Evidence for the decay X ( 3872 )-> J / psi omega C

We present a study of the decays B^{0,+} -->J/psi pi^+ pi^- pi^0 K^{0,+}, using 467 10^6 BBbar pairs recorded with the BABAR detector. We present evidence for the decay mode X(3872) -->J/psi omega, with product branching fractions B(B^+ -->X(3872)K^+) B(X(3872) -->J/psi omega) =[0.6\pm0.2\stat \pm 0.1\syst ] 10^{-5}, and B(B^0 -->X(3872)K^0) B(X(3872) -->J/psi omega) =[0.6\pm0.3\stat \pm 0.1\syst ] 10^{-5}. A detailed study of the pi^+ pi^- pi^0 mass distribution from X(3872) decay favors a negative-parity assignment.

In a previous BABAR publication [23], we have confirmed the observation of the Y (3940) meson (denoted in the following as the Y meson) in the decay mode Y → J/ψω reported by the Belle Collaboration in B 0,+ → J/ψωK 0,+ decay [24]. In the BABAR analysis of this decay mode, the ω → π + π − π 0 mass (m 3π ) region was defined as 0.7695 ≤ m 3π ≤ 0.7965 GeV/c 2 . With this requirement and the other selection criteria of Ref. [23], we reported no evidence for the decay X → J/ψω, although Monte Carlo (MC) simulation of X-meson decay to an S-wave J/ψω system indicated that this decay could have been observed. An unpublished Belle analysis of B + → J/ψπ + π − π 0 K + [7], which required m(J/ψπ + π − π 0 ) − 3.872 < 0.0165 GeV/c 2 , reported evidence for the decay X → J/ψω on the basis of 12.4 ± 4.1 events in the mass interval 0.750 ≤ m 3π ≤ 0.775 GeV/c 2 .
In this study we repeat our analysis of the decay modes B 0,+ → J/ψπ + π − π 0 K 0,+ [23,25], extending the selected m 3π region to 0.5 <m 3π < 0.9 GeV/c 2 in order to investigate the m 3π distribution in a broader region around the ω meson.
The data were collected with the BABAR detector [26] at the PEP-II asymmetric-energy e + e − collider operated at the Υ (4S) resonance. We use the entire integrated luminosity at this center-of-mass (c.m.) energy (∼ 426 fb −1 ), which yields a data sample corresponding to about 467 × 10 6 BB pairs. The data were reprocessed with improved charged-particle-track reconstruction and identification.
The event-selection criteria are identical to those in Table I of Ref. [23], except for the initial m 3π requirement.
The B-meson signal region is defined using the c.m. energy difference ∆E = E * B − √ s/2, and the beam-energy substituted mass [26], where (E i , p i ) 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 B + (B 0 ) candidates satisfy |∆E| < 20 MeV (15 MeV). In events with multiple B candidates (12% of events in the region 5.274<m ES <5.284 GeV/c 2 ), the candidate with the smallest |∆E| is chosen.
For the B + -candidate sample, the m 3π distribution is shown in Fig. 1. The contribution in each mass interval is obtained by fitting the corresponding m ES distribution in the region 5.2 <m ES < 5.3 GeV/c 2 with a B + signal Gaussian function and an ARGUS background function [27]. The Gaussian mean value (µ), width (σ), and the ARGUS parameter (C ARG ), are fixed to the values obtained when fitting m ES for the entire J/ψπ + π − π 0 mass region separately for the B + and B 0 samples (for the B + sample µ = 5278.95 ± 0.13 MeV/c 2 , σ = 2.83 ± 0.14 MeV/c 2 , and C ARG = −37.9 ± 1.8). A binned Poisson likelihood fit is performed to the m ES distribution in each m 3π interval to obtain the Gaussian and ARGUS normalization parameter values, and hence to extract the B-meson signal.
In Fig. 1 there is a small, but clear, η-meson signal, a large ω-meson signal, and nothing of significance in between. The J/ψη mass distribution shows no significant structure, and will not be discussed any further. In the ω-meson region, the signal extends down to ∼ 0.74 GeV/c 2 ; there is also a high-mass tail above ∼ 0.8 GeV/c 2 , and possibly some small nonresonant contribution in this region. When we assign ω-Dalitz-plot weights [29] to the events in the region 0.74−0.80 GeV/c 2 , the sum of weights (1030±90) is consistent with the signal size (1160 ± 60), indicating that any non-ω background is small, and so we ignore such contributions. Similar behavior is observed for B 0 decay, but with a selectedevent sample which is about six times smaller. In the following, we define the lower limit of the ω-meson mass region as 0.74 GeV/c 2 , but leave the upper limit at 0.7965 and 0.8055 GeV/c 2 for the B + and B 0 samples [23], respectively, in order to focus on the impact of this one change on the observed J/ψω mass distribution. The extension of the m 3π region towards lower values increases the efficiency slightly.
The J/ψω mass distributions for B 0,+ → J/ψωK 0,+ candidates are obtained by using the same fit procedure used to obtain the m 3π distribution. We then correct the observed signal yields for selection efficiency. Events corresponding to B 0,+ → J/ψωK 0,+ decay are created by MC simulation, based on Geant4 [30], in order to provide uniform coverage of the the entire m J/ψω range. The generated events are subjected to the reconstruction and selection procedures applied to the data. For B + (B 0 ) decay it is found that the efficiency increases (decreases) gradually from ∼ 6% (∼ 5%) close to m J/ψω threshold to ∼ 7% (∼ 4%) for m J/ψω ∼ 4.8 GeV/c 2 . Comparison of generated and reconstructed m J/ψω values within each reconstructed m J/ψω mass interval enables the measurement of the m J/ψω dependence of the mass resolution. From a single-Gaussian fit to each distribution, the rms deviation is found to degrade gradually from 6.5 MeV/c 2 at m J/ψω ∼3.84 GeV/c 2 , to 9 MeV/c 2 at m J/ψω ∼4.8 GeV/c 2 .
The m J/ψω distributions for B + → J/ψωK + and B 0 → J/ψωK 0 decay, after efficiency correction in each mass interval, are shown in Fig. 2(a) and Fig. 2(b), respectively. For the latter, corrections for K 0 L production and K 0 S → π 0 π 0 decay have been incorporated. The m J/ψω range from 3.8425 to 3.9925 GeV/c 2 is divided into 10 MeV/c 2 intervals, while beyond this 50 MeV/c 2 intervals are used. The same choice of intervals was used in Ref. [23], where the first two were inaccessible, and the third was only partly accessible, because of the value of the lower limit on m 3π . Clear enhancements are observed in the vicinity of the X and Y mesons in the B + distribution, and similar effects are present in the B 0 distribution, with lower statistical significance.
The function used to fit the distributions of Fig. 2 is a sum of three components. The X meson component is a Gaussian resolution function with fixed rms deviation σ = 6.7 MeV/c 2 obtained from MC simulation; the intrinsic width of the X meson (estimated to be < ∼ 3 MeV [28]) is ignored. The Y -meson intensity contribution is represented by a relativistic S-wave Breit-Wigner (BW) function [23]. The nonresonant contribution is described empirically by a Gaussian function multiplied by m J/ψω . The Y -meson and nonresonant intensity contributions are multiplied by the phase space factor p × q, where p is the K momentum in the B rest frame, and q is the J/ψ momentum in the rest frame of the J/ψ3π system. A simultaneous χ 2 fit to the distributions of Figs. 2(a) and 2(b) is carried out, in which only the normalization parameters of the three contributions are allowed to differ between Fig. 2(a) and Fig. 2(b). The fit describes the data well (χ 2 /NDF = 54.7/51, NDF=number of degrees of freedom), as shown by the solid curves in Fig. 2. The dashed and dotted curves show the X-and Y -meson contributions, respectively, while the dot-dashed curves represent the nonresonant distribution.
From the fits of Fig. 2, we obtain product branch- We define R X , R Y , and R N R as the ratios of the B 0 to B + branching fractions to the final states XK, Y K, and nonresonant J/ψωK, and extract these ratios from a simultaneous fit to the data, with the fit function adjusted to explicitly contain these parameters. This yields R X = 1.0 +0.8 −0.6 (stat) , and R N R = 0.7 ± 0.1(stat) ± 0.1(syst). The values of R Y and R N R are consistent with those in Ref. [23]. The statistical uncertainty on R N R has been reduced significantly with respect to Ref. [23] as a result of the increased luminosity, improvements in event reconstruction efficiency, and the use of much larger MC samples in the measurement of the selection efficiency as a function of m J/ψω , especially for m J/ψω > 4 GeV/c 2 .
In obtaining the quoted systematic errors, systematic uncertainties due to tracking (2%), particle identification (4.4% and 5.2% for B 0 and B + events), π 0 reconstruction efficiency (3.6%), K 0 S reconstruction efficiency (2%) for the B 0 events, and BB event counting (1.1%), have been taken into account. The uncertainties on the branching fraction values for J/ψ → ℓ + ℓ − and ω → 3π [28] have been treated as sources of systematic uncertainty. When fitting the m ES distributions in each m J/ψω or m 3π mass interval, the parameters µ, σ, and C ARG were fixed to the values obtained from the fit to the corresponding total m ES distribution. Associated systematic uncertainties were estimated by increasing and decreasing the central value of each parameter by one standard deviation, repeating the analysis, and taking the change in each fitted quantity as an estimate of systematic uncertainty. Similarly, the systematic uncertainty associated with the efficiency-correction procedure was estimated by varying its m J/ψω dependence within a ±1σ envelope, repeating the fits to the data of Fig. 2, and taking the corresponding changes in fit parameter values as estimates of systematic uncertainty. Additional systematic uncertainties on the mass and width of the Y meson were estimated as described in Ref. [23]. The main contributions described there result from a comparison of the MC input values to those obtained after event reconstruction, and from the difference in fitted values when a P -wave BW was used instead of an S-wave BW to describe the Y -meson lineshape.
Since the X-meson signal occurs at a low statistical level and at very low values of m J/ψω , there is concern that the measured signal-event yield might be biased because of the low mass tails of the Y -meson and nonresonant contributions. A detailed MC study using samples of X-meson events ranging in size from 10-500 events showed no evidence of bias, and the spread in extracted signal yield was consistent with the corresponding statistical uncertainty obtained from the fit to the data.
We now consider the relationship between the Xmeson signal and the choice of lower mass limit for the ω-meson region. In Fig. 3 we show the data corresponding to the first five mass intervals of Fig. 2 (3.8425< m J/ψω <3.8925 GeV/c 2 ) before applying the efficiency and K 0 branching fraction corrections. The points shown by open squares indicate the effect of choosing the m 3π lower limit to be 0.7695 GeV/c 2 rather than 0.740 GeV/c 2 . The three lowest intervals then yield no signal, and the other two contain only 11 (0.5) events in Fig. 3(a) (Fig. 3(b)). This is to be compared with 42.4 +7.8 −7.2 (8.5 +3.7 −3.0 ) events obtained when the m 3π lower limit is 0.74 GeV/c 2 . Since the number of events in Fig. 3 is much smaller than the total number of ω-meson events (1160 ± 60 for B + and 206 ± 26 for B 0 decay), and since the m 3π distribution (Fig. 4(c)) differs greatly from the ω-meson lineshape, these might be nonresonant 3π events. To check the ω-meson interpretation, we sum the ω-Dalitz-plot weights [29] for the events contributing to Fig. 3(a) (solid points) in the m ES signal region and obtain 41 ± 13, in good agreement with the number from the m ES fits. This justifies the ω-meson interpretation. In contrast, we note that for the 152 ± 20 η-meson events in Fig. 1 the sum of the weights [29] is −1 ± 42, as expected for a uniform Dalitz-plot distribution.
To determine the significance of the X → J/ψω signal, we extract the signal yields from a fit to the data, prior to the corrections for efficiency and K 0 branching fractions, as shown in Fig. 3. The fitted values of the masses and widths are in agreement with those obtained from the fit to the corrected data. An X-meson signal of 21.1 ± 7.0 events is obtained for B + decay, and 5.6 ± 3.0 events for B 0 decay, so that the combined signal is 26.7 ± 7.6 events. For the combined distribution, the mass region 3.8625 − 3.8825 GeV/c 2 contains 34.0 ± 6.6 events, and the fitted curves indicate that only 8.9 ± 1.0 events are due to the tails of the Y -meson and nonresonant distributions. We convolve a Gaussian ensemble of background Poisson distributions with a Gaussian distribution of observed events, and obtain probability 3.6×10 −5 that the 34.0±6.6 events can result from upward background fluctuation. This corresponds to a significance of 4.0σ for a normal distribution. On this basis we report evidence for the decay mode X → J/ψω.
For the 3.8625 − 3.8825 GeV/c 2 region of Fig. 3, we plot the m 3π distributions in Fig. 4. Each data point results from a fit to the corresponding m ES distribution; for the points with no error bars, the m ES distribution is empty. For the combined distribution, Fig. 4(c), ∼ 84% of the events have m 3π < 0.7695 GeV/c 2 , the mass limit used in Ref. [23]. The dashed histogram in Fig. 4(c) results from normalizing the reconstructed X-meson MC events to the observed 34 events. Since the J/ψω system was generated with zero orbital angular momentum, this corresponds to positive X-meson parity. One unit of orbital angular momentum creates a centrifugal barrier factor q 2 /(1 + R 2 q 2 ) in the description of the J/ψω final state, where R = 3 GeV −1 is the P -wave Blatt-Weisskopf barrier factor radius [31] (values in the range 0 < R < 5 GeV −1 yield no significant difference). This factor suppresses the π + π − π 0 mass spectrum near the upper kinematic limit, as shown by the solid histogram of Fig. 4(c) (also normalized to 34 events). For the dashed histogram χ 2 /NDF = 10.17/5 and the χ 2 -distribution probability is P (χ 2 , NDF) = 7.1%, while for the solid his- togram χ 2 /NDF = 3.53/5 and P (χ 2 , NDF) = 61.9%. It follows that the observed distribution favors the P -wave description both quantitatively and qualitatively. If both histograms are normalized to the region m 3π < 0.7695 GeV/c 2 (which was excluded in Ref. [23]), we expect for m 3π > 0.7695 GeV/c 2 , and hence for the m J/ψω interval 3.8725 − 3.8825 GeV/c 2 , ∼ 4.3 events for the P -wave description, and ∼ 16.6 events for the S-wave description. However, in Fig. 3 we observe ∼ 6 events. In Ref. [32], it was pointed out that for X(3872) → D * 0D0 , the introduction of one unit of orbital angular momentum in the final state could explain the shift in measured Xmeson mass [12,13]. This observation and the present analysis, together with the spin-parity (J P ) analysis of Ref. [11], favor J P = 2 − for the X(3872) meson. For I = 0 and J P C = 2 −+ , the X-meson mass falls within the broad range of estimates for the η c2 (1D) charmonium state [33,34]. We conclude that this interpretation is favored by the data.
In summary, we have used the entire BABAR data sample collected at the Υ (4S) resonance to obtain evidence for X → J/ψω in B 0,+ → J/ψωK 0,+ with product branching fraction values [0.6 ± 0.2(stat) ± 0.1(syst)] × 10 −5 and [0.6 ± 0.3(stat) ± 0.1(syst)] × 10 −5 for B + and B 0 , respectively. A comparison of the observed m 3π mass distribution from X → J/ψω decay to those from MC simulations leads us to conclude that the inclusion of one unit of orbital angular momentum in the J/ψω system  [28]. In (c), the solid (dashed) histogram represents reconstructed MC P -wave (S-wave) events normalized to the number of data events.
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.