Search for the $B \to Y(4260) K, ~Y(4260) \to J/\psi \pi^+\pi^-$ decays

We report the results of a search for the $B \to Y(4260) K, ~Y(4260)\to J/\psi\pi^+\pi^-$ decays. This study is based on a data sample corresponding to an integrated luminosity of 711~fb$^{-1}$, collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We investigate the $J/\psi\pi^+\pi^-$ invariant mass distribution in the range 4.0 to 4.6 GeV/$c^2$ using both $B^+ \to J/\psi \pi^+\pi^- K^+$ and $B^0 \to J/\psi \pi^+\pi^- K^0_S$ decays. We find excesses of events above the background levels, with a significances of 2.1 and 0.9 standard deviations for charged and neutral $B \to Y(4260) K$ decays, respectively, taking into account the systematic uncertainties. These correspond to upper limits on the product of branching fractions, ${\cal B}(B^+ \to Y(4260) K^+) \times {\cal B}(Y(4260) \to J/\psi \pi^+ \pi^-)<1.4 \times 10^{-5}$ and ${\cal B}(B^0 \to Y(4260) K^0) \times {\cal B}(Y(4260) \to J/\psi \pi^+ \pi^-)<1.7 \times 10^{-5}$ at the 90\% confidence level.

PACS numbers: 13.20.Gd,13.20.He,14.40.Nd The Y (4260) state, also known as ψ(4260) [1], was first seen by the BABAR collaboration in 2005 [2] in the initial-state radiation (ISR) process e + e − → γ ISR Y (4260), Y (4260) → J/ψπ + π − and confirmed by the Belle and CLEO collaborations using the same process [3,4]. The world average mass and decay width of the Y (4260) are (4230±8) MeV/c 2 and (55±19) MeV [1], respectively. Due to its observation in ISR production, the J P C of the Y (4260) is expected to be 1 −− . The decay of Y (4260) to J/ψπ + π − indicates the presence of a cc pair among its quark constituents. However, its mass and properties are not consistent with those expected for any of the cc states in the charmonium spectrum, which makes it problematic to assign the Y (4260) to one of the conventional cc states with J P C = 1 −− .
Attempts have been made to identify Y (4260) as a candidate for a mixed state, which is an admixture of charmonium and tetraquark states [5], a hybrid charmonium state, which is a bound state of charmonium with a gluon [6], a tetraquark [7], a mesonic molecule [8][9][10], or a charmonium baryonium [11]. The Z c (3900) ± state, which as it is charged makes it a natural tetraquark candidate, has been observed by the BESIII and Belle collaborations in the J/ψπ ± invariant mass spectrum of the e + e − → Y (4260) → J/ψπ + π − process [12,13], provides further evidence of the unconventional nature of the Y (4260).
A mixed-state model, based upon a QCD sumrule approach [14], suggests the possible interval on the product of the branching fractions of B + → Y (4260)K + , Y (4260) → J/ψπ + π − to be in the range 3.0 × 10 −8 − 1.8 × 10 −6 . The BABAR collaboration has measured a signal for the charged B decay with a statistical significance of 3.1 standard deviations (σ) based on a data sample of 211 fb −1 which contains (232±3)×10 6 BB pairs [15]. They set the upper limit at the 95% confidence interval to be B(B + → Y (4260)K + ) × B(Y (4260) → J/ψπ + π − ) < 2.9 × 10 −5 . Further improvement is required on the precision of both the theoretical estimate and experimental measurement to elucidate the structure of Y (4260).
Recently, two resonance structures have been observed by the BESIII collaboration in a fit to the cross section of the e + e − → J/ψπ + π − process [16]. The resonance structures are interpreted as Y (4260) and Y (4360) with measured masses (4222.0 ± 3.1 ± 1.4) MeV/c 2 and (4320.0 ± 10.4 ± 7.0) MeV/c 2 , respectively. The measured Y (4260) mass is not significantly lower than world average [1], from which it deviates merely about 1σ, and the Y (4360) has not yet been confirmed. We assume the presence of Y (4260) only in the J/ψπ + π − invariant mass region of interest as in the previous measurements [2][3][4] instead of adopting the search for the improved mass region.
The charged tracks used in the analysis are required to originate from the interaction point (IP) and have their point of closest approach to the IP within 3.5 cm along the beam axis and 1.0 cm in the plane transverse to the beam axis. Identification of charged pions and kaons are based on the information from the aerogel Cherenkov counter system, time-of-flight scintillation counter (TOF) and central drift chamber. All of the information is combined to form the pion (kaon) likelihood, L π (L K ), and the selections are made on the basis of the likelihood ratio R π(K) = L π(K) /(L π + L K ). Charged pions (kaons) are identified requiring R π (R K ) > 0.6 with an identification efficiency of 94% (86%) and a misidentification rate of 7.5% (4%) for misidentifying kaon (pion) as a pion (kaon), respectively. These efficiencies and misidentification rates are determined using a control sample of D * + → D 0 (K − π + )π + decays in the kinematic region of interest.
A K 0 S → π + π − candidate decay is reconstructed from a pair of oppositely charged tracks with a π + π − invariant mass in the range 488 MeV/c 2 < M ππ < 508 MeV/c 2 (±4σ around the nominal K 0 S mass [1]). The selected candidates are required to satisfy the criteria described in Ref. [23].
Muon identification [24] utilizes the track penetration depth and hit-distribution pattern in the K 0 L and µ detector, which are combined to form the muon likelihood, L µ , and the selection is made on the basis of the likelihood ratio R µ = L µ /(L µ + L π + L K ). Muons are identified requiring R µ > 0.1 with an identification efficiency of 93% and a misidentification rate of 3% for misidentifying a pion as a muon. Electron identification [25] utilizes the electromagnetic shower shape and E ECL /p ratio, where E ECL is the energy deposition in electromagnetic calorimeter and p is the track momentum, as well as the information used in the charged hadron identification, except that from the TOF. All the information is combined to form the electron likelihood ratio, R e . Electrons are identified requiring R e > 0.01.
A J/ψ candidate is reconstructed in its decay mode J/ψ → ℓ + ℓ − , where ℓ stands for e or µ. In the J/ψ → e + e − mode, the energy loss due to bremsstrahlung photons is recovered by including the four-momenta of the photons detected within 0.05 radians around the electron or positron initial direction in the invariant mass calculation; this mode is, hereinafter, referred to as J/ψ → e + e − (γ). An invariant mass of a J/ψ candidate is required to be in the range 3.05 The asymmetric interval is taken for e + e − (γ) to include the radiative tail due to the imperfect energy loss recovery. A vertex-and mass-constrained fit is performed to the selected J/ψ candidates in order to improve their momentum resolution.
To identify the B meson, two kinematic variables, the beam-constrained mass (M bc , are used to discriminate the signal from the background. Here, E beam is the beam energy and p * i (E * i ) is the momentum (energy) of the i th final-state particle of the reconstructed signal candidate, where both are evaluated in the e + e − center-of-mass (CM) frame. The B candidates with M bc > 5.27 GeV/c 2 are selected for further analysis.
Even after applying all the selection criteria, multiple B candidates can be reconstructed from wrong combinations of the retained particles in an event. The mean number of B candidates per event is found to be 1.6 (1.6), 1.7 (1.6) and 1.4 (1.2) for the charged (neu-tral) B → ψ(2S)(→ J/ψπ + π − )K, B → X(3872)(→ J/ψπ + π − )K and B → Y (4260)K decays, respectively. In an event with multiple B candidates, we select the best candidate that has the smallest value of where χ 2 vtx represents the χ 2 value obtained from a kinematic fit to the B decay vertex for all the charged daughter particles, and the other χ 2 values are evaluated using the reconstructed mass M i and its resolution σ i and the nominal mass m PDG Here, beam-constrained M bc is used for the reconstructed mass in χ 2 M bc , and χ 2 K 0 S is used only for the neutral B decays. The reconstructed mass resolutions σ M bc , σ J/ψ , and σ K 0 S are evaluated in the B → ψ(2S)K decays to be 2.6 MeV/c 2 , 9.8 MeV/c 2 and 1.6 MeV/c 2 , respectively. According to MC simulations, the best candidate selection identifies the true signal at rates of 76% (72%) for the charged (neutral) B → Y (4260)K decays. The same best candidate selection criterion are applied in the reconstruction of the control sample decays.
The dominant background comes from e + e − → qq (q = u, d, s or c) continuum events. To suppress this background, we utilize the difference in event topology between the isotropic distribution of particles in BB events and the jet-like collimation of particles in qq events by placing a requirement on the ratio of the second-and zeroth-order Fox-Wolfram moments [26] to be less than 0.5.
Among the backgrounds from BB events, the main contribution is expected to arise from inclusive B decays to J/ψ. To understand possible backgrounds, simulated sample of inclusive B decays with a J/ψ (ℓ + ℓ − ) in the final state are studied; the sample corresponds to an integrated luminosity that is two orders of magnitude larger than that of data. No peaking structures are found in the M J/ψππ signal regions of B → ψ(2S)K, B → X(3872)K, and B → Y (4260)K decays. In order to check possible contributions from non-J/ψ sources, the J/ψ mass sidebands (2.54 GeV/c 2 < M J/ψ < 2.72 GeV/c 2 and 3.32 GeV/c 2 < M J/ψ < 3.50 GeV/c 2 ) are studied. The contributions are found to be negligible.
An unbinned extended maximum likelihood (UML) fit is performed to the ∆E distribution of each decay mode. The statistical weight for each candidate to be a signal decay is determined by using the s Plot technique [27]. The statistical weights can be used to effectively subtract the combinatorial background from the M J/ψππ distribution of each decay mode. The signal yield of the intended resonance, then, can be extracted from the weighted M J/ψππ distribution, having a single background component of the non-resonant B → J/ψπ + π − K decays.
The ∆E variable is required to satisfy −0.11 GeV < ∆E < 0.11 GeV for the B → ψ(2S)K, X(3872)K and Y (4260)K decay modes. The UML function used here is [NS ×PS(xi)+NB ×PB(xi)] (1) where N is the total number of events, N S (N B ) is the number of signal (background) events, P S (P B ) is the signal (background) probability density function (PDF) of the variable x, and the index i runs over the total number of events. Here, the signal refers to the charged or neutral B → J/ψπ + π − K decays, the background refers to the combinatorial background, and x refers to the ∆E variable. The signal PDF is modeled by a sum of three Gaussians for the B → Y (4260)K decay modes and by a sum of two Gaussians and a bifurcated Gaussian for the B → ψ(2S)K and B → X(3872)K modes. The mean and resolution of the core Gaussian are allowed to vary in the fit while the remaining shape and normalization parameters are fixed to those obtained in the fit to the signal MC. The background PDF is modeled by a firstorder polynomial except for the B → X(3872)K decay mode, in which a second-order polynomial is used. All parameters of the background PDF are allowed to vary in the fit. The yields of the B → ψ(2S)K, X(3872)K, and Y (4260)K decays are extracted using independent UML fits to the weighted M J/ψππ distributions. Here, while the functional form of Eq. 1 is used to evaluate the likelihood, the signal refers to the charged or neutral decay of B → ψ(2S)K, X(3872)K, or Y (4260)K, the background refers to the corresponding non-resonant B → J/ψπ + π − K decay, and x refers to the M J/ψππ variable. The signal PDF is modeled by a sum of two Gaussians for the B → ψ(2S)K and Y (4260)K decays while an additional bifurcated Gaussian is used for the B → X(3872)K decays. The core Gaussian parameters for the B → ψ(2S)K and B + → X(3872)K + decays are allowed to vary in the fit, while those for the B 0 → X(3872)K 0 and B → Y (4260)K decays are fixed to the values obtained in the fit to the signal MC and calibrated with data; the calibration is based on the comparison of the shape parameters between the data and simulation of the B + → X(3872)K + decay. All the remaining shape and normalization parameters of the signal PDF are fixed to those obtained in the fit to the signal MC. The background PDF is modeled by a first-order polynomial except for the B → ψ(2S)K decay modes, in which a second-order polynomial is used. All parameters of the background PDF are allowed to vary in the fit. The ∆E distributions, weighted M J/ψππ distributions and projections of their PDFs obtained from the fits are shown in Fig. 1, 2, and 3 for the B → ψ(2S)K, X(3872)K, and Y (4260)K decay samples, respectively. The obtained signal yields of the B → ψ(2S)K, and B → X(3872)K, X(3872) → J/ψπ + π − decays are listed in Table I and for B → Y (4260)K, Y (4260) → J/ψπ + π − decays are listed in Table II. For the B → Y (4260)K decays, the statistical significance of the signal yield is evaluated using the likelihood ratio as −2ln(L 0 /L max ), where L max and L 0 denote the maximum likelihood of the nominal fit and that of the fit with the null signal hypothesis. The statistical significances are evaluated to be 2.9σ and 1.4σ for the charged and neutral B → Y (4260)K decays, respectively. The likelihood ratio is smeared with the systematic uncertainties, discussed later, and listed in Table III. The signal significances taking into account the systematic uncertainties are determined to be 2.1σ and 0.9σ for the charged and neutral B → Y (4260)K decays, respectively.
The branching fractions (B) of the B → ψ(2S)K decays are obtained as where N S is the number of signal decays, N BB is the number of BB events in the data sample, and the branching fractions of the secondary decays are taken from Ref. [1]. Here, equal production of B + B − and B 0B0 pairs from Υ(4S) decays is assumed. The reconstruction efficiency, ǫ, is estimated from the signal MC simulation, with the application of calibrations to account for discrepancies between the data and signal MC related to particle identifications and K 0 S reconstruction. These calibrations use dedicated control samples as discussed later. The coefficient f K is introduced to translate the branching fractions for the final states with K 0 S into those for the ones with K 0 and set 1 I. Summary of the reconstruction efficiency (ǫ), signal yield (NS) and branching fraction (B) measured for the B → ψ(2S)K and B → X(3872)K, X(3872) → J/ψπ + π − decays, together with the world average of the branching fraction (BPDG) [1] for reference. Only the statistical uncertainty is included on the measured values of NS and B.
With the absence of significant signals for the B → Y (4260)K decays, an upper limit (U.L.) is set on each signal yield at the 90% confidence level (C.L.) using a frequentist approach [29]. The upper limits on the signal yields at the 90% C.L. (N UL S ) are found to be 259 and 84 events for the B + → Y (4260)K + and B 0 → Y (4260)K 0 S decays, respectively. The upper limits on the branching fraction products are calculated using Eq. 2, with N S replaced by N UL S (systematic uncertainties are included in the upper limit calculation, as will be described later in this paper). The resulting upper limits are listed in Table II.
In order to improve the signal sensitivity, a simultaneous fit to the charged and neutral signal decays is performed keeping the fit procedure same as in the nominal fits for the individual signal decays, except for incorporating the constraint that [30]. The simultaneous fit for the B → Y (4260)K decays obtains 218 ± 68 signal events, where the quoted uncertainty is statistical only. The combined statistical significance of the B → Y (4260)K, Y (4260) → J/ψπ + π − decays is found to be 3.2σ, which reduces to 2.2σ once systematic uncertainties are taken into account. The simultaneous fit does not increase the significance of the Y (4260) signal.
All the systematic uncertainties are summarized in Table III. The tracking efficiency in MC simulation is calibrated using a control sample of D * → πD 0 , D 0 → π + π − K 0 S , K 0 S → π + π − decays, and the uncertainty on the calibration factor is 0.35% per track. The calibration factor for the K 0 S reconstruction efficiency is obtained using D * ± → D 0 (→ K 0 S π 0 )π ± decays with an uncertainty of 0.7%. For the particle identification efficiencies, the calibration factors are obtained using the dedicated control samples mentioned earlier, and the resulting systematic uncertainty is 0.9% and 1.3% for kaon and pion identification, respectively. The dominant systematic uncertainties are due to the PDF modeling, and the values of the Y (4260) mass and decay width [1] assumed in the fit. The changes on the signal yield from the nominal one due to the uncertainty in the PDF modeling is estimated by varying each of the fixed parameters independently by ±1σ. The corresponding changes due to the uncertainties on the Y (4260) mass and decay width are estimated by separately applying the variation in the signal PDF based on the alternative signal MC simulations, which are generated varying each of the mass and decay width in the same manner. The resulting changes are added in quadrature. The uncertainty in the PDF modeling for the B 0 → Y (4260)K 0 S decay gives an exceptionally large systematic uncertainty of 77.0%. This is due to the systematic uncertainty associated with the background PDF modeling. The fit procedures are validated in fully simulated MC experiments with ensembles   of signal and inclusive B decays involving J/ψ. The small biases of 4.3%-4.8% seen in the validation are taken as systematic uncertainties. The uncertainties on N BB and B(J/ψ → ℓ + ℓ − ), 1.4% and 0.4%, respectively, are also included in the systematic uncertainties. The total systematic uncertainties are estimated to be +30.5 −23.0 %, +17.5 −79.2 % and +26.2 −24.3 % on the results for the charged, neutral and combined B → Y (4260)K, Y (4260) → J/ψπ + π − decays, respectively, by adding all the sources in quadrature. In summary, a search for the B → Y (4260)K, Y (4260) → J/ψπ + π − decays is performed using BB pairs collected at the Υ(4S) resonance by the Belle experiment at the KEKB. The observed signal yields are 179 ± 53 +55 −41 events and 39 ± 28 + 7 −31 events for the charged and neutral B → Y (4260)K, Y (4260) → J/ψπ + π − decays, respectively, from fits to the individual decay samples; the first and second uncertainties are statistical and systematic, respectively. The signal significances are obtained to be 2.1σ and 0.9σ for the charged and neutral decays, respectively, taking into account the systematic uncertainties associated with the signal extraction. In the absence of any significant signals, the upper limits on the branching fraction products at the 90% C.L. are determined to be 1.4×10 −5 and 1.7×10 −5 for the charged and neutral decays, respectively, taking into account the systematic uncertainties.
The obtained results give the most stringent upper limits, to date, on the branching fraction products of the charged and neutral B → Y (4260)K, Y (4260) → J/ψπ + π − decays. The upper limits on the branching fraction products at the 95% C.L. are also determined and are 1.56 × 10 −5 and 2.16 × 10 −5 for the charged and neutral decays, respectively. The upper limit for the charged decay is consistent with the 95% confidence interval set by the BABAR collaboration [15] and the one for the neutral decay is given for the first time. While an excess of events above background is seen, improved measurements with a larger data sample are demanded to establish signals and to elucidate the nature of the Y (4260) state.