Evidence of a Broad Structure at an Invariant Mass of 4.32 GeV/$c^2$ in the Reaction $e^+e^-\to\pi^+\pi^-\psi(2S)$ Measured at BaBar

We present a measurement of the cross section of the process $e^+e^-\to\pi^+pi^-\psi(2S)$ from threshold up to 8 GeV center-of-mass energy using events containing initial-state radiation, produced at the PEP-II $e^+e^-$ storage rings. The study is based on 298 fb$^{-1}$ of data recorded with the BaBar detector. A structure is observed in the cross-section not far above threshold, near 4.32 GeV. We also investigate the compatibility of this structure with the Y(4260) previously reported by this experiment.

We present a measurement of the cross section of the process e + e − → π + π − ψ(2S) from threshold up to 8 GeV center-of-mass energy using events containing initial-state radiation, produced at the PEP-II e + e − storage rings. The study is based on 298 fb −1 of data recorded with the BABAR detector. A structure is observed in the cross-section not far above threshold, near 4.32 GeV. We also investigate the compatibility of this structure with the Y (4260) previously reported by this experiment. PACS numbers: 14.40.Gx,13.25.Gv,13.66.Bc Until recently, charmonium spectroscopy has been well described by potential models. Observations of the X(3872) [1] and the Y (4260) [2] decaying into π + π − J/ψ complicate this picture, and have stimulated both experimental and theoretical interest in this area. The Y (4260) can be produced by direct e + e − annihilation and is therefore known to have J P C = 1 −− . Weak evidence for the Y (4260) structure in B decays was also reported by BABAR [3]. In addition, the Y (4260) has been confirmed by the CLEO-c experiment in direct e + e − → Y (4260) interactions where the Y (4260) is detected in decays to π + π − J/ψ and π 0 π 0 J/ψ [4]; the observation of the latter mode and the measured ratio B(Y (4260) → π 0 π 0 J/ψ )/B(Y (4260) → π + π − J/ψ ) ≈ 0.5 implies that the Y (4260) has isospin zero, as expected for a charmonium state.
It is peculiar that the Y (4260) is wide and yet has a large branching fraction into the hidden charm mode π + π − J/ψ , and that at the Y (4260) mass the cross section for e + e − → hadrons exhibits a local minimum. Many theoretical interpretations for the Y (4260) have been proposed, including unconventional scenarios: quarkantiquark gluon hybrids [5] and hadronic molecules [6]. We undertook this study with the intent of clarifying the nature of the Y (4260).
In this Letter we study the process e + e − → π + π − ψ(2S), ψ(2S) → π + π − J/ψ , for e + e − center-ofmass (CM) energies from threshold up to 8 GeV using initial-state radiation (ISR) events. The ISR cross section for a particular hadronic final state f is given by where s is the square of the e + e − CM energy, x ≡ 2E γ / √ s is the ratio of the photon energy to the beam energy in the e + e − CM frame, and W (s, x) is the spectrum for ISR photon emission for which we use a calculation good to O(α 2 ); the effective CM energy √ s ′ is the invariant mass of the final state m = s(1 − x).
We use data recorded with the BABAR detector [7] at the PEP-II asymmetric-energy e + e − storage rings, located at the Stanford Linear Accelerator Center. These data represent an integrated luminosity of 272 fb −1 recorded at √ s = 10.58 GeV, near the Υ (4S) resonance, and 26 fb −1 recorded near 10.54 GeV. Charged-particle momenta are measured in a tracking system consisting of a five-layer double-sided silicon vertex tracker (SVT) and a 40-layer central drift chamber (DCH), both situated in a 1.5-T axial magnetic field. An internally reflecting ring-imaging Cherenkov detector (DIRC) provides charged-particle identification. A CsI(Tl) electromagnetic calorimeter (EMC) is used to detect and identify photons and electrons, while muons are identified in the instrumented magnetic-flux return system (IFR). Optimized selection criteria are chosen based on a simulated sample of e + e − → γ ISR π + π − ψ(2S) events and a sample of e + e − → γ ISR ψ(2S), ψ(2S) → π + π − J/ψ candidates in data, which serves as a clean control sample [8].
A candidate J/ψ meson is reconstructed via its decay to e + e − or µ + µ − . The lepton tracks must be well reconstructed, and at least one must be identified as an electron or a muon candidate. An algorithm to recover energy lost to bremsstrahlung is applied to electron candidates. An e + e − pair with its invariant mass within the interval of (-100,+40) MeV/c 2 of the nominal J/ψ mass is taken as a J/ψ candidate. For a µ + µ − pair, the interval is (-60,+40) MeV/c 2 . The J/ψ candidate is then kinematically constrained to the nominal J/ψ mass and combined with a pair of oppositely-charged tracks identified as pion candidates. The π + π − J/ψ combinations with invariant mass within 10 MeV/c 2 of the nominal ψ(2S) mass are taken as ψ(2S) candidates. Another pair of oppositelycharged pion candidates (primary pions) is then combined with the ψ(2S) candidate. The π + π − ψ(2S) massresolution function is well described by a Cauchy distribution [9] with a FWHM of about 7 MeV/c 2 . We do not require observation of the ISR photon (γ ISR ) as it is preferentially produced along the beam directions.
A clean ψ(2S) signal is apparent in Fig. 1. An examination of the π + π − ψ(2S) combinations reveals that about half the background results from recombinations within the same 2(π + π − )J/ψ system where at least one of the primary pions is combined with the J/ψ to form a π + π − J/ψ candidate. After subtracting the self-combinatorial background, we estimate 3.8±1.1 nonψ(2S) background events in the final sample of 78 events within the ψ(2S) mass window. The invariant mass distribution for all π + π − J/ψ candidates where more than one entry per event is allowed. The solid curve is a fit to the distribution in which the ψ(2S) signal is described by a Cauchy function and the background by a quadratic function (represented by the dashed curve).
The arrows indicate the ψ(2S) mass window.
In Fig. 2 the distributions of (a) ∆p * and (b) cos θ * for 2(π + π − )J/ψ candidates, where θ * is the angle between the positron beam and the (π + π − π + π − J/ψ ) momentum in the e + e − CM frame, are shown and compared to expectations from simulations. There are 16 events that have a well reconstructed gamma with energy greater than 3 GeV, while the Monte Carlo simulation predicts 16.4 for the same total number of ISR π + π − ψ(2S) candidates. Furthermore, all events within |cos θ * | < 0.9 are accompanied by a reconstructed gamma with energy greater than 3.0 GeV. We find excellent agreement in the ISR characteristics between the data and signal Monte Carlo sample. The good agreement in the ∆p * distribution rules out any significant feeddown from higher mass charmonia decaying to the ψ(2S) with one or more undetected particles. As an example, the ∆p * distribution for ψ(4415) → π + π − π 0 ψ(2S) events would peak around −0.2 GeV/c with a long tail extending to well below −0.2 GeV/c. We estimate the non-ISR π + π − ψ(2S) background to be less than 1 event.
The track quality, particle identification information, and kinematic variables of all pion candidates are examined, and displays of the events are scanned visually to check for possible track duplications and other potential problems. No evidence for improper reconstruction or event quality problems is found. The 2(π + π − )J/ψ invariant-mass spectrum up to 5.7 GeV/c 2 for the final sample is represented as data points in Fig. 3. A structure around 4.32 GeV/c 2 is observed in the mass spectrum.
To clarify the peaking structure observed in Fig. 3, we perform an unbinned maximum likelihood fit to the mass spectrum up to 5.7 GeV/c 2 in terms of a single resonance with the following probability density function (PDF): where M, Γ tot , Γ ee , Γ f , N are the nominal mass, total width, partial width to e + e − , partial width to π + π − ψ(2S), and yield for a resonance, respectively, and m is the 2(π + π − )J/ψ invariant mass, ε(m) is the massdependent efficiency, Φ(m) is the mass-dependent phasespace factor for a S-wave three-body π + π − ψ(2S) system, a is a normalization factor, and B(m) is the PDF (the shaded histogram in Fig. 3) for the non-ψ(2S) background. The shape of B was obtained from ψ(2S) sideband events with its integral fixed to 3.1 events corresponding to the mass region in the fit, where the total number of events is 68. The mass dependence of Γ tot is ignored in the fit. We perform fits to the distribution in Fig. 3 to test hypotheses that the data are a result of the decay of the Y (4260) (dashed curve) using resonance parameters fixed to those of Ref [2], and alternatively those of the ψ(4415) (not shown) with the mass and width taken from Ref [10]. In the third fit (solid curve) we assume a single resonance whose mass and width are free parameters, which are then found to be (4324 ± 24) MeV/c 2 and (172 ± 33) MeV (after unfolding mass-resolution) by the fit. We calculate the χ 2 /dof value for each fit to test these hypotheses. In the calculation the events in Fig. 3 are regrouped so that at least seven events are expected in each bin. The χ 2 /dof values are found to be 21. 3/8, 54.4/7, and 7.3/7 for hypotheses of the Y (4260), the ψ (4415), and a new resonance, respectively, corresponding to χ 2probabilities of 6.5 × 10 −3 , 2.0 × 10 −9 , and 29%. The low probabilities associated with the Y (4260) and the ψ(4415) indicate that the structure is not consistent with the ψ(4415), and is not well described by the Y (4260) either. We also perform a fit including both the Y (4260) and ψ(4415) plus their interference, and find the χ 2 /dof value to be 17.8/6, corresponding to a χ 2 -probability of 6.7 × 10 −3 , but no much improvement from the fit to the Y (4260) only. In order to further compare the structure reported here with the Y (4260) reported in Ref. [2], we perform simultaneous fits to both the π + π − ψ(2S) mass spectrum in Fig. 3 and the π + π − J/ψ mass distribution in [2] under the hypotheses that (1) both signals are a single resonance and (2) these signals are manifestations of two independent resonances, with a single resonance for each signal. The PDF as used in Ref. [2] is applied to the fit to the π + π − J/ψ mass distribution. The logarithmic likelihood obtained from the single-resonance hypothesis (1) is 5.4 units less than that obtained from the two-resonance hypothesis (2), which corresponds to a χ 2 -probability of 4.5×10 −3 for the single-resonance hypothesis assuming a χ 2 distribution for the difference in the logarithmic likelihood between the two hypotheses. However, none of the probabilities associated with the Y (4260) can exclude the possibility that the structure observed is a manifestation of a new decay mode for the Y (4260). The primary π + π − invariant mass distribution for the selected events within m(2(π + π − )J/ψ ) < 5.7 GeV/c 2 is shown in Fig. 4. For the two events having more than one ψ(2S) candidates, the dipion invariant mass is only included for the ψ(2S) candidate closest to its nominal mass. The Monte Carlo distribution is also shown in Fig. 4 for a single resonance decaying to π + π − ψ(2S) in a S-wave three-body phase-space using the resonance pa-rameters obtained in the above paragraph. The primary π + π − invariant-mass spectrum within region m(2(π + π − )J/ψ ) < 5.7 GeV/c 2 for the final sample.
Only one entry per event is included in the plot, as described in the text. The histogram shows the distribution for Monte Carlo events (see text).
We extract the energy-dependent cross section for e + e − → π + π − ψ(2S) up to 8 GeV for the final sample. The average cross section over a mass range of width ∆m is calculated as where L is the integrated luminosity, B is the product of B(ψ(2S) → π + π − J/ψ ) and B(J/ψ → ℓ + ℓ − ), the sum is over all events within the mass range, m i is the 2(π + π − )J/ψ invariant mass, and ε i is the estimated efficiency at that mass. The measured cross section is shown in Fig. 5 and the numerical results can be found in [11], where the background has been subtracted from bins with non-zero content. The energy-dependent selection efficiency (solid histogram in Fig. 5) is determined from Monte Carlo events for which the ψ(2S) polarization has been properly considered while the primary π + π − is generated in S-wave phase-space. The uncertainty in the selection efficiency due to model dependence is estimated from the efficiency difference between S-wave phase-space model and multipole model [12] in the primary π + π − generation. The main systematic uncertainties are listed in Table I, and are added in quadrature, resulting in a total systematic uncertainty of 12.3%. In summary, we have used ISR events to study the exclusive process e + e − → π + π − ψ(2S) and to measure its energy-dependent cross section from threshold to 8 GeV CM energy. A structure is observed at ∼ 4.32 GeV/c 2 in the π + π − ψ(2S) invariant mass spectrum that is not consistent with the decay ψ(4415) → π + π − ψ(2S). A fit to the mass spectrum with a single resonance yields a mass of (4324 ± 24) MeV/c 2 and a width of (172 ± 33) MeV, where the errors are statistical only. The structure in Fig. 3 has a mass that differs somewhat from that reported for the Y (4260) in Ref. [2]. However, the possibility that it represents evidence for a new decay mode for the Y (4260) cannot be ruled out at this time.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.