample, and the triangles (red) show
the background training sample, while the shaded (blue) histogram shows the
signal test sample, and the diagonal (red) line-shaded histogram the
background test sample. (b) Efficiencies of signal, solid (blue) curve, and
background, dotted (red) curve, and the value of the $S/(\sqrt{B}+1.5)$,
dashed (green) curve, called “significance,” as a function of the BDT output.

Discrimination between signal candidates, $S$, and background, $B$, is
accomplished by choosing a BDT value that maximizes the metric
$\frac{S}{a/2+\sqrt{B}}$, where $a$ is the significance of the signal sought,
which has the advantage of being independent of the signal cross section [22].
We choose $a$ to be 3 for all modes, based on the assumption that we are in a
situation of looking for a small signal in the midst of larger backgrounds.
The variation of the signal and background efficiencies and the metric’s value
with the BDT output is shown in Fig. 4(b) for mode I. This variation of
efficiencies and the metric with respect to the BDT value is similar for the
other modes. After optimization, the BDT signal efficiency varies from 42.9%
to 71.4% depending on the decay mode.

One cause of concern is reflections where the particle identification fails
leading to the inclusion of other well-known final states. These are
eliminated with a small loss of efficiency by removing candidate combinations
within $\pm 12~{}\\!$MeV of the appropriate $b$-hadron mass. A list of these
reflections in the particular modes of interest is given in Table 2.

Table 2: Decay modes that are vetoed for each pentaquark candidate mode and the specific particle misidentification that causes the reflection. Search mode |  Reflection | Particle misidentification
---|---|---
$P^{+}_{B^{0}p}~{}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$ | $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}\pi^{+}$ |  $\pi^{+}$ to $p$
| $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}\pi^{-}K^{+}$ |  $\pi^{+}$ to $K^{+}$ and $K^{+}$ to $p$
$P^{-}_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{-}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p$ | $B^{-}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}\pi^{+}$ |  $\pi^{+}$ to $p$
| $B^{-}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}(\phi\rightarrow K^{-}K^{+})\pi^{-}$ |  $K^{+}$ to $p$
$P^{+}_{{{\mathchar 28931\relax}^{0}_{b}}\pi^{+}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$ | $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}(\phi\rightarrow K^{-}K^{+})\pi^{+}$ |  $K^{+}$ to $p$
$P^{+}_{{{B}^{0}_{s}}p}~{}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$ | $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$ |  $K^{+}$ to $p$

##  5 Results

After the selections were decided upon, the analysis was unblinded. A search
is conducted by scanning the $P_{B}$ invariant mass distributions in the four
final states shown in Fig. 5. The step size used in these scans is
4.0$\mathrm{\,Me\kern-1.00006ptV}$, corresponding to about half the invariant
mass resolution. No signal is observed with the expected width of
approximately 7.5 MeV. The $P_{B}$ mass resolution seen in the simulated
samples is 6.0 MeV for modes I, II, III, and 5.2 MeV for mode IV which, as
expected, is similar to the 7.5 MeV width seen in data for the ${{\mathchar
28931\relax}^{0}_{b}}$ baryon in the $({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-})K^{-}p$ final state, when the two muons are
constrained to the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass. In
order to obtain conservative results, we set upper limits based on the wider
7.5 MeV signal width.

At each $P_{B}$ scan mass value $m_{P_{B}}$, the signal region is a $\pm
2\sigma(m_{P_{B}})$ window around $m_{P_{B}}$, while the background is
estimated by interpolating the yields in the sidebands starting at
$3\sigma(m_{P_{B}})$ from $m_{P_{B}}$ and extending to $5\sigma(m_{P_{B}})$,
both below and above $m_{P_{B}}$ following Ref. [23]. The statistical test at
each mass is based on the profile likelihood ratio of Poisson-process
hypotheses with and without a signal contribution, where the uncertainty on
the background interpolation is modeled as purely Poisson (see Ref. [23] for
details). No significant excess of signal candidates is observed over the
expected background. The upper limits are set on the signal yields using the
profile likelihood technique, in which systematic uncertainties are handled by
including additional Gaussian terms in the likelihood.

Figure 5: Reconstructed mass distributions after the BDT selection for the (a)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$, (b)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p,$ (c)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$, and (d)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$ final states.

In the absence of a significant signal, we set upper limits in each $P_{B}$
candidate mass interval on the ratio

$R=\frac{\sigma(pp\rightarrow
P_{B}X)\cdot{\cal{B}}(P_{B}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}X)}{\sigma(pp\rightarrow{{\mathchar
28931\relax}^{0}_{b}}X)\cdot{\cal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p)}~{},$ (1)

where we use the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p$ channel for normalization. The product of the production cross
section and branching fraction of this channel has been measured by the LHCb
collaboration [20] to be

$\displaystyle\sigma({{\mathchar 28931\relax}^{0}_{b}},\sqrt{s}=7\,{\rm
TeV})\cdot{\cal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p)=6.12\pm 0.10\pm 0.25\,{\rm nb},$ (2)
$\displaystyle\sigma({{\mathchar 28931\relax}^{0}_{b}},\sqrt{s}=8\,{\rm
TeV})\cdot{\cal{B}}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p)=7.51\pm 0.08\pm 0.31\,{\rm nb},$

where the uncertainties are statistical and systematic, respectively. The
systematic uncertainties include those on the luminosity and detection
efficiencies that partially cancel, lowering the effective systematic
uncertainty on the normalization. These measurements are averaged, taking into
account the different luminosities at the two energies, to produce the overall
normalization factor of $NF=7.03\pm 0.06\pm 0.17$ nb.

Simulations have been generated at four different $P_{B}$ masses for each
decay mode. The total selection efficiency varies from 0.45% to 1.4% depending
on mass and decay mode. The mass dependence of the efficiencies is
parametrized by a second-order polynomial, for each decay mode, and
incorporated into the upper limit calculation. The dominant source of
uncertainty on the efficiency is systematic, and arises from the calibration
applied to the particle identification as calculated by the simulation. This
absolute efficiency uncertainty varies from 0.02% to 0.17% depending on the
decay mode. The statistical uncertainties on the efficiency are negligible.
Note that we are taking the $P_{B}$ lifetime as 1.5 ps, and all simulated
efficiencies assume that the $P_{B}$ decays are given by phase space.

For modes I, II, and III, the upper limits on $S$ are normalized to obtain the
upper limits on $R$ according to

${\rm UL}(R)=\frac{{\rm
UL}(S)}{{\cal{L}}\cdot{\cal{B}}({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-})\cdot NF}~{},$ (3)

where ${\rm UL}(S)$ is the efficiency corrected upper limit on $S$ in each
particular mass bin, ${\cal{L}}$ is the integrated luminosity and
${\cal{B}}({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-})$ is the branching fraction for the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$
decay. For mode IV, an additional factor of ${\cal{B}}(\phi\rightarrow
K^{+}K^{-})$, which is the branching fraction for the $\phi\rightarrow
K^{+}K^{-}$ decay, is included in the denominator of Eq. 3.

The systematic uncertainty on UL$(R)$ arises from the differences in analysis
requirements between the search mode and the normalization mode (2%), which is
estimated based on the differences the selection requirements could make in
the relative efficiencies. The detection of an additional track (1%), given by
the uncertainty in the data-driven tracking efficiency corrections, and the
identification of this track (1%), given by the uncertainties in the particle
identification calibration procedure, leads to an overall systematic
uncertainty of 2.4%. For mode IV, the small uncertainty on
${\cal{B}}(\phi\rightarrow K^{+}K^{-}$) is also taken into account. These
uncertainties are added in quadrature with the uncertainty on $NF$. The upper
limits on $R$ are then increased linearly by this small systematic
uncertainty. The results for UL($R$) at 90% confidence level (CL) are shown in
Fig. 6. Low invariant mass cut-offs in each mode are imposed when the
efficiency uncertainty becomes large.

Figure 6: Upper limits on $R$ at 90% CL for (a)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$, (b)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p$, (c)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$, and (d)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$ final states.

##  6 Conclusions

We have searched for pentaquark states containing a $b$ quark that decay
weakly via the $b\rightarrow c\overline{c}s$ transition in the final states
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}p$,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{-}p$,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}\pi^{+}p$, and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi p$. Such states have been
speculated to exist [3, 4, 5, 6]. No evidence for these decays is found. Upper
limits at 90% confidence level on the ratio of the production cross sections
of these states times the branching fractions into the search modes, with
respect to the production and decay of the ${\mathchar 28931\relax}^{0}_{b}$
baryon in the mode ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}p$
($R$, see Eq. 1) are found to be about $10^{-3}$, depending on the final state
and the hypothesized mass of the pentaquark state.

## Acknowledgements

We thank I. Klebanov for useful discussions. We express our gratitude to our
colleagues in the CERN accelerator departments for the excellent performance
of the LHC. We thank the technical and administrative staff at the LHCb
institutes. We acknowledge support from CERN and from the national agencies:
CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3
(France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (The Netherlands);
MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo
(Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom);
NSF (USA). We acknowledge the computing resources that are provided by CERN,
IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands),
PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS
(Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC
(USA). We are indebted to the communities behind the multiple open-source
software packages on which we depend. Individual groups or members have
received support from AvH Foundation (Germany), EPLANET, Marie Skłodowska-
Curie Actions and ERC (European Union), ANR, Labex P2IO, ENIGMASS and OCEVU,
and Région Auvergne-Rhône-Alpes (France), RFBR and Yandex LLC (Russia), GVA,
XuntaGal and GENCAT (Spain), Herchel Smith Fund, the Royal Society, the
English-Speaking Union and the Leverhulme Trust (United Kingdom).

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Tomassetti17,g, D. Tonelli24, R. Tourinho Jadallah Aoude1, E. Tournefier4, M.
Traill53, M.T. Tran41, M. Tresch42, A. Trisovic49, A. Tsaregorodtsev6, P.
Tsopelas43, A. Tully49, N. Tuning43,40, A. Ukleja29, A. Usachov7, A.
Ustyuzhanin35, U. Uwer12, C. Vacca16,f, A. Vagner70, V. Vagnoni15,40, A.
Valassi40, S. Valat40, G. Valenti15, R. Vazquez Gomez40, P. Vazquez
Regueiro39, S. Vecchi17, M. van Veghel43, J.J. Velthuis48, M. Veltri18,r, G.
Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M. Vesterinen57,
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Vilasis-Cardona38,m, M. Vitti49, V. Volkov33, A. Vollhardt42, B. Voneki40, A.
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Zonneveld52, S. Zucchelli15.

1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National University of Science and Technology MISIS, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

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