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

We present a study of the decays B^(0,+)→J/ψπ^+π^-π^0K^(0,+), using 467×10^6 BB[overbar] pairs recorded with the BABAR detector. We present evidence for the decay mode X(3872)→J/ψω, with product branching fractions B(B^+→X(3872)K^+)×B(X(3872)→J/ψω)=[0.6±0.2(stat)±0.1(syst)]×10^(-5), and B(B^0→X(3872)K^0)×B(X(3872)→J/ψω)=[0.6±0.3(stat)±0.1(syst)]×10^(-5). A detailed study of the π^+π^-π^0 mass distribution from X(3872) decay favors a negative-parity assignment.

The Xð3872Þ meson (denoted in the following as the X meson) has been observed primarily in its J=c % þ % À decay mode [1][2][3][4][5][6].Evidence for its decay to the J=c [7][8][9] and c ð2SÞ [9] final states has established positive C parity.Analyses by the CDF Collaboration of the % þ % À mass distribution [10], and of the decay angular distribution [11], for the J=c % þ % À decay mode have narrowed the possible spin-parity (J P ) assignment to 1 þ or 2 À .The decay X !D 0 " D 0 % 0 has also been observed [12] and interpreted as evidence for X !D Ã0 " D 0 ; this has been confirmed by subsequent analyses [13,14].There has been much theoretical interest in the nature of the X meson [15][16][17][18][19][20][21][22].Hence, additional experimental information on new decay modes, especially those sensitive to the J P assignment, is germane to the theoretical understanding of this state.
In a previous BABAR publication [23], we have confirmed the observation of the Yð3940Þ meson (denoted in the following as the Y meson) in the decay mode Y !J=c ! reported by the Belle Collaboration in B 0;þ !J=c !K 0;þ decay [24].In the BABAR analysis of this decay mode, the !! % þ% À % 0 mass (m 3% ) region was defined as 0:7695 m 3% 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=c !, although Monte Carlo (MC) simulation of X-meson decay to an S-wave J=c !system indicated that this decay could have been observed.An unpublished Belle analysis of B þ !J=c % þ % À % 0 K þ [7], which required jmðJ=c % þ % À % 0 Þ À 3:872j < 0:0165 GeV=c 2 , reported evidence for the decay X !J=c ! on the basis of 12:4 AE 4:1 events in the mass interval 0:750 m 3% 0:775 GeV=c 2 .
In this study we repeat our analysis of the decay modes [23,25], extending the selected m 3% region to 0:5 < m 3% < 0:9 GeV=c 2 in order to investigate the m 3% distribution in a broader region around the !meson.
The data were collected with the BABAR detector [26] at the PEP-II asymmetric-energy e þ e À collider operated at the Çð4SÞ resonance.We use the entire integrated luminosity at this center-of-mass (c.m.) energy ( $ 426 fb À1 ), which yields a data sample corresponding to about 467 Â 10 6 B " B pairs.The entire data sample was reprocessed using the most recent version of the event-reconstruction and particle-identification code.
The event-selection criteria are identical to those in Table I of Ref. [23], except for the initial m 3% requirement.
The B-meson signal region is defined using the c.m. energy difference ffiffi ffi s p =2, and the beam-energy substi- [26], where ðE i ; pi Þ is the initial state four-momentum vector in the laboratory frame, ffiffi ffi s p is the c.m. energy, E Ã B is the B-meson energy in the c.m., and pB is its laboratory-frame momentum.Signal B þ (B 0 ) candidates satisfy jÁEj < 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 jÁEj is chosen.
For the B þ -candidate sample, the m 3% 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 þ signal Gaussian function and an ARGUS background function [28].The Gaussian mean value ("), width ('), and the ARGUS parameter (C ARG ), are fixed to the values obtained when fitting m ES for the entire J=c % þ % À % 0 mass region separately for the B þ and B 0 samples (for the B þ sample " ¼ 5278:95 AE 0: obtained as described in the text; the dashed vertical lines denote the central mass values of the and !meson [27].
in each m 3% 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, -meson signal, a large !-meson signal, and nothing of significance in between.The J=c mass distribution shows no significant structure, and will not be discussed any further.
In the !-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 !-Dalitz-plot weights [29] to the events in the region 0:74-0:80 GeV=c 2 , the sum of weights (1030 AE 90) is consistent with the signal size (1160 AE 60), indicating that any non-!background is small, and so we ignore such contributions.Similar behavior is observed for B 0 decay, but with a selected-event sample which is about 6 times smaller.In the following, we define the lower limit of the !-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 þ and B 0 samples [23], respectively, in order to focus on the impact of this one change on the observed J=c !mass distribution.The extension of the m 3% region toward lower values increases the efficiency slightly.
The J=c !mass distributions for B 0;þ !J=c !K 0;þ candidates are obtained by using the same fit procedure used to obtain the m 3% distribution.We then correct the observed signal yields for selection efficiency.Events corresponding to B 0;þ !J=c !K 0;þ decay are created by MC simulation, based on GEANT4 [30], in order to provide uniform coverage of the entire m J=c !range.The generated events are subjected to the reconstruction and selection procedures applied to the data.For B þ (B 0 ) decay it is found that the efficiency increases (decreases) gradually from $6% ( $ 5%) close to m J=c !threshold to $7% ( $ 4%) for m J=c !$ 4:8 GeV=c 2 .Comparison of generated and reconstructed m J=c !values within each reconstructed m J=c !mass interval enables the measurement of the m J=c !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=c !$ 3:84 GeV=c 2 , to 9 MeV=c 2 at m J=c !$ 4:8 GeV=c 2 .
The m J=c !distributions for B þ !J=c !K þ and B 0 !J=c !K 0 decay, after efficiency correction in each mass interval, are shown in Figs.2(a) and 2(b) respectively.For the latter, corrections for K 0 L production and K 0 S !% 0 % 0 decay have been incorporated.The m J=c !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 3% .Clear enhancements are observed in the vicinity of the X and Y mesons in the B þ 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 ' ¼ 6:7 MeV=c 2 obtained from MC simulation; the intrinsic width of the X meson (estimated to be & 3 MeV [27]) 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=c ! .The Y-meson and nonresonant intensity contributions are multiplied by the phase space factor p Â q, where p is the K momentum in the B rest frame, and q is the J=c momentum in the rest frame of the J=c 3% system.A simultaneous 1 2 fit to the distributions of Figs.2(a À8 ðstatÞ AE 5ðsystÞ MeV, respectively.These results are consistent with earlier BABAR measurements [6,23].
We define R X , R Y , and R NR as the ratios of the B 0 to B þ branching fractions to the final states XK, YK, and nonresonant J=c !K, 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 ¼ 1:0 þ0:8 À0:6 ðstatÞ þ0:1 À0:2 ðsystÞ, R Y ¼ 0:7 þ0:4 À0:3 ðstatÞ AE 0:1ðsystÞ, and R NR ¼ 0:7 AE 0:1ðstatÞ AE 0:1ðsystÞ.The values of R Y and R NR are consistent with those in Ref. [23].The statistical uncertainty on R NR has been reduced significantly with respect to Ref. [23] as a result of the increased luminosity, improvements in event reconstruction efficiency, but primarily through the use of much larger MC samples in the measurement of the selection efficiency as a function of m J=c !, especially for m J=c !> 4 GeV=c 2 .
In Ref. [6], it was found that We combine these results with those from the present analysis to obtain the ratio of the branching fractions BðX !J=c !Þ=BðX !J=c % þ % À Þ.For B þ (B 0 ) events, this ratio is 0:7 AE 0:3 (1:7 AE 1:3), where the statistical uncertainties, and those systematic uncertainties which do not cancel in the ratio, have been added in quadrature; the weighted average is 0:8 AE 0:3.This is consistent with that reported in Ref. [7] (1:0 AE 0:4ðstatÞ AE 0:3ðsystÞ).
In obtaining the quoted systematic errors, systematic uncertainties due to tracking (2%), particle identification (4.4% and 5.2% for B 0 and B þ events), % 0 reconstruction efficiency (3.6%),K 0 S reconstruction efficiency (2%) for the B 0 events, and B " B event counting (1.1%), have been taken into account.The uncertainties on the branching fraction values for J=c !' þ ' À and !!3% [27] have been treated as sources of systematic uncertainty.When fitting the m ES distributions in each m J=c ! or m 3% mass interval, the parameters ", ', 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 1 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 efficiencycorrection procedure was estimated by varying its m J=c !dependence within a AE1' 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 line shape.
Since the X-meson signal occurs at a low statistical level and at very low values of m J=c !, 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 X-meson signal and the choice of lower mass limit for the !-meson region.In Fig. 3 we show the data corresponding to the first five mass intervals of Fig. 2 (3:8425 < m J=c !< 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 3% 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) (3(b)).This is to be compared with 42:4 þ7:8 À7:2 (8:5 þ3:7 À3:0 ) events obtained when the m 3% lower limit is 0:74 GeV=c 2 .Since the number of events in Fig. 3 is much smaller than the total number of !-meson events (1160 AE 60 for B þ and 206 AE 26 for B 0 decay), and since the m 3% distribution [Fig.4(c)] differs greatly from the !-meson line shape, these might be nonresonant 3% events.To check the !-meson interpretation, we sum the !-Dalitz-plot weights [29] for the events contributing to Fig. 3(a) (solid points) in the m ES signal region and obtain 41 AE 13, in good agreement with the number from the m ES fits.This justifies the !-meson interpretation.In contrast, we note that for the 152 AE 20 -meson events in Fig. 1 the sum of the weights [29] is À1 AE 42, as expected for a uniform Dalitz-plot distribution.
To determine the significance of the X !J=c !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 AE 7:0 events is obtained for B þ decay, and 5:6 AE 3:0 events for B 0 decay, so that the combined signal is 26:7 AE 7:6 events.For the combined distribution, the mass region 3:8625-3:8825 GeV=c 2 contains 34:0 AE 6:6 events, and the fitted curves indicate that only 8:9 AE 1:0 events are due to the tails of the Y-meson and nonresonant distribu-tions.We convolve a Gaussian ensemble of background Poisson distributions with a Gaussian distribution of observed events, and obtain probability 3:6 Â 10 À5 that the 34:0 AE 6:6 events can result from upward background fluctuation.This corresponds to a significance of 4:0' for a normal distribution.On this basis we report evidence for the decay mode X !J=c !.
For the 3:8625-3:8825 GeV=c 2 region of Fig. 3, we plot the m 3% 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 3% < 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=c !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 =ð1 þ R 2 q 2 Þ in the description of the J=c !final state, where R ¼ 3 GeV À1 is the P-wave Blatt-Weisskopf barrier factor radius [31] (values in the range 0 < R < 5 GeV À1 yield no significant difference).This factor suppresses the % þ % À % 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 1 2 =NDF ¼ 10:17=5 and the 1 2 -distribution probability is Pð1 2 ; NDFÞ ¼ 7:1%, while for the solid histogram 1 2 =NDF ¼ 3:53=5 and Pð1 2 ; NDFÞ ¼ 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 3% < 0:7695 GeV=c 2 (which was excluded in Ref. [23]), we expect for m 3% > 0:7695 GeV=c 2 , and hence for the m J=c !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 Xð3872Þ !D Ã0 " D 0 , the introduction of one unit of orbital angular momentum in the final state could explain the shift in measured X-meson mass [12,13].This observation and the present analysis, together with the spin-parity (J P ) analysis of Ref. [11], favor J P ¼ 2 À for the Xð3872Þ meson.For I ¼ 0 and J PC ¼ 2 Àþ , the X-meson mass falls within the broad range of estimates for the c2 ð1DÞ 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 Çð4SÞ resonance to obtain evidence for X !J=c ! in B 0;þ !J=c !K 0;þ with product branching fraction values ½0:6 AE 0:2ðstatÞ AE 0:1ðsystÞ Â 10 À5 and ½0:6 AE 0:3ðstatÞ AE 0:1ðsystÞ Â 10 À5 for B þ and B 0 , respectively.A comparison of the observed m 3% mass distribution from X !J=c !decay to those from MC simulations leads us to conclude that the inclusion of one unit of orbital angular momentum in the J=c !system  [27].In (c), the solid (dashed) histogram represents reconstructed MC P-wave (S-wave) events normalized to the number of data events.
) and 2(b) is carried out, in which only the normalization parameters of the three contributions are allowed to differ between Figs. 2(a) and 2(b).The fit describes the data well (1 2 =NDF ¼ 54:7=51, NDF ¼ number of degrees of freedom), as shown by the solid curves in Fig.2.The dashed and dotted curves show the Xand Y-meson contributions, respectively, while the dotdashed curves represent the nonresonant distribution.For the X meson, the fitted mass is 3873:0 þ1:8 À1:6 ðstatÞ AE 1:3ðsystÞ MeV=c 2 , while the mass and width values for the Y meson are 3919:1 þ3:8 À3:4 ðstatÞ AE 2:0ðsystÞ MeV=c 2 and 31 þ10

FIG. 2 (
FIG. 2 (color online).The corrected m J=c !distribution for (a) B þ , (b) B 0 decays; (c) (inset) shows the low-mass region of (a) in detail.The curves indicate the results of the fit.