Search for beautiful tetraquarks in the $\Upsilon(1S)\mu\mu$ invariant-mass spectrum

The $\Upsilon(1S)\mu^+\mu^-$ invariant-mass distribution is investigated for a possible exotic meson state composed of two $b$ quarks and two $\overline{b}$ quarks, $X_{b\overline{b}b\overline{b}}$. The analysis is based on a data sample of $pp$ collisions recorded with the LHCb detector at centre-of-mass energies $\sqrt{s} =$ 7, 8 and 13 TeV, corresponding to an integrated luminosity of 6.3 fb$^{-1}$. No significant excess is found, and upper limits are set on the product of the production cross-section and the branching fraction as functions of the mass of the $X_{b\overline{b}b\overline{b}}$ state. The limits are set in the fiducial volume where all muons have pseudorapidity in the range $[2.0,5.0]$, and the $X_{b\overline{b}b\overline{b}}$ state has rapidity in the range $[2.0,4.5]$ and transverse momentum less than 15 GeV/$c$.


Introduction
Since the discovery of the X(3872) state [1], over thirty exotic hadrons have been observed by several experiments (see refs. [2][3][4][5][6][7] for recent reviews). Most progress has been seen in the charmonium sector, where tetraquark (pentaquark) candidates with masses around 4 GeV/c 2 have been found decaying to final states containing charmonia and are believed to have a minimal quark content of ccqq (ccqq q ), where q refers to a light quark (u, d, s). Two tetraquark states have also been seen in the bottomonium sector, via their decay to Υ π final states [8].
So far, no exotic hadron that is composed of more than two heavy quarks has been observed. However, there have recently been several predictions for the mass and width of an exotic state, X bbbb (denoted by X in the following), with quark composition bbbb [9][10][11][12][13][14][15][16][17][18][19]. These predictions indicate that the X state would have a mass in the region [18.4, 18.8] GeV/c 2 , placing it close to, but typically below, the η b η b threshold of 18.798 ± 0.005 GeV/c 2 [20], which implies that it could decay to Υ + − ( = e, µ) final states. Further motivation is provided by the recent observation of Υ (1S)Υ (1S) production by the CMS collaboration [21]. Possible search strategies for the X state have been outlined in ref. [22], and the product of its production cross-section at the LHC and the branching fraction to four muons is estimated to be of O(1 fb). However, recent lattice QCD calculations do not find evidence for such a state in the hadron spectrum [23].

JHEP10(2018)086
The current paper presents the first search for this state decaying to Υ (1S)µ + µ − through a study of the four-muon invariant-mass distribution, m(2µ + 2µ − ), between 17.5 and 20.0 GeV/c 2 . The dataset consists of pp collision data recorded by the LHCb experiment at centre-of-mass energies of √ s = 7 TeV, 8 TeV and 13 TeV between 2011 and 2017. The corresponding integrated luminosities are 1.0 fb −1 , 2.0 fb −1 and 3.3 fb −1 , respectively. The Υ (1S) → µ + µ − decay is used as a normalisation channel to calculate the X production cross-section relative to that of the Υ (1S) meson.

Detector and simulation
The LHCb detector [24,25] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 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 Tm, and three stations of silicon-strip detectors and straw drift tubes 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 GeV/c. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [26].
Simulated datasets are used to evaluate reconstruction and selection efficiencies of the Υ (1S) and X decays studied in this paper. In the simulation, pp collisions are generated using Pythia [27,28] with a specific LHCb configuration [29]. Decays of hadronic particles are described by EvtGen [30], in which final-state radiation is generated using Photos [31]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [32,33] as described in ref. [34]. The X state is produced using the same production model as the Υ (4S) meson, with the mass changed to one of three values in the range 18 450 − 18 830 MeV/c 2 . The natural width of the X state is assumed to be 1.2 MeV/c 2 and its decay to the Υ (1S)µ + µ − final state is modelled by a phase-space distribution. The kinematic distribution of simulated X particles is shown in appendix A.

Event selection
For both signal and normalisation channels, the Υ (1S) → µ + µ − candidates are first required to pass the trigger [35], 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. At the hardware level, a minimum requirement is placed on the product of -2 -

JHEP10(2018)086
the transverse momenta of the two muons. At the software level, requirements are made on the total and transverse momentum of these muons, the dimuon invariant mass and on the quality of the dimuon vertex fit. Additionally, requirements are placed on the track quality of the muons and on particle identification (PID) quantities of the muons.
In the offline selection, all muons are required to have p ∈ [8, 500] GeV/c, p T larger than 1 GeV/c and η ∈ [2.0, 5.0]. Stringent requirements are also applied to muon trackquality and PID quantities to reduce backgrounds from particles that are misidentified as muons. For both signal and normalisation channels, all muons are required to be consistent with originating from a common PV. The Υ (1S) → µ + µ − candidates are required to have invariant masses m(µ + µ − ) ∈ [8.5, 11.5] GeV/c 2 and a good vertex-fit quality.
For the X → Υ (1S)µ + µ − decay, the Υ (1S) candidates are combined with an additional dimuon pair with a good vertex-fit quality. In addition to the four-muon vertex fit having good quality, the X candidates are required to have invariant masses m(2µ + 2µ − ) ∈ [16.0, 22.0] GeV/c 2 , rapidities in the range [2.0, 4.5] and p T less than 15 GeV/c. If a same-charge pair of muons has an invariant mass less than 220 MeV/c 2 or an opening angle smaller than 0.002 radians, then the corresponding X candidate is removed. This requirement eliminates pairs of muon candidates that are wrongly reconstructed from one single track. Candidates are also rejected if the combination of either muon from the Υ (1S) decay with the oppositely charged additional muon has an invariant mass consistent with that of the J/ψ meson, m(µ + µ − ) ∈ [3050, 3150] MeV/c 2 . The signal sample is a subset of the normalisation sample, smaller by a factor of O(10 4 ).
Multiple X candidates are seen in approximately 10 % of events that pass the full selection and have m(µ + µ − ) within ±100 MeV/c 2 of the known Υ (1S) mass [20]. These are mostly due to the same Υ (1S) candidate being combined with different additional dimuons. These candidates are retained and treated as combinatorial background. Events with multiple candidates in the normalization Υ (1S) dataset occur at a negligible level.

Invariant-mass fits
Unbinned extended maximum-likelihood fits are made to the m(2µ + 2µ − ) and m(µ + µ − ) distributions to determine X and Υ (1S) yields, respectively. Fits to three datasets collected at pp centre-of-mass energies of √ s = 7 TeV in 2011, 8 TeV in 2012 and 13 TeV in 2015-2017 are performed. In addition, a fit is made to a merged dataset that combines all 7, 8 and 13 TeV subsets. In each fit, the combinatorial background component is described by an exponential function with the slope and normalisation as free parameters. Signal components are described by Crystal Ball functions [36] with the tail parameters fixed to values obtained from fits to the simulated samples.
In fits to the m(µ + µ − ) distributions, contributions from the Υ (1S), Υ (2S) and Υ (3S) states are included. For the Υ (1S) contribution, the mean, µ Υ (1S) , and width, σ Υ (1S) , of the shape are free parameters. For the Υ (nS) contributions (n = 2, 3) the means are free parameters while each width is fixed to that of the Υ (1S) component scaled by the ratio of the Υ (1S) and Υ (nS) masses. The number of candidates of each component is free in each fit. In the fits to the m(2µ + 2µ − ) distributions, the mean of the X contribution, µ X , takes a value in the range [17.5, 20.0] GeV/c 2 , while the width, σ X , is calculated as the product of the corresponding Υ (1S) resolution and a linear X-mass-dependent scaling factor [37],

Normalisation factor
Upper limits are set for different X mass hypotheses on the quantity where σ(pp → X) is the X production cross-section, and B(X → Υ (1S)µ + µ − ) and decays, respectively. To set limits on S, the signal yield is parameterised as N sig = S/f norm with where σ(pp → Υ (1S)) is the production cross-section of the Υ (1S) meson [38, 39] within the same fiducial volume as the signal. The Υ (1S) → µ + µ − yield within the range R Υ (1S) is given by N norm , and sig(norm) is the efficiency with which the signal (normalisation) channel is triggered, reconstructed and selected. The relative efficiency of the reconstruction and selection requirements placed on the corresponding signal and normalisation datasets is defined as where geom is the efficiency with which the products of the X or Υ (1S) decay all enter the LHCb geometric acceptance; sel is the efficiency of the reconstruction and selection of X or Υ (1S) candidates within the geometric acceptance; PID sig is the efficiency of the PID requirements placed on the additional muons in the signal decay; and f trk sig accounts for  differences between data and simulation in the tracking efficiency of the additional muons. The geometric and selection efficiencies are determined from simulated samples, while the PID efficiency is determined from calibration data samples. The ratio of efficiencies between the signal and normalisation samples is determined to be 31.7 ± 0.6 % (35.2 ± 1.2 %) for the 7, 8 TeV (13 TeV) dataset, where the same efficiency is used for 7 and 8 TeV collisions due to the similar performance of the LHCb detector during these operational periods.
Uncertainties on these quantities give rise to systematic uncertainties in the fits to the signal datasets and enter these fits as a Gaussian function constraining the value of f norm . These systematic uncertainties are detailed further in section 6. In the case of the combined dataset, averages of the efficiency ratio and normalisation cross-section, weighted by the integrated luminosity of each subset, are used to calculate f norm . The values of f norm are 11.1 ± 1.5, 6.49 ± 0.25, 3.27 ± 0.24 and 1.82 ± 0.10 fb for the 7, 8, 13 TeV and combined datasets, respectively. Systematic uncertainties are included in the fits to the distribution of m(2µ + 2µ − ) through additional Gaussian terms in the likelihood function that constrain the values of four nuisance parameters: f norm , σ Υ (1S) , p 0 and p 1 . Uncertainties on the normalisation yields, the Υ (1S) production cross-sections, and the relative efficiencies of the signal and normalisation channels all contribute to the uncertainty on the f norm parameter. The uncertainty on σ Υ (1S) is obtained from the fit to the m(µ + µ − ) distribution of the normalisation channel. The linear coefficients of the X-mass-dependent resolution scale term are constrained according to the uncertainties on these parameters from fits to simulated data.
The relative uncertainties on the σ Υ (1S) , p 0 and p 1 parameters are 0.1 %, 0.5 % and 46 %, respectively. Since these parameters are weakly correlated with the signal yield their effects on the measured cross-section upper limits are negligible. The uncertainty on the f norm parameter for each dataset is dominated by uncertainties on the normalisation crosssection (2.8 to 6.3 %) and the tracking efficiency correction (0.8 to 3.1 %). The systematic uncertainties from efficiencies related to particle identification or geometrical acceptance are at the level of 1.0 % or less. For the 7 TeV result, a discrepancy is observed in the efficiency-and cross-section-corrected Υ (1S) yield relative to the other datasets. An additional uncertainty of 13.5 % is assigned to account for this. This uncertainty increases the limits on the cross section at 7 TeV by < 4 % and has no effect on the quoted combined limits. The limits reported on the X production cross-section are all statistically dominated.

Limit setting
For each signal dataset, upper limits are set on S as functions of the X mass, µ X , in the range [17.5, 20.0] GeV/c 2 using the following procedure. For each fixed X mass, the likelihood profile as a function of S is integrated to determine upper limits on the crosssection at 90 % and 95 % confidence levels (CL). This procedure is applied at each of 101 values of the X mass. The 90 % and 95 % CL limits are tabulated in appendix A. Background-only pseudoexperiments are generated at each scan point to determine the expected 95 % CL upper limit and corresponding one and two standard deviation intervals, as shown in figure 4. No significant excess is seen at any mass hypothesis for any dataset.
The analysis is repeated with only a single candidate decay retained for each event (chosen at random), with a more stringent requirement on the pseudorapidity of the muons as was previously used in ref. [40]. In addition, the effect of the assumption that the X decays according to a phase-space distribution is tested by evaluating the efficiency for both m(µ + µ − ) less than 2 GeV/c 2 and m(µ + µ − ) greater than 7 GeV/c 2 for the muon pairs that do not come from the Υ (1S) decay. The efficiency varies ±24 % with respect to the total efficiency under the assumption of a phase-space decay. Finally, the limits are evaluated using different ranges around the Υ (1S) mass to select the signal dataset, separately for each year of the √ s = 13 TeV dataset, and for the 7 and 8 TeV datasets combined. No significant differences are observed in the limits determined in each of these cross-checks. [fb] Obs. 95% CL limit Obs. 95% CL limit Exp. 95% CL limit, median [fb] Obs. 95% CL limit Exp. 95% CL limit, median

Conclusions
In conclusion, a search is performed for the decay of the beautiful tetraquark, X, to the Υ (1S)µ + µ − final state.
No significant excess is seen for any mass hypothesis in the range [17.5, 20.0] GeV/c 2 .