Observation of Y(3940) ->J/psi omega in B ->J/psi omega K at BABAR

We present a study of the decays $B^{0,+}\to J/\psi\omega K^{0,+}$ using $383\times 10^{6}$ $B\bar{B}$ events obtained with the \babar detector at PEP-II. We observe $Y(3940) \to J/\psi \omega$, with mass $3914.6 ^{+3.8}_{-3.4} (stat) \pm{2.0} (syst)$ \mevcc, and width $34^{+12}_{-8}(stat)\pm{5}(syst)$ \mev. The ratio of $B^0$ and $B^+$ decay to $YK$ is $0.27^{+0.28}_{-0.23}(stat)^{+0.04}_{-0.01}(syst)$, and the relevant $B^0$ and $B^+$ branching fractions are reported.

We present a study of the decays B 0,+ → J/ψωK 0,+ using 383 × 10 6 BB events obtained with the BABAR detector at PEP-II. We observe Y (3940) → J/ψω, with mass 3914.6 +3.8 −3.4 (stat) ± 2.0(syst) MeV/c 2 , and width 34 +12 −8 (stat) ± 5(syst) MeV. The ratio of B 0 and B + decay to Y K is 0.27 +0.28 −0.23 (stat) +0.04 −0.01 (syst), and the relevant B 0 and B + branching fractions are reported. The BELLE Collaboration has reported evidence for the X(3940) [1], the Y (3940) [2], and the Z(3930) [3]. The mass and width values are the same within error, the states have positive C parity, and spin-parity (J P ) 2 + is favored for the Z, which may then be the first radial excitation of the χ c2 (3556), i.e., a charmonium state. The mass and width consistency with the X and Y suggests the possibility that these may be the Z in different production contexts. The Z was found in twophoton production of DD, so that it may be a charmonium state. The X was observed in e + e − → J/ψX, and decays mainly to D * D , suggesting a charmonium interpretation. In contrast, the Y was found in B → Y K, Y → J/ψω, which is OZI suppressed for a charmonium state [4]. Also, an analysis of B → KDD and B → KD * D [5] shows no evidence for the Y (nor for the X or Z), although ψ(3770) → DD and X(3872) → D * D are observed. Other possibilities for the nature of this state, already suggested for the X(3872), include a hybrid charmonium-gluon bound state, ccg [6,7], a molecular state of a cc(uū + dd) system [8,9,10,11,12], or a multiquark state [13]. The S−wave molecule model [9] predicts a very small B 0 /B + ratio for B → KX(3872). The previous low value has been confirmed [14], although the uncertainties are still large, so that a measurement of this ratio for the Y (3940) may be important to an understanding of this state.
In this Letter, we examine the decays B 0,+ → J/ψπ + π − π 0 K 0,+ [15], with π + π − π 0 mass in the ω region. We confirm the Y (3940), improve the precision of the mass and width significantly, and measure the (B 0 /B + ) production ratio for the first time. Branching fraction values for B → Y K, Y → J/ψω, and for B → J/ψωK are obtained for B 0 and B + decay separately; each is a first measurement.
The data were collected with the BABAR detector [16] at the PEP-II asymmetric-energy e + e − storage rings operating at the Υ (4S) resonance. The integrated luminosity for this analysis is 348 fb −1 . The decays B 0,+ → J/ψπ + π − π 0 K 0,+ are reconstructed as follows (Table I). A candidate J/ψ → e + e − (µ + µ − ) decay has invariant mass in the J/ψ mass region, and is then constrained to the nominal mass [17]. A K 0 S candidate has π + π − invariant mass in the K 0 S region. The J/ψ and K 0 S distributions from the B signal region show no significant background. A π 0 candidate consists of a photon pair with invariant mass in the π 0 region. After a π 0 mass constraint, an ω → π + π − π 0 candidate has invariant mass in the ω region. We form a B + B 0 candidate by com-bining J/ψ, ω and K + [18] (K 0 S ) candidates. We define the B signal region using the center of mass (c.m.) energy difference ∆E ≡ E * B − √ s/2, and the beam-energy substituted mass m ES ≡ is the initial state four-momentum vector in the laboratory frame (l.f.); √ s is the c.m. energy, E * B is the B meson energy in the c.m., and p B is its l.f. momentum. Signal events have ∆E ∼ zero and m ES ∼ m B ; 12% of the events have multiple candidates, and for these the combination with the smallest |∆E| is chosen.
The selection criteria were established by optimizing signal-to-background ratio using Monte Carlo (MC) simulated signal events, B → Y K, Y → J/ψω, and background BB and e + e − → qq (q = u, d, s, c) events.
The 3π mass, m ES , and ∆E distributions are shown in Fig. 1, where we apply all Table I criteria except the requirement on the variable plotted. We fit the 3π mass distributions with an ω-meson Breit-Wigner (BW) line shape (nominal ω mass and width [17]) convolved with a MC-determined triple-Gaussian resolution function as signal, and a quadratic background function. We fit the m ES distributions with a signal Gaussian with mass and width fixed from MC, and an ARGUS background function [19], and fit the ∆E distributions with a double-Gaussian signal function determined from MC, and a linear background function. There is a large ω signal for the B + mode, and a smaller signal for B 0 ; the m ES and ∆E distributions exhibit clear B signals. We establish the correlation between the ω and B signals with a projection procedure based on the ω decay angular distribution. The helicity angle, θ h , is the angle between the π + and π 0 directions in the π + π − r.f.. The cos θ h distribution is proportional to sin 2 θ h , and the ω signal is projected by giving the i th event weight w i = 5 2 (1 − 3 cos 2 θ i h ). The effect is shown in Fig 1. For the B + mode, the omega signal survives, and background is removed. For the B 0 mode the effect is qualitatively similar. Confirmation is obtained from a fit to the 3π mass distribution in each interval. We conclude that there is one-to-one correspondence between the ω and B-meson signals in m ES and ∆E, and that, at the present level of statistics, the 3π system in the ω mass region results entirely from ω decay for B → J/ψπ + π − π 0 K. The ω − m ES (or ∆E) signal correlation is important to an analysis of the J/ψω threshold mass region. Near threshold, the 3π mass distribution above the ω mass is limited in range and distorted in shape. The m ES distribution is not affected, and so we use m ES fits to extract the J/ψω mass distribution.
For each B decay mode, the m ES distribution in each interval of J/ψπ + π − π 0 invariant mass is fitted to extract the J/ψω signal. The m ES signal, and ARGUS background, functions are those of Fig. 1; the fits use a binned Poisson likelihood function with signal and background normalizations free [20]. All fits converge properly and provide good descriptions of the data. From threshold to 4 GeV/c 2 , the J/ψω mass resolution varies from 5 − 8 MeV/c 2 , and so in this region the spectrum is investigated in 11 intervals of 10 MeV/c 2 starting at 3.8725 GeV/c 2 . At higher mass, there is no evidence of narrow structure, and we show the results in 50 MeV/c 2 intervals. In Fig. 2, there is a clear enhancement near threshold for B + decay, while at higher mass no structure is apparent. The total B + (B 0 ) signal in Fig. 2 is 236 +18 −15 (32 +8 −7 ) events of which 109 +15 −13 (16 +7 −6 ) have J/ψω mass less than 4 GeV/c 2 (statistical errors only).
We correct the mass distributions of Fig. 2 for efficiency and resolution. In the MC simulation of the Y signal, we assume phase space decays of B → Y K and Y → J/ψω, but use the correct angular distribution for ω decay. Initially we used a relativistic S-wave BW line shape with M (Y ) = 3.940 GeV/c 2 and Γ(Y ) = 0.06 GeV [2]. Mass resolution effects result in a net flow of events away from the peak mass value. For a given mass interval we define acceptance as the ratio of events reconstructed in that interval to events generated in the interval; this accounts for efficiency and resolution effects. The acceptance-corrected spectrum is fit to a relativistic BW line shape without convolving resolution, since the acceptance correction takes this into account. We obtain values of M (Y ) and Γ(Y ) which are smaller than in the initial simulation, and so generate new MC samples with the new values in order to correctly reproduce resolution effects. This iterative procedure converges quickly, and the acceptance results in Figs. 2(c), (d) are obtained with M (Y ) = 3.915 GeV/c 2 and Γ(Y ) = 0.02 GeV. The dip at ∼ 3.91 GeV/c 2 is due to net flow of events away from the resonance maximum because of mass resolution. At lower mass, the acceptance is slightly lower than at higher mass because of the proximity to threshold. Although the acceptance variation in the Y signal region is significant, the effect on the Y fit parameters, and on the corrected number of signal events, is small because of the large statistical uncertainties on the data.
The decrease in acceptance at high mass in Fig. 2(d) results from decreasing K 0 S l.f. momentum. The decay pion reconstruction probability decreases because its l.f. momentum is too small, or because the decay opening angle is so large that the pion does not intersect enough detector planes. Fig. 3 shows the corrected mass distributions. Below ∼ 4 GeV/c 2 we correct interval-by-interval, while for higher mass we use a linear fit to the J/ψω mass dependence. The B 0 data are corrected for K 0 L and K 0 S → π 0 π 0 decays. We associate the near-threshold enhancement in Fig. 3(a) with Y production [2], and obtain the mass, width and decay rate from χ 2 fits. The fit function consists of a relativistic S−wave BW describing the Y and a Gaussian nonresonant contribution. The corrected B + and B 0 distributions are fitted simultaneously, with mass, width and Gaussian parameters as common free parameters. The fit describes the data well (χ 2 /N DF = 45/44, NDF=number of degrees of freedom ), as shown in Fig. 3. In Fig. 3(a), the acceptancecorrected number of events with J/ψω mass less than 3.98 GeV/c 2 is 2140 ± 290(stat), while for the Gaussian it is 420 ± 90(stat). Our average efficiency of ∼ 5% implies that a background fluctuation of ∼ 19 standard deviations would be required to describe the near-threshold enhancement. This occurrence has negligible probability, and so we have instead a clear observation of the Y (3940). The simultaneous fit yields a Y signal of 1980 +396 −379 (stat) events (i.e. magnitude 5.2 standard deviations) for B + , and 527 +534 −454 (stat) for B 0 . Since the acceptance-correction procedure may depend on the input MC Y (3940) line shape, we combine the first 11 mass intervals for data and MC and make an overall efficiency correction. The results differ by 1.9%, and we incorporate this as a systematic error associated with the MC line shape. Other systematic errors are estimated by repeating the entire process, separately varying by ±1σ the signal peak and width, and the ARGUS parameter, for the m ES fits. The largest systematic uncertainty contributions to the B + branching fraction are 5 − 6% due to the uncertainties in the secondary branching fractions, tracking efficiency, and particle identification. For B 0 , the largest contribution is 10% due to m ES mass variation; secondary branching fractions, particle identification, tracking and K S reconstruction efficiency contribute also. For both modes, there are uncertainties associated with the number of BB events produced, and with MC sample size. The product branching fraction for B + → Y K + , Y → J/ψω is (4.9 +1.0 −0.9 (stat) ± 0.5(syst)) × 10 −5 , and that for B 0 → Y K 0 , Y → J/ψω is (1.3 +1.3 −1.1 (stat) ± 0.2(syst)) × 10 −5 , with upper limit (95% C.L.) 3.9 × 10 −5 for the latter. The corresponding branching fractions for B → J/ψωK are (3.5 ± 0.2(stat) ± 0.4(syst)) × 10 −4 , and (3.1 ± 0.6(stat) ± 0.3(syst)) × 10 −4 , respectively.
We define R Y and R N R as the ratios between the number of B 0 and B + events (after all corrections) for the Y signal and for the nonresonant contribution, respectively. Simultaneous fits to Figs  The Y mass and width measurements are subject to additional systematic effects. When MC-generated signal events are fitted using the input line shape with mass and width as free parameters, the fitted value of the mass is 1.6 MeV/c 2 lower than the input value of 3.915 GeV/c 2 . This results from the limited 3π phase space near J/ψω threshold, and so we increase the fitted Y mass value by 1.6 MeV/c 2 , and assign this as a systematic uncertainty. Also, we have used an S-wave BW line shape to describe the Y . We repeat the fit using a P -wave line shape. The fitted mass value decreases by 1 MeV/c 2 , and the width increases by 5 MeV. We assign these as systematic uncertainties due to the choice of orbital angular momentum. Finally, a fit to the uncorrected distributions (Fig. 2) yields a mass value 1.4 MeV/c 2 larger, and a width 4 MeV larger, than obtained for the corrected distributions. The mass dependence of the acceptance depends on the MC line shape and so systematic uncertainties of 0.7 MeV/c 2 and 2 MeV, respectively are associated with the MC line shape choice. These contributions dominate all other sources of systematic uncertainty, and the final mass and width values are (3914.6 +3.8 −3.4 (stat) ± 2.0(syst)) MeV/c 2 , and (34 +12 −8 (stat) ± 5(syst)) MeV, respectively. In summary, in the decays B 0,+ → J/ψωK 0,+ we find a J/ψω mass enhancement at ∼ 3.915 GeV/c 2 , confirming the BELLE result [2], but obtain lower mass, smaller width, and reduce the uncertainty on each by a factor ∼ 3. The mass is two standard deviations lower than the Z(3930) mass, and three standard deviations lower than for the X(3940); the width agrees with the Z(3930) and X(3940) values. The ratio of B 0 and B + decay to Y K, R Y , is measured for the first time and found to be ∼ 3 standard deviations below the isospin expectation, but agrees with that for the X(3872) [14]. The ratio for the nonresonant contribution R N R agrees with the isospin expectation. We have obtained first measurements of the branching fractions for B → J/ψωK and for B → Y K, Y → J/ψω, for B 0 and B + decays separately.
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), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.