Edinburgh Research Explorer Search for the X(4140) state in B+J/K+ decays with the D0 detector

We investigate the decay B + → J/ψφK + in a search for the X (4140) state, a narrow threshold resonance in the J/ψφ system. The data sample corresponds to an integrated luminosity of 10 . 4 fb − 1 of pp collisions at √ s = 1 . 96 TeV collected by the D0 experiment at the Fermilab Tevatron collider. We observe a mass peak with a statistical signiﬁcance of 3.1 standard deviations and measure its invariant mass to be M = 4159 . 0 ± 4 . 3 (stat) ± 6 . 6 (syst) MeV and its width to be Γ = 19 . 9 ± 12 . 6 (stat) +1 . 0 − 8 . 0 (syst) MeV. Identifying this mass peak as the X (4140), we measure, for M ( J/ψφ ) < 4 . 59 GeV, the relative branching fraction B rel = B ( B + → X (4140) K + ) / B ( B + → J/ψφK + ) to be 21 ± 8 (stat) ± 4 (syst)%. In addition, the data can accommodate the presence of a second enhancement at a mass of 4328 . 5 ± 12 . 0 MeV.

We investigate the decay B + → J/ψφK + in a search for the X(4140) state, a narrow threshold resonance in the J/ψφ system. The data sample corresponds to an integrated luminosity of 10.4 fb −1 of pp collisions at √ s = 1.96 TeV collected by the D0 experiment at the Fermilab Tevatron collider.
We observe a mass peak with a statistical significance of 3.1 standard deviations and measure its invariant mass to be M = 4159.0 ± 4.3 (stat) ± 6.6 (syst) MeV and its width to be Γ = 19.9 ± 12.6 (stat) +1.0 −8.0 (syst) MeV. Identifying this mass peak as the X(4140), we measure, for M (J/ψφ) < 4.59 GeV, the relative branching fraction B rel = B(B + → X(4140)K + )/B(B + → J/ψφK + ) to be 21 ± 8 (stat) ± 4 (syst)%. In addition, the data can accommodate the presence of a second enhancement at a mass of 4328.5 ± 12.0 MeV. The X(4140) state [1] is a narrow resonance in the J/ψφ system produced near threshold. The CDF Collaboration reported the first evidence [2] for this state (termed Y (4140)) in the decay B + → J/ψφK + (charge conjugation is implied throughout) and measured the invariant mass M = 4143.0 ± 2.9(stat) ± 1.2 (syst) MeV and width Γ = 11.7 +8.3 −5.0 (stat) ± 3.7 (syst) MeV. The Belle Collaboration searched for X(4140) in the process γγ → J/ψφ and, finding no significant signal, reported upper limits on the product of the partial width Γ γγ and branching fraction X(4140) → J/ψφ for J P = 0 + and 2 + [3]. At the LHC, both the LHCb and CMS Collaborations have searched for the state. The LHCb Collaboration found no evidence [4], in disagreement with the CDF measurement. A preliminary report [5] from the CMS Collaboration on a search for the same signature supports the CDF observation. With two out of four experiments failing to observe the X(4140) resonance the question of the existence of this state still remains open. A detailed review is given in Ref. [6].
The quark model of three-quark baryons and quarkantiquark mesons does not predict a hadronic state at this mass. The decay channel suggests that this resonance may be a cc bound state. However, at this mass, * with visitors from a Augustana College, Sioux Falls, SD, USA, above the open-charm threshold of 3740 MeV, it is unlikely to be a conventional charmonium state. Such states are expected to decay predominantly to pairs of charmed mesons and they would have a much larger width than experimentally observed. It has been suggested that X(4140) is a molecular structure made of two charmed mesons, e.g. (D s , D s ), but other possible states are hybrid particles composed of two quarks and a valence gluon (qqg) or four-quark combinations (ccss). For details see the review of hadronic spectroscopy in Ref. [7] and references therein.
In addition to X(4140), the CDF Collaboration reported seing a second enhancement in the same channel, located near 4.29 GeV. A similar structure is also seen by the CMS Collaboration [5]. Belle also reports a new structure at M = 4350.6 +4.6 −5.1 (stat) ± 0.7 (syst) MeV. In this Article we present results of a search for the X(4140) resonance and any excited states in the J/ψφ system in the decay sequence B + → J/ψφK + , J/ψ → µ + µ − , φ → K + K − . The data sample corresponds to an integrated luminosity of 10.4 fb −1 collected with the D0 detector in pp collisions at the Fermilab Tevatron collider.
The D0 detector consists of a central tracking system, calorimetry system and muon detectors, as detailed in Ref. [8]. The central tracking system comprises a silicon microstrip tracker (SMT) and a central fiber tracker (CFT), both located inside a 1.9 T superconducting solenoidal magnet. The tracking system is designed to optimize tracking and vertexing for pseudorapidities |η| < 3, where η = − ln[tan(θ/2)], and θ is the polar angle with respect to the proton beam direction. The SMT can reconstruct the pp interaction vertex (PV) for interactions with at least three tracks with a precision of 40 µm in the plane transverse to the beam direction and determine the impact parameter of a track relative to the PV with a precision between 20 and 50 µm, depending on the number of hits in the SMT. The muon detector, positioned outside the calorimeter, consists of a central muon system covering the pseudorapidity region of |η| < 1 and a forward muon system covering the pseudorapidity region of 1 < |η| < 2. Both central and forward systems consist of a layer of drift tubes and scintillators inside 1.8 T toroidal magnets and two similar layers outside the toroids [9].
We use the Monte Carlo (MC) event generator pythia [10] interfaced with the particle decay package EvtGen [11] to simulate the decay chain B + → J/ψφK + , J/ψ → µ + µ − , φ → K + K − . The B + decay is simulated according to three-body phase space. The detector response is simulated with geant [12]. Simulated signal events are overlayed with events from randomly collected pp bunch crossings to simulate multiple interactions.
Events used in this analysis are collected with both single-muon and dimuon triggers. Candidate events are required to include a pair of oppositely charged muons accompanied by three additional charged particles with transverse momenta above 0.7 GeV. Both muons are required to be detected in the muon chambers inside the toroid magnet, and at least one of the muons is required to be also detected outside the toroid [13]. Each of the five final-state tracks is required to have at least one SMT hit and at least one CFT hit.
To form B + candidates, muon pairs in the invariant mass range 2.9 < M (µ + µ − ) < 3.3 GeV, consistent with J/ψ decay, are combined with pairs of oppositely charged particles (assigned the kaon mass hypothesis) with an invariant mass in the range 0.99 < M (K + K − ) < 1.07 GeV and with a third charged particle, also assigned the kaon mass hypothesis. The third kaon is required to have at least three SMT hits. The dimuon invariant mass is constrained in the kinematic fit to the world-average J/ψ mass [1] and the five-track system is constrained to a common vertex. The trajectories of the five B + decay products are adjusted according to the decay and kinematic fit. The adjusted track parameters are used in the calculation of the B + candidate mass. The B + candidates are required to have an invariant mass in the range 5.15 < M (J/ψK + K − K + ) < 5.45 GeV. The χ 2 of the B + vertex fit is required to be less than 20 for 6 degrees of freedom, with the contribution of the third kaon to the χ 2 required to be less than 4.
To reconstruct the PV, tracks are selected that do not originate from the candidate B + decay, and a constraint is applied to the average beam-spot position in the transverse plane. We define the signed decay length of a B + meson, L B xy , as the vector pointing from the PV to the decay vertex, projected on the transverse plane. We require L B xy to be greater than 250 µm to suppress background from prompt J/ψ production. The angle between the pointing vector and the B + meson transverse momentum is required to be less than 3.6 • . We also reconstruct the decay vertex of the J/ψφ pair and require the dis-tance between the B + and J/ψφ vertices in the transverse plane and in the beam direction to be less than 50 µm and less than 150 µm, respectively (five times the RM S determined by MC). The selection is limited to events with M (J/ψφ) below 4.59 GeV. At larger masses background from other b hadron decays is large.
Background arises from a misidentified φ meson or a misidentified third kaon. To suppress background contribution from combinations including particles produced in the hadronization process or in other B hadron decays, we require the transverse momentum of the B + meson to be between 7 and 30 GeV. The fraction of the B + transverse momentum carried by the three kaons is required to be greater than 0.2. We remove decays B → ψ(2S) + X by vetoing the mass range 3.661 < M (J/ψπ + π − ) < 3.711 GeV, equivalent to ±2.5 standard deviations around the world-average ψ(2S) mass [1], for all combinations of J/ψ produced with a pair of oppositely charged particles assigned a pion mass hypothesis. For the remaining sample, we accept one candidate per event, selecting the combination with the lower φ candidate mass. Simulations show that this choice is 95% efficient for the signal. Any sample bias resulting from the above selection is quantified and corrected using the efficiency determined by MC simulations.
The J/ψφK + invariant mass distribution for B + decay candidates satisfying the mass requirement 1.005 < M (φ) < 1.035 GeV consistent with the φ mass is shown in Fig. 1(a). A binned maximum-likelihood fit of a Gaussian signal with a mass resolution set to the value of 18 MeV (obtained from simulations), with a second-order Chebyshev polynomial background, yields 215 ± 37 B + events with a mean mass of M (B + ) = 5277.8 ± 3.3 MeV, consistent with the world-average value of B + mass [1]. We define the signal mass range as 5.23 < M (B + ) < 5.33 GeV. Figure 1(b) shows the J/ψ signal for events in the B + signal region. A fit of a Gaussian function and a second-order Chebyshev polynomial background yields 1124 ± 70 J/ψ events out of a total of 1269 µ + µ − candidates, showing that most of the selected events, including background, have a J/ψ in the final state.
To establish a correspondence between the B + signal and the φ → K + K − decay, we compare the invariant mass distributions of the φ candidates in the B + signal region and in the sidebands, defined as 5.15 < M (J/ψφK + ) < 5.23 GeV or 5.33 < M (J/ψφK + ) < 5.45 GeV. As seen in Fig. 2(a), there is a clear φ signal in the B + signal region, while the φ signal is much less pronounced in the B + sidebands. A fit, shown in Fig. 2(b), of a relativistic P -wave Breit-Wigner function with parameters set to the world-average values and a resolution of 3 MeV taken from simulations, together with a secondorder Chebyshev polynomial background, yields 284 ± 40 φ candidates. A similar fit to the M (K + K − ) distribution in the B + sideband yields 115 ± 51 φ candidates. Scaling the φ yield to the signal region leads to approximately 50 candidates. Thus, the total number of φ events in the B + signal region is consistent with the sum of the num- ber of B + events determined in Fig. 1 and the expected contribution from background processes.
We examine combinations of J/ψ with one, two, or three charged particles, searching for structures that would affect the analysis of the J/ψφ distribution. There are multiple reasons for this study: (i) a resonance in a subsystem may create an enhancement in the M (J/ψφ) distribution leading to a false signal, (ii) identifying resonances and applying appropriate mass restrictions to eliminate their effects would reduce background, (iii) finding a resonance and fitting its mass and width provides an in situ calibration of the mass and resolution for a given configuration.
Of particular concern is the new charged charmoniumlike object, Z(3900) ± , observed independently by the BESIII [14] and Belle [15] Collaborations in the J/ψπ + decay channel. The distributions of M (J/ψK), where the J/ψ is paired with the particle that is not associated with the φ decay in the reconstructed B + decay, is shown in Fig. 3(a). No structures that would indicate resonances or reflections of other decays are observed. The mass distribution for the same pair under the pion mass assignment, shown in Fig. 3(b), is also structureless.
The M (J/ψπ + π − ) distribution, before application of  Fig. 4. In the fit the resonance mass is set at the world-average value of ψ(2S) mass [1]. A fit with the mass allowed to vary gives the value consistent with the world-average value. The resolution of 10 MeV is consistent with simulations. There are no enhancements other than the ψ(2S) meson peak that we remove from the sample. Figure 5 shows the invariant mass distribution of the J/ψφ candidates within the B + and φ mass windows. Overlaid is the background distribution estimated from the B + sidebands. An enhancement at low masses and a broader enhancement near 4.3 GeV are seen, consistent with the CDF [2] and CMS [5] results.
Small statistics and high background do not allow a detailed two-dimensional analysis of the three-body B + decay. We therefore focus on the one-dimensional projection of data on M (J/ψφ). In the search for the particular state X(4140), we define the allowed region for a possible resonance mass as M (J/ψφ) < 4.20 GeV, well above the X(4140) mass value, taking into account our mass resolution. There are 80 events in this region. According to ensemble tests, with a large number of pseudo-experiments with the same signal and backgroud statistics, and assuming a direct three-body B + decay, the probability of  Fig. 7. The relative efficiency as a function of J/ψφ mass is obtained by comparing the reconstructed spectrum from a full detector simulation with the three-body phase space distribution. The efficiency correction includes effects of the kinematic acceptance, as well as the reconstruction efficiency, the resolution, and the candidate selection efficiency. As shown in Fig. 8, the efficiency is fairly uniform, with bin-to-bin variations within 10%.
To estimate the significance of the threshold structure, we perform a binned least-squares fit of the B + yield to a sum of a resonance and a phase-space continuum template. We assume a relativistic Breit-Wigner signal shape, with mass and width allowed to vary, convoluted with the detector resolution of 4 MeV from simulations. From the fit, shown in Fig. 7(b), we obtain 52 ± 19 (stat) signal events out of the total of 250 ± 36 events. The statistical significance of the structure, estimated from the χ 2 difference with and without a res- 19.9 ± 12.6 (stat) MeV. We identify this structure with X(4140) and we find that the quasi-two body decay B + → X(4140)K + constitutes (21 ± 8 (stat))% of the B + → J/ψφK + decay rate. The data also support the presence of a structure around 4300 MeV, however they do not allow a stable fit with an unconstrained width. When a second resonance is allowed by setting the natural width to 30 MeV, consistent with the CDF data, the fit as shown in Fig. 7(c) returns 47 ± 20 events at an invariant mass of 4328.5 ± 12.0 MeV.
The X(4140) mass and width measurements and the relative branching fraction are subject to systematic uncertainties associated with the precision of the B + mass measurement, with the J/ψφ mass resolution in the vicinity of X(4140), and with the variation of the reconstruction efficiency with M (J/ψφ). To estimate these uncertainties, we perform alternative fits applying more restrictive event selection criteria, using a different bin size, and fitting the net mass distribution of J/ψφ pairs coming from B + decay obtained by subtracting the properly normalized background from the sideband region. In addition, we consider the following variations of the cesses with a similar topology, ψ(2S) → J/ψπ + π − and X(3872) → J/ψπ + π − , the measured mass resolutions are 9.9±0.3 MeV, and 15.9±3.2 MeV, respectively. Both are in a good agreement with simulations. Since the mass resolution is better for lower values of the kinetic energy released in the decay, the resolution for the structures under study is not larger than that for the ψ(2S) decay. We repeat the analysis using the value of 10 MeV. The change in the resolution does not affect the results for the resonance mass and yield but it reduces its width. We assign an asymmetric uncertainty of −8 MeV due to this effect.
We vary the efficiency dependence on M (J/ψφ) within the statistical uncertainties. In alternative fits, we use a relative efficiency that is independent of M (J/ψφ) and also a relative efficiency that drops to the value of 0.8 (instead of the default value of 0.9±0.1) at the M (J/ψφ) threshold.
From the results of the alternative fits we estimate the systematic uncertainties on the X(4140) mass and width to be ±4 MeV and +1 −8 MeV, and the systematic uncertainty of the relative branching fraction to be ±4%. We estimate the uncertainty in the J/ψφ mass scale from the vertex reconstruction by comparing M def = M (J/ψφ) value used in this analysis with the alternative estimate, obtained from the mass difference M alt = M (µ + µ − K + K − ) − M (µ + µ − ) + M (J/ψ). The difference ∆M = M def − M alt is on average 1.3 MeV, and the RM S is 5.2 MeV. We conclude that there is no significant mass bias due to the vertexing procedure and we conservatively assign a systematic uncertainty of ±5.2 MeV due to the uncertainty in the J/ψφ mass scale. The statistical significance of the X(4140) signal is larger than 3 standard deviations in all alternative fits. A search conducted in the entire mass range (4.11, 4.59) GeV, ignoring the prior observation of X(4140), would result in the signal significance reduced due to the "look elsewhere effect" [16] by the trial factor of 5 to 2.6 standard deviations.
In summary, in the decay B + → J/ψφK + , we find a threshold enhancement in the J/ψφ mass distribution consistent with the X(4140) state with a statistical significance of 3.1 standard deviations. The data can also accommodate a second structure, at M 2 = 4328.5 ± 12.0 MeV, consistent with Ref. [3]. The measured invariant mass of the lower-mass peak is 4159.0 ± 4.3 (stat) ± 6.6 (syst) MeV and the measured width is 19.9 ± 12.6 (stat)