Observation of B0 ->chi_c0K*0 and evidence for B+ ->chi_c0K*+

We present the observation of the decay B0 ->chi_c0K*0 as well as evidence of B+ ->chi_c0K*+, with an 8.9 and a 3.6 standard deviation significance, respectively, using a data sample of 454 million Y(4S) ->BB decays collected with the BaBar detector at the PEP-II B meson factory located at the Stanford Linear Accelerator Center (SLAC). The measured branching fractions are: B(B0 ->chi_c0K*0) = (1.7 +/- 0.3 +/- 0.2) * 10^{-4} and B(B+ ->chi_c0K^*+) = (1.4 +/- 0.5 +/- 0.2) * 10^{-4}, where the first quoted errors are statistical and the second are systematic. We obtain a branching fraction upper limit of B(B+ ->chi_c0K*+)<2.1 * 10^{-4} at the 90% confidence level.

the first quoted errors are statistical and the second are systematic. We obtain a branching fraction upper limit of B(B + → χc0K * + ) < 2.1 × 10 −4 at the 90% confidence level.
PACS numbers: 13.25.Hw Theoretical predictions of branching fractions and rate asymmetries in non-leptonic heavy-flavor meson decays are difficult due to our limited understanding of the process of quark hadronization. In the simplest approximation, weak decays such as B → J/ψ K arise from the quark-level process b → ccs through a current-current interaction that can be written as [cγ µ (1 − γ 5 )c][sγ µ (1 − γ 5 )b], where γ µ are Dirac matrices ( µ = 0,1,2,3), γ 5 = γ 0 γ 1 γ 2 γ 3 and c, c, s, b are quark spinor fields. The colorless current cγ µ (1 − γ 5 )c, which can create the J/ψ , can also create the P -wave state χ c1 . It cannot, however, create the χ c0 , χ c2 or h c states, so their appearance would have to be explained by a more complex hypothesis. A theoretical prediction can be obtained with the factorization hypothesis [1], assuming that the weak decay matrix element can be described as a product of two independent hadronic currents. Under the factorization hypothesis, B → ccK ( * ) decays are allowed when the cc pair hadronizes to J/ψ , ψ(2S) or χ c1 , but suppressed when the cc pair hadronizes to χ c0 [2]. In lowest-order Heavy Quark Effective Theory, the decay rate to the scalar χ c0 is zero due to charge conjugation invariance [3].
The decay B + → χ c0 K + has been observed by Belle and BABAR with an average branching fraction (B) of (1.40 +0.23 −0.19 ) × 10 −4 [4], using χ c0 decays to K + K − or π + π − . This result is of the same order of magnitude as the branching fraction of the decay B + → χ c1 K + , (4.9±0.5)×10 −4 [4], and is surprisingly large given the expectation from factorization. Using the hadronic χ c0 decays, Belle has obtained an upper limit on B 0 → χ c0 K 0 of 1.1 × 10 −4 at 90% confidence level [5]. No predictions are available for B decays to χ c0 K * , so the branching fraction measurement of B → χ c0 K * should improve our understanding of the limitations of factorization and of models that do not rely on factorization.
The data on which this analysis is based were collected with the BABAR detector [8] at the PEP-II asymmetricenergy e + e − storage ring. The BABAR detector consists of a double-sided five-layer silicon tracker, a 40-layer drift chamber, a Cherenkov detector, an electromagnetic calorimeter, and a magnet with instrumented flux return (IFR) consisting of layers of iron interspersed with resistive plate chambers and limited streamer tubes. The data sample has an integrated luminosity of 413 fb −1 collected at the Υ (4S) resonance, which corresponds to (454 ± 5) × 10 6 BB pairs. It is assumed that the Υ (4S) decays equally to neutral and charged B meson pairs. In addition, 41 fb −1 of data collected 40 MeV below the Υ (4S) resonance (off-resonance data) are used for background studies.
Candidate B mesons are reconstructed from five tracks for charged B decays and four tracks for neutral B decays, where three and four tracks, respectively, are consistent with originating from a common decay point within the PEP-II luminous region. Each of the tracks is required to have a transverse momentum greater than 50 MeV/c and an absolute momentum less than 10 GeV/c. The tracks are identified as either pion or kaon candidates, with protons vetoed, using Cherenkov-angle information and ionization energy-loss rate (dE/dx) measurements. The efficiency for kaon selection is approximately 80%, including geometric acceptance, while the probability of misidentification of pions as kaons is below 5% up to a laboratory momentum of 4 GeV/c. Muons are rejected using information predominantly from the IFR. Furthermore, the tracks are required to fail an electron selection based on their ratio of energy deposited in the calorimeter to momentum measured in the drift chamber, shower shape in the calorimeter, dE/dx, and Cherenkov-angle information. Candidate K 0 S mesons are reconstructed from π + π − candidates, and are required to have a reconstructed mass within 15 MeV/c 2 of the nominal K 0 mass [4], a decay vertex separated from the B + decay vertex with a significance of at least five standard deviations, a flight distance in the transverse direction of at least 0.3 cm and a cosine of the angle between the line joining the B and K 0 S decay vertices and the K 0 S momentum greater than 0.999. Four kinematic variables and one event-shape variable are used to characterize signal events. The first kinematic variable, ∆E, is the difference between the center-of-mass (c.m.) energy of the B candidate and √ s/2, where √ s is the total c.m. energy. The second is the beam-energysubstituted mass m ES = (s/2 + p i · p B ) 2 /E 2 i − p 2 B , where p B is the reconstructed momentum of the B candidate, and the four-momentum of its parent Υ (4S) in the laboratory frame, (E i , p i ), is determined from nominal colliding beam parameters. The third kinematic variable is the Kπ invariant mass, m K * , used to identify K * candidates, where Kπ is K 0 S π + or K + π − for K * + or K * 0 candidates, respectively. The fourth kinematic variable is the h + h − invariant mass, m hh , used to iden-tify χ c0 candidates. Candidate B mesons are required to satisfy |∆E| < 0.1 GeV, 5.25 < m ES < 5.29 GeV/c 2 , 0.772(0.776) < m K * < 0.992(0.996) GeV/c 2 for B + (B 0 ) candidates and 3.35 < m hh < 3.50 GeV/c 2 . The eventshape variable is a Fisher discriminant F [9], constructed as a linear combination of the absolute value of the cosine of the angle between the B candidate momentum and the beam axis, the absolute value of the cosine of the angle between the thrust axis of the decay products of the B candidate and the beam axis, and the zeroth and second angular moments of energy flow about the thrust axis of the reconstructed B.
Continuum quark production (e + e − → qq, where q = u,d,s,c) is the dominant source of background. It is suppressed using another event-shape variable, | cos θ T |, which is the absolute value of the cosine of the angle θ T between the thrust axis [10] of the selected B candidate and the thrust axis of the rest of the event. For continuum background, the distribution of | cos θ T | is strongly peaked towards 1 whereas the distribution is essentially flat for signal events. Therefore, the relative amount of continuum background is reduced by requiring | cos θ T | < 0.9.
Backgrounds from other B meson decays are studied with Monte Carlo (MC) events, using at least 10 3 times the number of events expected in data for specific decay modes that are the possible sources of background for this analysis.
Potential charm contributions from B → D(→ K * h − )h + events are removed by vetoing events with a reconstructed K * h − invariant mass in the range 1.83 < m K * h < 1.91 GeV/c 2 . To remove background from D 0 mesons, a veto is applied to any Kπ pair with an invariant mass in the range 1.83 < m Kπ < 1.91 GeV/c 2 for each B → χ c0 (→ h + h − )K * decay. Studies of MC events show that the largest remaining charmed backgrounds are B + → D 0 (→ K 0 S π + π − )π + and B 0 → D − (→ K + π − π − )π + , with 12% and 10% passing the veto, respectively. Surviving charmed events have a reconstructed D mass outside the veto range as a result of using a π or K candidate that is incorrectly selected from the other B decay in the event.
A fraction of signal events has more than one B candidate reconstructed. For those events, the candidate with the highest χ 2 probability of the fitted B decay vertex is selected. Studies of MC events show that less than 11% of events are reconstructed from the wrong candidate, where these incorrectly reconstructed events are modeled in the fit to data.
After applying all selection criteria, there are five main categories of background from B decays: two-and threebody decays proceeding via a D meson; non-resonant B → K * h + h − and B → Kπχ c0 ; combinatorial background from three unrelated particles (K * h + h − ); two-or four-body B decays with an extra or missing particle and three-body decays with one or more particles misidenti-fied. Along with selection efficiencies obtained from MC simulation, existing branching fractions for these modes [4,11] are used to estimate their background contributions that are included separately and fixed in fits to data. For the non-resonant backgrounds, where there is no branching fraction information, fits to sideband data (0.996 < m K * < 1.53 GeV/c 2 and 3.2 < m hh < 3.35 GeV/c 2 ) are performed to estimate the background contributions.
In order to extract the signal event yield for the channel under study, an unbinned extended maximum likelihood fit is used. The likelihood function for N events is where M = 3 is the number of hypotheses (signal, continuum background, and B background), n i is the number of events for each hypothesis determined by maximizing the likelihood function, and P i ( α, x j ) is a probability density function (PDF) with the parameters α and variables x = (m ES , ∆E, F , m K * and m hh ). The PDF is a product . Studies of MC simulation show that correlations between these variables are small for the signal and continuum background hypotheses. However, for B background, correlations of a few percent are observed between m ES and ∆E, which are taken into account by forming a 2-dimensional PDF for these variables. The parameters for signal and B background PDFs are determined from MC simulation. All continuum background parameters are allowed to vary in the fit, in order to help reduce systematic effects from this dominant event type. Sideband data, defined to be in the region 0.1 < ∆E < 0.3 GeV and 5.25 < m ES < 5.29 GeV/c 2 , as well as off-resonance data, are used to model the continuum background PDFs. For the m ES PDFs, a Gaussian distribution is used for signal and a threshold function [12] for continuum background. For the ∆E PDFs, a sum of two Gaussian distributions with distinct means and widths is used for the signal and a first-order polynomial for the continuum background. A two-dimensional (m ES , ∆E ) histogram is used for B background. The signal, continuum and B background F PDFs are described using a sum of two Gaussian distributions with distinct means and widths. For m K * PDFs, a sum of a relativistic Breit-Wigner function [4] and a first-order polynomial describes each of the signal, continuum, and B background distributions. Within the m K * fit range, there is also the possibility of B background contributions from non-resonant and higher K * resonances; these contributions are modeled in the fit using the LASS parameterization [13,14]. The contribution from this background is estimated by extrapolating a Kπ invariant mass projec-tion fitted in a higher-mass region (0.996 < m K * < 1.53 GeV/c 2 ) into the signal region. This estimated background is modeled in the final fit to the signal region and assumes there are no interference effects between the Kπ background and the K * (892) signal. Finally, for m hh PDFs, a sum of a relativistic Breit-Wigner function and a first-order polynomial is used to describe signal and a first-order polynomial to describe the continuum and B background distributions. The non-resonant h + h − background is modeled by a first-order polynomial, and the background is estimated by extrapolating the invariant mass projection fitted in the lower mass region (3.2 < m hh < 3.35 GeV/c 2 ) into the signal region. The signal first-order polynomial component of the m K * and m hh PDFs is used to model misreconstructed events; for example where a K + from the K * 0 is reconstructed as a χ c0 daughter particle, and vice versa.
We observe the decay B 0 → χ c0 K * 0 with an 8.9 standard deviation significance and measure the branching fraction B(B 0 → χ c0 K * 0 ) = (1.7 ± 0.3 ± 0.2) × 10 −4 . We find evidence for B + → χ c0 K * + with a 3.6 standard deviation significance and set a 90% confidence level upper limit on the branching fraction of 2.1 × 10 −4 . Figure 1 shows the fitted m ES and m hh projections for the B + → χ c0 K * + (χ c0 → K + K − ), B + → χ c0 K * + (χ c0 → π + π − ), B 0 → χ c0 K * 0 (χ c0 → K + K − ) and B 0 → χ c0 K * 0 (χ c0 → π + π − ) candidates, while the fitted signal yields, measured branching fractions and upper limits are shown in Table I. The candidates in Fig. 1 are signal-enhanced, with a requirement on the probability ratio P sig /(P sig + P bkg ), optimized to enhance the visibility of potential signal, where P sig and P bkg are the signal and the total background probabilities, respectively (computed without using the variable plotted). Figure 2 shows the −2 ln L distributions for both B + → χ c0 K * + and B 0 → χ c0 K * 0 as a function of branching fraction. The −2 ln L distributions for the final states (χ c0 → K + K − and χ c0 → π + π − ) are combined to give final branching fractions shown in Table I. The 90% confidence level branching fraction upper limit (B UL ) is determined by integrating the likelihood dis-tribution (with systematic uncertainties included) as a function of the branching fraction from 0 to B UL , so that BUL 0 LdB = 0.9 ∞ 0 LdB. The signal significance S, in units of standard deviation, is defined as √ 2∆ ln L, where ∆ ln L represents the change in log-likelihood (with systematic uncertainties included) between the maximum value and the value when the signal yield is set to zero. The points indicate the data. The plot shows projections for B + → χc0K * + (χc0 → K + K − ) (a) and (b), for B + → χc0K * + (χc0 → π + π − ) (c) and (d), for B 0 → χc0K * 0 (χc0 → K + K − ) (e) and (f), and B 0 → χc0K * 0 (χc0 → π + π − ) (g) and (f).
Contributions to the branching fraction systematic uncertainty are shown in Table II. The presence of a nonresonant K + K − and π + π − can give rise to interference effects, resulting in a departure from the m hh PDF used in the fit to data. In order to estimate how much this can affect the extracted yields, the fit is repeated with the inclusion of a PDF describing the interference between the Breit-Wigner and non-resonant amplitudes in the m hh distribution. This shape consists of the squared modulus of the sum of a Breit-Wigner and a constant amplitude, carrying an arbitrary phase difference. The relative weight of these two components and their phase difference are allowed to vary to obtain the best fit. The signal yields derived from this fit are larger than the nominal fit in Table I and the difference from the nominal fit is used as an estimate of the systematic error in Table II due to neglecting interference effects. Interference I: Total number of events in the fit, B background yields (B bkg), signal yields, efficiencies, and branching fractions B, measured using B → χc0K * events. Fit bias corrections are applied to the signal yields and branching fractions. The first error is statistical and the second error is systematic. The significance S is shown for B + → χc0K * + and B 0 → χc0K * 0 and the branching fraction upper limit, BUL, at the 90% confidence level is shown for B + → χc0K * + .

Mode
Total effects between the K * (892) and spin-0 final states (nonresonant and K * 0 (1430)) integrate to zero if the acceptance of the detector and analysis is uniform; the same is true of the interference between the K * (892) and spin-2 final states (K * 2 (1430)). Studies of MC events show the efficiency variations are small enough to consider these interference effects insignificant. The integrated interference between K * (892) and other spin-1 amplitudes such as K * (1410) is in principle non-zero, but in practice is negligible due to the small branching fraction of Error K * (1410) → K + π − (6.6 ± 1.3% [4]) and the fact that the Kπ mass lineshapes have little overlap. Errors due to tracking efficiency, K 0 S reconstruction efficiency and particle identification are assigned by comparing control channels in MC simulation and data. The branching fraction error of χ c0 → h + h − is taken from the combination of previous measurements [4]. The number of BB events is determined with an uncertainty of 1.1%. To estimate errors due to the fit procedure, 500 MC samples containing the numbers of signal and continuum events measured in data and the estimated number of exclusive B background events are used. The differences between the generated and fitted values are used to estimate small fit biases (see Table II) that are a consequence of correlations between fit variables. These biases are applied as corrections to obtain the final signal yields, and half of the correction is added as a systematic uncertainty. The uncertainty of the B background contribution to the fit is estimated by varying the known branching fractions within their errors. Each background is varied individually and the effect on the fitted signal yield is added in quadrature as a contribution to the uncertainty. The uncertainty due to PDF modeling is estimated by varying the PDFs by the parameter errors. In order to take correlations between parameters into account, the full correlation matrix is used when varying the parameters. All PDF parameters that are originally fixed in the fit are then varied in turn, and each difference from the nominal fit is combined in quadrature and taken as a systematic contribution.
In summary, we have observed the decay B 0 → χ c0 K * 0 with an 8.9 standard deviation significance and find evidence for B + → χ c0 K * + with a 3.6 standard deviation significance, placing an upper limit on the branching fraction. The B 0 → χ c0 K * 0 branching fraction does not agree with the zero value expected from the color-singlet current-current contribution alone, and is approximately half the B 0 → χ c1 K * 0 branching fraction ((3.2 ± 0.6) × 10 −4 [4]), which is surprising when taking into account factorization expectations.
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. * Deceased † Now at Temple University, Philadelphia, Pennsylvania 19122, USA ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy ¶ Also with Università di Roma La Sapienza, I-00185 Roma, Italy * * Now at University of South Alabama, Mobile, Alabama 36688, USA † † Also with Università di Sassari, Sassari, Italy