Observation of a peaking structure in the J/psi phi mass spectrum from B(+/-) to J/psi phi K(+/-) decays

A peaking structure in the J/psi phi mass spectrum near threshold is observed in B(+/-) to J/psi phi K(+/-) decays, produced in pp collisions at sqrt(s) = 7 TeV collected with the CMS detector at the LHC. The data sample, selected on the basis of the dimuon decay mode of the J/psi, corresponds to an integrated luminosity of 5.2 inverse femtobarns. Fitting the structure to an S-wave relativistic Breit-Wigner lineshape above a three-body phase-space nonresonant component gives a signal statistical significance exceeding five standard deviations. The fitted mass and width values are m = 4148.0 +- 2.4 (stat.) +- 6.3 (syst.) MeV and Gamma = 28 +15 -11 (stat.) +- 19 (syst.) MeV, respectively. Evidence for an additional peaking structure at higher J/psi phi mass is also reported.


Introduction
The discovery of new charmonium-like states [1][2][3][4][5][6] over the last decade poses a challenge to the conventional quark model.Many explanations, such as charmed hybrids, tetraquarks, and molecular states, have been proposed for these new entities, but their nature remains a puzzle [7,8].In 2009, the CDF Collaboration reported evidence for a narrow structure, which they called Y(4140), near the J/ψφ threshold in B ± → J/ψφK ± decays [9].This structure, if confirmed as a new resonance, would be a candidate for an exotic meson [10][11][12][13][14][15][16][17][18].The Belle Collaboration searched for the Y(4140) through the same B ± decay channel [19] and in the two-photon process γγ → J/ψφ [20], but did not confirm it.Using the same B ± decay channel, the LHCb Collaboration recently reported finding no evidence for such a state, in disagreement with the CDF result [21].
In this Letter, a study of the J/ψφ mass spectrum from B + → J/ψφK + decays is reported, where charge conjugate decay modes are implied throughout.The data were collected in 2011 with the Compact Muon Solenoid (CMS) detector from proton-proton collisions at the Large Hadron Collider (LHC) operating at a center-of-mass energy of 7 TeV and corresponding to an integrated luminosity of 5.2 ± 0.1 fb −1 [22].
A detailed description of CMS can be found elsewhere [23].The central feature of the CMS apparatus is a superconducting solenoid, 13 m long with a 6 m internal diameter, which provides an axial magnetic field of 3.8 T. Within the field volume is the silicon tracker, which consists of a pixel-based detector in the inner region and layers of microstrip detectors in the outer region.Charged-particle trajectories are measured with the silicon tracker, covering 0 < φ ≤ 2π in azimuth and |η| < 2.5, where the pseudorapidity η is defined as − ln(tan[θ/2]) and θ is the polar angle of the trajectory of the particle with respect to the counterclockwise-beam direction.Muons are detected in the pseudorapidity range |η| < 2.4 by three types of gas-ionization detectors embedded in the steel flux-return yoke of the magnet: drift tubes in the barrel, cathode strip chambers in the endcaps, and resistive-plate chambers in both the barrel and endcaps.The strong magnetic field and excellent position resolution of the silicon tracker enable the transverse momentum (p T ) of a muon matched to a reconstructed track to be measured with a resolution of approximately 0.7% for p T of 1 GeV.The pixel detector, with its excellent spatial resolution and low occupancy, enables the separation of B + -decay vertices from the primary interaction vertex.Monte Carlo (MC) simulated data were created using PYTHIA 6 [24] for the particle production, EVTGEN [25] for the particle decays, and GEANT4 [26] for tracing the particles through a detailed model of the detector.These samples were created with the appropriate conditions for the data analyzed, including the effects of alignment, efficiency, and number of simultaneous pp collisions.ments are already applied with the HLT.The dimuon p T is required to be greater than 6.9 GeV, the two muons must be oppositely charged and form a three-dimensional (3D) vertex with a χ 2 probability greater than 0.5-10%, depending on the running period.The resulting J/ψ vertex must be displaced from the average interaction point (beamspot) in the transverse plane by at least three times its uncertainty, which is the sum in quadrature of the secondary-vertex uncertainty and the beamspot size in the transverse plane.The cosine of the angle between the transverse projections of the line joining the beamspot and dimuon vertex and the dimuon momentum direction must exceed 0.9.For the later data set, there is an additional requirement that the p T of each muon be greater than 4 GeV.In the final selection of J/ψ candidates, the dimuon p T is required to be greater than 7 GeV, the χ 2 probability of the dimuon vertex is demanded to be greater than 10%, and the reconstructed dimuon invariant mass must be within 150 MeV of the J/ψ mass [27].
The B + → J/ψφK + candidates are reconstructed by combining three additional charged-particle tracks that are consistent with originating from the displaced J/ψ vertex and have a total charge of ±1.These tracks are assigned the kaon mass and this mass is used in accounting for the effects of energy loss and multiple-scattering.We do not apply a mass constraint on the φ candidate because our experimental K + K − mass resolution (1.3 MeV) is less than the φ meson natural width (4.3 MeV).The p T of all kaon tracks are required to be greater than 1 GeV.Only tracks that pass the standard CMS quality requirements [28] are used.The five tracks, with the µ + µ − invariant mass constrained to the J/ψ mass, are required to form a good 3D vertex with a χ 2 probability greater than 1%.There are two K + K − combinations from the three charged kaon tracks, and we use the lower invariant mass as the φ candidate; MC simulations of the B + decay predict that the φ signal from the other combination is negligible, which is verified in the data.The reconstructed K + K − invariant mass must satisfy 1.008 GeV < m(K + K − ) < 1.035 GeV to be considered as a φ candidate.These selection requirements were designed to maintain high efficiency for B + decays and were fixed before the J/ψφ mass spectrum in data was examined.

Results
The invariant-mass spectrum of the selected J/ψφK + candidates is shown in the left plot of Fig. 1 for a mass difference ∆m ≡ m(µ 568 GeV.We only investigate candidates with ∆m < 1.568 GeV because of possible background from B 0 s → ψ(2S)φ → J/ψπ + π − φ at higher values, as discussed below.The invariant-mass spectrum is fit with a Gaussian signal function and a second-degree polynomial background function.The fit returns a B + mass of 5.2796 ± 0.0006 (stat.)GeV, which agrees with the nominal value [27], and a Gaussian width of 9.6 ± 0.7 (stat.)MeV, which is consistent with the prediction from the MC simulation.The B + yield is 2480 ± 160 (stat.)events, which is the world's largest B + → J/ψ φK + sample.The combined B + yield is 2340 ± 120 (stat.)events when each data set is fit with two Gaussian signal functions and the width of each function is fixed to the prediction from MC simulation.Approximately 5% of the selected events have more than one B + candidate within 1.5 times our mass resolution (σ) of the B + mass; all candidates are kept.
The right plot in Fig. 1 displays the J/ψ K + K − K + invariant-mass distribution after making the following tighter requirements: the p T of the kaons must be greater than 1.5 GeV, the B + vertex probability must be greater than 10%, the B + vertex must be displaced from the primary vertex in the transverse plane by at least seven times its uncertainty, and m(K + K − ) must be within 7 MeV of the φ meson mass [27].With these requirements, 40% of the B + candidates are retained, while the background is reduced by more than a factor of ten.This sample of cleaner signal candidates is used as a cross-check of the results obtained by employing the background-corrected J/ψφ mass spectrum, as described below.With the exception of this cross-check, all results are obtained with the less-restrictive criteria.

Data Fit Background
Figure 1: The J/ψφK + mass distribution with the standard event selection (left) and the tighter requirements (right).The solid curves show the result of fitting these distributions to a Gaussian signal and a second-degree polynomial background while the dashed curves show the background contribution.
Figure 2 shows the K + K − invariant-mass distribution for J/ψ K + K − K + candidates that have an invariant mass within ±3σ of the B + mass.We define events in the range [−12, −6]σ and [6,12]σ of the B + mass as sidebands.The φ mass restriction has been removed and a sideband subtraction has been performed in Fig. 2. We fit this distribution to a P-wave relativistic Breit-Wigner (BW) function convolved with a Gaussian resolution function.The width of the Gaussian is fixed to 1.3 MeV, obtained from MC simulation.The fit has a χ 2 probability of 23% and returns a mass of 1019.4 ± 0.1 MeV and a width of 4.7 ± 0.4 MeV, consistent with the φ meson [27].The good fit to only a φ component in Fig. 2 indicates that after the J/ψ and φ mass requirements are made and the combinatorial background is subtracted, the B + → µ + µ − K + K − K + candidates are consistent with being solely J/ψφK + , with negligible contribution from J/ψf 0 (980)K + or nonresonant J/ψK + K − K + .
As seen in Fig. 1, there are two main components to the J/ψφK + invariant-mass spectrum: the B + signal and a smooth background.Possible contributions from other B-hadron decays are examined using MC simulations of inclusive B + , B 0 , and B 0 s decays.Based on this study, the mass-difference region (∆m > 1.568 GeV) is excluded from the analysis to avoid potential background from B 0 s → ψ(2S)φ → J/ψπ + π − φ decays, where one pion is assumed to be a kaon and the other is not reconstructed.
To investigate the J/ψφ invariant-mass distribution, rather than fitting the distribution itself with its large combinatorial background, the J/ψφK + candidates are divided into 20 MeV-wide ∆m intervals, and the J/ψφK + mass distributions for each interval are fit to extract the B + signal yield in that interval.We use a second-degree polynomial for the combinatorial background and two Gaussians for the B + signal.The fit is performed separately for each data set.The mean values of the two Gaussians are fixed to the B + mass [27], and the width values of the Gaussians, as well as their relative ratio, are fixed to the values obtained from MC simulation for each specific ∆m interval in each data set.The results of all the fits are good descriptions of the data distributions with an average χ 2 per degree of freedom (dof) close to 1.The resulting ∆m distribution for the combined data sets is shown in Fig. 3. Two peaking structures are observed above the simulated phase-space (PS) continuum distribution shown by the dotted Results obtained from both data sets are consistent.We have checked that events with multiple B + candidates do not artificially enhance the two structures.The total number of B + signal events in the ∆m intervals below 1.568 GeV is 2320 ± 110 (stat.), which is consistent with the total number of B + candidates estimated from the mass spectrum in Fig. 1.
A full study of the J/ψφ resonant pattern in the B + → µ + µ − K + K − K + decay via an amplitude analysis of the five-body decay would require a data sample at least an order of magnitude larger than is currently available, as well as more precise information on possible φK + or J/ψK + resonances that may contribute to this decay.Instead, the ∆m distribution is studied, since it is related to the projection of the two-dimensional (2D) J/ψφK + Dalitz plot onto the m 2 (J/ψφ) axis.
Before fitting the ∆m distribution, it must be corrected for the relative detection and reconstruction efficiencies of the candidate events.Since no branching fractions are being determined, only the relative efficiency over the Dalitz plot is required.If a possible φK + or J/ψK + resonance did exist, the density of events would depend on the quantum numbers of the resonance and on the interference of the two structures with the possible resonance.Ignoring these possible interference effects, the MC simulation is used to determine the efficiency over the m 2 (φK + ) vs. m 2 (J/ψφ) Dalitz plot, assuming a PS distribution for the three-body decay B + → J/ψφK + .

m [GeV] ∆
The solid curve is the global unbinned maximum-likelihood fit of the data, and the dotted curve is the background contribution assuming three-body PS.The band is the ±1σ uncertainty range for the background obtained from the global fit.The dashed and dash-dotted curves are background curves obtained from two different event-mixing procedures, as described in the text, and normalized to the number of three-body PS background events.The short dashed curve is the 1D fit to the data.
The J/ψ and φ vector meson decays are simulated using their known angular distributions according to the VLL and VSS model in EVTGEN, while we assume there is no polarization for the two vectors.The PS MC simulation is reweighted assuming either transverse or longitudinal J/ψ and φ polarization.The effect of either polarization is found to be negligible.The measured efficiency is fairly uniform, varying by less than 25% over the entire allowed three-body PS.Assuming a uniform PS distribution, the efficiency for each ∆m bin is taken to be the average of the efficiencies over the full kinematically allowed m(φK + ) range.To estimate the systematic uncertainty in the efficiency caused by its dependence on the unknown quantum numbers of the structures, and hence on their unknown decay angular distributions, the efficiency is evaluated under the assumption of both a cos 2 θ and sin 2 θ dependence, where θ is the helicity angle, defined as the angle in the J/ψφ rest frame between the direction of the boost from the laboratory frame and the J/ψ direction.Since the efficiency tends to be lower towards the edge of the Dalitz plot, the cos 2 θ dependence gives a lower average efficiency than the default efficiency, while the sin 2 θ dependence gives a slightly higher average efficiency.This variation (10%) is taken as the systematic uncertainty in the efficiency from our lack of knowledge of the quantum numbers of the structures and the effects of interference with possible two-body resonances.
We investigate the possibility that the two structures in the ∆m distribution are caused by reflections from resonances in the other two-body systems, J/ψK + and φK + .Such reflections are well known in the two-body systems from other three-body decays because of kinematic constraints.There are candidate states that decay to φK + [27], although they are not well established.These could potentially produce reflected structures in the J/ψφ spectrum.In particular, a D-wave contribution to K − p scattering in the mass region around 1.7-1.8GeV has been reported by several fixed-target experiments [29][30][31].This is interpreted as two interfering broad J P = 2 − resonances, labeled K 2 (1770) and K 2 (1820), with widths in the range 200-300 MeV.These resonances at relatively low φK + mass cannot affect the J/ψφ structure near threshold, but could contribute to the second J/ψφ structure near ∆m = 1.2 GeV.To study possible reflections from the φK + spectrum, we consider φK + resonances with various masses, widths, and helicity angle distributions, but are not able to reproduce the pattern of structures seen in the J/ψφ spectrum.Moreover, we separately analyze the J/ψφ spectrum for values of the φK + masses larger than 1.9 GeV, a region of the Dalitz plot unaffected by postulated φK + resonances, and still observe the structure near ∆m = 1.2 GeV.
There are no candidate J/ψK + resonances reported in the literature.Still, we have considered such resonances with various masses, widths, and helicity angle distributions.No combination produces a reflected spectrum that matches the observed J/ψφ spectrum.
We have also checked the events with ∆m larger than 1.568 GeV that had been eliminated from the analysis to ensure that they could not cause similar reflections in the low-∆m region.After subtraction of the B 0 s background the ∆m distribution of events with ∆m larger than 1.568 GeV is consistent with the prediction based on the three-body phase-space hypothesis for the nonresonant background.The extended ∆m plot is shown in Fig. 6 of Appendix A, and the corresponding fitted numbers of B + → J/ψφK + events for the 7 bins from the previously eliminated ∆m region are displayed in Fig. 7 of Appendix A, after subtracting the expected B 0 s background from simulation.Both distributions are consistent with the extrapolation from three-body phase-space.
The results of these studies make it improbable that the two structures seen in the J/ψφ spectrum are solely caused by reflections from resonances in the other two-body systems.However, we cannot entirely exclude the possibility of such resonances.For instance, the K + K − K + spectrum shown in Fig. 4 displays an excess of events above the predicted PS distribution in the 1.7-1.8GeV region, an excess that cannot be attributed to the presence of the J/ψφ structure near threshold.Figure 4 is obtained by dividing the J/ψφK + candidates into 40 MeV-wide K + K − K + mass intervals and fitting the J/ψφK + invariant-mass distributions for each interval to extract the B + signal yield in that interval.The ∆m distribution after excluding the region (1.68 < m(K + K − K + ) < 1.88 GeV) with the excess of events is shown in the left plot of Fig. 5 and the corresponding distribution for the excluded ∆m region in the right plot.The presence of the lower-mass structure is still apparent in the left plot, while that of the higher-mass structure is reduced though still visible.Possible interference effects over the Dalitz plot could therefore distort the shape of the observed J/ψφ structures and affect the extraction of the resonance parameters.The event sample is not large enough to investigate these effects further.We assume that any interference effects can be neglected.The structures in the J/ψφ mass spectrum are described in terms of zero, one, or two noninterfering resonances and a nonresonant continuum component.
We fit the two structures with S-wave relativistic BW functions convolved with a Gaussian mass resolution function whose width varies linearly from 1 MeV at threshold to about 4 MeV    at ∆m = 1.25 GeV, as determined from simulation.Each structure is described by a mass, width, and yield, all determined from the fit.The continuum is assumed to follow a three-body PS shape.As an alternative, to check the sensitivity of the result to this assumption, the shape of the continuum is obtained from an event-mixing technique where the J/ψ, φ, and K + candidates are selected from different events.We use two versions of the event mixing, which differ by the φ and K + candidates being selected in the same event or not; they lead to almost identical shapes.The differences between the two event-mixing shapes and the three-body PS are used to evaluate the systematic uncertainties in the continuum modeling.To further investigate the effect of a possible φK + resonance around 1.7 GeV as shown in Fig. 4, we reweight our phase-space MC events with a φK + mass distribution corresponding to a BW with a mass of 1.773 GeV and a width of 200-300 MeV [27].The helicity angle in the φK + system is then weighted to correspond to several different assumptions about the decay of the possible resonance.We estimate the yield of the possible φK + resonance in Fig. 4 to be 10% of the total number of events.We find that the shape of the PS ∆m distribution is always above the various distributions obtained from the above mixing in the range ∆m < 1.12 GeV.Thus, we conclude that using the PS distribution as the default background curve is more conservative with respect to the significance of the low-mass peak if there is a possible effect from a φK + resonance.
The masses and widths of the two structures are extracted by dividing the J/ψφK + candidates into 20 MeV-wide intervals of ∆m from 1.008 to 1.568 GeV and performing a global unbinned maximum-likelihood (UML) fit to the J/ψφK + invariant-mass distribution in each ∆m interval.The two data sets are fitted separately, with a total of 56 mass spectra fitted simultaneously.In each fit, the B + mass is fixed to its nominal value and the mass resolution δ is calculated using: where ∆m is the value of ∆m at the center of the bin, and a 0 , a 1 , and a 2 are determined from simulation, separately for the two data sets.The combinatorial background in each bin is modeled as a second-degree polynomial.In the global fit, the B + yield is expressed as the product of the relative efficiency times the number of signal events from the two BWs and the nonresonant continuum events.We fit the J/ψφK + invariant-mass distribution for each ∆m bin from the two data sets simultaneously by projecting the above product into each bin.The UML fit returns signal event yields of 310 ± 70 (stat.)and 418 ± 170 (stat.)for the lower-and higher-mass structures, respectively.The corresponding mass difference and width values are: −15 (stat.)MeV.The projection of the UML fit assuming two structures onto the J/ψφ mass spectrum is represented as the solid line in Fig. 3.
As a check on the fitting procedure, we perform an alternative one-dimensional (1D) binned χ 2 fit to the ∆m spectrum shown in Fig. 3.The same signal and background functions are used in the 1D fit as in the global fit.The result of the 1D fit, assuming two structures, is shown as the dashed line in Fig. 3.The measurements of the masses, widths, and yields of the two structures from the global and 1D fits are in good agreement.
To evaluate the significance of each of the two structures, three UML and three 1D (binned χ 2 ) fits are performed on the data shown in Fig. 3: (1) a background-only fit (null-hypothesis); (2) a background plus a single S-wave relativistic BW signal function convolved with a Gaussian resolution function having a width of 2 MeV for the lower-mass structure; and (3) a background plus two S-wave relativistic BW functions convolved with a Gaussian resolution function to model both structures.The log-likelihood ratio −2∆ ln L in the case of the UML fits or the χ 2 change ∆χ 2 for the 1D fits between 1) and 2) is then a measure of the statistical significance of the lower-mass structure, while the corresponding values between fits (2) and (3) give a measure of the statistical significance of the higher-mass structure.The resulting values for a decrease in dof of 3 are −2∆ ln L = 58 and ∆χ 2 = 53 for the lower-mass structure, and 36 and 37 for the higher-mass structure.Simulated samples are used to estimate the probability that background fluctuations alone could give rise to a signal as significant as that seen in the data for the lower-mass structure.Over 50 million ∆m spectra were generated between 1.008 and 1.568 GeV with 2300 events for each spectrum based on a three-body PS shape.The most significant fluctuation in each spectrum is found whose J/ψφ invariant mass is within ±3 times the uncertainty in the CDF mass value of 4.140 GeV and having a width between 10 MeV (half the ∆m bin width) to 80 MeV (half the separation between the two structures).We then obtain the ∆χ 2 distributions in the simulated pure background samples and compare them with the corresponding value of the signal in the data.No generated spectrum is found with a fluctuation having a ∆χ 2 greater than or equal to the value obtained in the data (53).The resulting p-value, taken as the fraction of the simulated samples with a ∆χ 2 value greater than or equal to the value obtained in the data, is less than 2 × 10 −8 , which corresponds to a significance of more than 5 standard deviations.Because the second structure could be affected by possible φK + resonances, it is difficult to model the background shape in that mass range, and we do not quote a numeric significance for the higher-mass structure.However, there is clear evidence for a second structure around ∆m = 1.2 GeV even after excluding the region with possible K 2 resonances.There is also a small excess of events around ∆m = 1.4 GeV, but with a local significance of less than 3 standard deviations.
Various checks are made to examine the robustness of the two structures.Each selection criterion is individually varied, and in no case is there an indication of a bias in the selection procedure.The relative efficiencies for the first five ∆m bins are varied by ±20% and the fit repeated, confirming the robustness of the significance of the first structure.The ∆m distribution from an sPlot [32] projection is compared to the ∆m distribution shown in Fig. 3.No indication of bias is found.The sPlot algorithm is a background-subtraction technique that weights each event based on the observed signal-to-background ratio, in this case from the fit to the J/ψφK + mass distribution shown in Fig. 1.We repeat the analysis with the tighter requirements discussed earlier that lower the combinatorial background level by a factor of ten and retain 40% of the B + events, as shown in the right plot in Fig. 1.The ∆m plot for these events looks similar to Fig. 3, showing two peaking structures whose fitted mass and width values are consistent with the results from the nominal data sample.No indication of a possible bias is found.
The estimations of the contributions to the systematic uncertainties in the mass and width measurements of the two structures shown in Table 1, are determined from several studies.The uncertainties owing to the probability density functions (PDFs) for the combinatorial background shape in the m(J/ψφK + ) spectrum and the B + signal are studied by using different PDFs such as first-and third-degree polynomials, exponential functions, and a number of Gaussian functions.The uncertainties in the shape of the relative efficiency vs. ∆m are evaluated by varying the relative efficiency in various bins and comparing with the 2D efficiencies for correction of m(J/ψφ) vs. m(φK + ).The uncertainties caused by the binning of the ∆m spectrum are studied by using 10 MeV bins instead of 20 MeV bins.To estimate the uncertainty from the signal fitting function, we repeat the fit to the ∆m distribution using either a nonrelativistic BW or a P-wave relativistic BW function for each structure.The uncertainties from the ∆m mass resolution are studied by varying the mass resolution values obtained from simulation within their statistical uncertainties.To evaluate potential distortions in the ∆m background shape caused by possible φK + resonances, we obtain the ∆m background shape from data using an event-mixing technique by applying the same kinematic constraints and taking the φ and K + candidates from the same event, but the J/ψ candidate from a different event.The uncertainties due to selection requirements are studied in the MC sample.The overall systematic uncertainties in the measurement of the masses and widths of the two structures are found by adding in quadrature the individual combinations summarized in Table 1.

Summary
In summary, a peaking structure in the J/ψφ mass spectrum from B + → J/ψφK + decays has been observed in pp collisions at √ s = 7 TeV by the CMS Collaboration at the LHC.Assuming an S-wave relativistic BW lineshape for this structure above a three-body PS shape for the nonresonant background, a statistical significance of greater than 5 standard deviations is found.Adding the J/ψ mass [27] to the extracted ∆m values, the mass and width are measured to be m 1 = 4148.0± 2.4 (stat.)± 6.3 (syst.)MeV and Γ 1 = 28 +15 −11 (stat.)± 19 (syst.)MeV.The measured mass and width are consistent with the Y(4140) values reported by CDF experiment.The relative branching fraction of this peaking structure with respect to the total number of B + → J/ψφK + events is estimated to be about 0.10, with a statistical uncertainty of about 30%.This is consistent with both the value measured by CDF of 15% ± 5% and the upper limit reported by LHCb (0.07).In addition, evidence for a second peaking structure is found in the same mass spectrum, with measured mass and width values of m 2 = 4313.8± 5.3 (stat.)± 7.3 (syst.)MeV and Γ 2 = 38 +30 −15 (stat.)± 16 (syst.)MeV.Because of possible reflections from two-body decays, the statistical significance of the second structure cannot be reliably determined.The two structures are well above the threshold of open charm (DD) decays and have relatively narrow widths.Conventional charmonium mesons with these masses would be expected to have larger widths and to decay predominantly into open charm pairs with small branching fractions into J/ψφ.Angular analyses of the B + → J/ψφK + decays would help elucidate the nature of these structures.
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort.In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS,

A Supplemental Material
Figure 6 shows the continuation of the ∆m spectrum for ∆m > 1.568 GeV, including the contribution from non-B candidates, after subtracting the expected B 0 s contribution from simulation for candidate events with J/ψφK + invariant mass within ±1.5σ (σ = 9.3 MeV) of the B nominal mass.Figure 7 shows the extension of the ∆m spectrum in Fig. 3 in the paper, excluding non-B background, to the full phase space.The absence of strong activity in the high-∆m region reinforces our conclusion that the near-threshold narrow structure is not due to a reflection of other resonances.
m [GeV] ∆  The number of B + → J/ψφK + candidates as a function of ∆m.The filled circles to the left of the vertical dashed line are results used in the analysis.The solid curve is the result of the global fit described in the text.The points and the curve are a repeat of those in Fig. 3.The open circles to the right of the vertical dashed line are extracted in the seven bins of the previously eliminated ∆m region, after subtraction of the predicted B 0 s background from simulation.The short-dashed curve represents the prediction from three-body phase-space for the nonresonant background, normalized to the number of expected background events in the region to the left of the vertical dashed line.The long-dashed curve is an extrapolation of this prediction into the previously eliminated region.

Figure 2 :
Figure2: The B + sideband-subtracted K + K − invariant-mass distribution for J/ψK + K − K + candidates within ±3σ of the nominal B + mass.The solid curve is the result of the fit described in the text.The dashed line shows the zero-candidate baseline.

Figure 3 :
Figure 3: The number of B + → J/ψφK + candidates as a function of ∆m = m(µ+ µ − K + K − ) − m(µ + µ − ).The solid curve is the global unbinned maximum-likelihood fit of the data, and the dotted curve is the background contribution assuming three-body PS.The band is the ±1σ uncertainty range for the background obtained from the global fit.The dashed and dash-dotted curves are background curves obtained from two different event-mixing procedures, as described in the text, and normalized to the number of three-body PS background events.The short dashed curve is the 1D fit to the data.

Figure 4 :
Figure 4: The yield of B + → J/ψK + K − K + candidates in the data as a function of the K + K − K + invariant mass.The error bars represent the statistical uncertainties.The solid curve is the prediction from the PS simulation.

Figure 6 :
Figure 6: The ∆m spectrum, including non-B candidates after subtracting the expected B 0 s contribution from simulation for candidate events with J/ψφK + invariant mass within ±1.5σ (σ = 9.3 MeV) of the B nominal mass.The dashed vertical line indicates the boundary of the region eliminated from the analysis (the region to the right of the dashed line).The data points in the region to the left of the dashed line are from events used in the analysis and are represented by filled circles with error bars.The open circles in the region to the right of the dashed line are the result of subtracting the expected B 0s background from simulation, and their uncertainties are correlated.The solid curve is the prediction for a three-body phase-space distribution, normalized to the total number of events in the left region, after subtracting the yields from the two low-mass peaking structures.The extrapolation of the phase-space prediction into the right-hand region is shown by the dashed curve.

Figure 7 :
Figure 7:  The number of B + → J/ψφK + candidates as a function of ∆m.The filled circles to the left of the vertical dashed line are results used in the analysis.The solid curve is the result of the global fit described in the text.The points and the curve are a repeat of those in Fig.3.The open circles to the right of the vertical dashed line are extracted in the seven bins of the previously eliminated ∆m region, after subtraction of the predicted B 0 s background from simulation.The short-dashed curve represents the prediction from three-body phase-space for the nonresonant background, normalized to the number of expected background events in the region to the left of the vertical dashed line.The long-dashed curve is an extrapolation of this prediction into the previously eliminated region.

Table 1 :
Systematic uncertainties in the measured masses and widths of the two peaking structures from the sources listed and the total uncertainties.