Search for Factorization-Suppressed B ->chi_c K(*) Decays

We search for the factorization-suppressed decays B ->chi_c0 K(*) and B ->chi_c2 K(*), with chi_c0 and chi_c2 decaying into J/psi gamma using a sample of 124 10^6 BBbar events collected with the BABAR detector at the PEP-II storage ring of the Stanford Linear Accelerator Center.

We search for the factorization-suppressed decays B → χc0K ( * ) and B → χc2K ( * ) , with χc0 and χc2 decaying into J/ψ γ, using a sample of 124 × 10 6 BB events collected with the BABAR detector at the PEP-II storage ring of the Stanford Linear Accelerator Center. We find no significant signal and set upper bounds for the branching fractions. PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er Nonleptonic decays of heavy mesons are not easily described because the process involves quarks whose hadronization is not yet well understood. The factorization hypothesis allows one to make some predictions [1] by assuming that a weak decay matrix element can be described as the 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 or χ c2 [2]. Here, K ( * ) represents either K or K * . In lowest-order Heavy Quark Effective Theory, there is no J ≥ 2 current to create the tensor χ c2 from the vacuum. The decay rate to the scalar χ c0 is zero due to charge conjugation invariance [3].
Belle has recently observed B + → χ c0 K + decays with a branching fraction (BF) of (6.0 +2.1 −1.8 ± 1.1) × 10 −4 [4] using χ c0 decays to π + π − or K + K − . BABAR has confirmed the observation using the same decays with a branching fraction of (2.7 ± 0.7) × 10 −4 [5], somewhat lower than, but compatible with, the Belle measurement. These results are of the same order of magnitude as the BF of the decay B + → χ c1 K + and are surprisingly large given the expectation from factorization. Using the hadronic χ c0 decays, CLEO has obtained an upper limit on B 0 → χ c0 K 0 of 5.0 × 10 −4 [6]. Non-factorizable contributions to B + → χ c0 K + decays due to rescattering of intermediate charm states have been considered theoretically [7], and similar branching fractions are predicted for decays to χ c0 and χ c2 . No predictions are available for B decays to χ c(0,2) K * , but the branching fraction of decays to K * may be expected to be similar to the branching fraction of decays to K. The measurement of B → χ c(0,2) K ( * ) should improve our understanding of the limitations of factorization and of models that violate factorization.
In this Letter we report a search for the decays B → χ cJ K ( * ) , J = 0, 2, using the radiative decays χ cJ → J/ψ γ, with branching fractions of (1.18 ± 0.14)%, (20.2±1.7)%, respectively [8]. Since the radiative branching fraction for the χ c0 decay (including subsequent J/ψ decay to ℓ + ℓ − ) is much smaller than the corresponding π + π − or K + K − branching fractions, the search for the B + → χ c0 K + decay is less sensitive than previous searches, but it is free from the interference with the non-resonant decays to three mesons that affect the latter. The data used in this analysis were obtained with the BABAR detector at the PEP-II storage ring, comprising an integrated luminosity of 112 fb −1 of data taken at the Υ (4S) resonance. The BABAR detector is described elsewhere [9]. Surrounding the interaction point, a five-layer double-sided silicon vertex tracker (SVT) provides precise reconstruction of track angles and B-decay vertices. A 40-layer drift chamber (DCH) provides measurements of the transverse momenta of charged particles. An internally reflecting ring-imaging Cherenkov detector (DIRC) is used for particle identification (PID). A CsI(Tl) crystal electromagnetic calorimeter (EMC) detects photons and electrons. The calorimeter is surrounded by a solenoidal magnet providing a 1.5-T field. The flux return is instrumented with resistive plate chambers used for muon and neutralhadron identification.
Candidate J/ψ mesons are reconstructed from a pair of oppositely charged lepton candidates that form a good vertex. Muon (electron) candidates are identified with a neural-network (cut-based) selector and loose selection criteria. Electromagnetic depositions in the calorimeter in the polar-angle range 0.410 < θ lab < 2.409 rad that are not associated with charged tracks, have an energy larger than 30 MeV, and a shower shape consistent with a photon are taken as photon candidates. For J/ψ → e + e − decays, electron candidates are combined with nearby photon candidates in order to recover some of the energy lost through bremsstrahlung. The lepton-pair invariant mass must be in the range [2.95, 3.18] GeV/c 2 for both lepton flavors. The small remaining background is mainly due to J/ψ mesons not originating from χ c decays.
We form K 0 S candidates from oppositely-charged tracks originating from a common vertex with invariant mass in the range [487,510] MeV/c 2 . The K 0 S flight length must be greater than 1 mm, and its direction in the plane perpendicular to the beam line must be within 0.2 rad of the K 0 S momentum vector. Charged kaon candidates are identified with a likelihood selector, based on information from the DIRC, and dE/dx in the SVT and in the DCH.
A π 0 candidate is formed from a pair of photon candidates with invariant mass in the interval [117,152] MeV/c 2 and momentum greater than 350 MeV/c. K * candidates are formed from Kπ combinations with an invariant mass in the range [0.85, 0.94] GeV/c 2 .
The J/ψ , K 0 S , and π 0 candidates are constrained to their corresponding nominal masses [8] to improve the resolution of the measurement of the four-momentum of their parent B-candidate. The χ c candidates are formed from J/ψ and photon candidates. The photon is required to have an energy greater than 0.15 GeV and not to be part of π 0 candidates in the mass range [0.125, 0.140] GeV/c 2 .
Candidate B mesons are formed from χ c and K ( * ) candidates. Two kinematic variables are used to further remove incorrectly reconstructed B candidates. The first is the difference ∆E ≡ E * B − E * beam between the B-candidate energy and the beam energy in the Υ (4S) rest frame. In the absence of experimental effects, reconstructed signal candidates have ∆E = 0. The typical ∆E resolution is 20 MeV for channels with only charged tracks in the final state, and 25 MeV, with a low ∆E tail due to energy leakage in the calorimeter, for channels with a π 0 . The second variable is the beam-energy- The energy substituted mass m ES should peak at the B meson mass, 5.279 GeV/c 2 . Typical resolution for ∆E is 2.7 MeV/c 2 . For the signal region, ∆E is required to be in the range [−35, +20] MeV for channels involving a π 0 , and within ±20 MeV otherwise. We require m ES to be in the range [5.274, 5.284] GeV/c 2 . If more than one B candidate is found in an event, the one having the smallest |∆E| is retained.
The observation of χ c2 could be complicated by the presence of the prominent χ c1 peak. This is mitigated by measuring the spectrum in the variable m ℓ + ℓ − γ − m ℓ + ℓ − . The efficiencies obtained from fits to the mass difference distribution for exclusive MC samples, where one B decays to the final state under consideration and the other inclusively, are given in Table I. The χ c2 meson has a natural width of just 2 MeV [8] and is therefore fitted with a Gaussian to account for detector resolution. Since the χ c0 has a natural width of 10 MeV [8], comparable to the mass resolution (σ ≈ 10 MeV/c 2 ), we fit the χ c0 peak with the convolution of Breit-Wigner and Gaussian shapes.
The branching fractions are computed from BF = N S /(N B ǫf ), where N S is the number of signal events obtained from fitting the m ℓ + ℓ − γ − m ℓ + ℓ − distribution (Table II), N B is the number of produced BB events, ǫ is the selection efficiency (Table I) and f is the product of secondary branching fractions of the B daughters. The free parameters in the fits are the size of a constant background, the overall scale of m ℓ + ℓ − γ − m ℓ + ℓ − , and the amplitudes of the resonant peaks. The fixed parameters are the χ c0 natural width, the χ c0 -χ c1 and χ c2 -χ c1 mass differences (−95.4 and +45.7 MeV/c 2 , respectively) all taken from Ref. [8], and the mass resolution. The mass resolution, 10.2 ± 0.4 MeV/c 2 , is measured with χ c1 data and is assumed to be the same for the three χ c states. Performing such fits to an inclusive Υ (4S) → BB MC sample, we verify that the NR events are subtracted correctly, and that the proximity of the χ c1 does not induce any significant bias on the measurement of the nearby χ c2 .
Based on studies of B → J/ψ K * decays [10], the NR Kπ component appears to be in an S-wave state, with an unknown relative phase φ with respect to the main K * (892) P -wave peak. As no signal is found, the systematic uncertainty due to the unknown relative phase  is estimated here with a MC-based method. The K − π invariant mass is fitted with an amplitude that is the sum of a non-relativistic Breit-Wigner and an amplitude with a constant phase and the square of which has a quadratic dependence on m Kπ .
where a and b are real quantities and m K * = 892 MeV/c 2 . The slow variation of the phase of the S wave with m Kπ is neglected here. The free parameters in the fit are the three degrees of freedom of the quadratic dependence of b, the magnitude of the signal, and the relative phase φ. As the sideband is dominated by the NR contribution, no attempt is made to subtract the few combinatorial events. The fact that the phase φ is unknown is dealt with by randomly generating samples of events distributed as above for each value of φ, and applying NR subtraction. The number of events N (φ) thus measured is normalized to that obtained with the phase value φ 0 obtained in the fit. The ratio R = N (φ)/N (φ 0 ) shows a sinusoidal dependance. The average value is 1.44 with a deviation of ±35%, giving an RMS relative uncertainty of ±20%, which we will assume as systematic uncertainty (due to the interference with the NR component).
In the case of decays to the tensor χ c2 , the efficiency depends on the intensity fractions to each of three polarization states. The efficiency is mainly sensitive to the value of the K * helicity angle θ K * , because small values of θ K * occur for low momentum pions. The se-lection efficiency therefore depends, to first order, on the polarization of the K * population, through the angular distribution: where A 0 is the fraction of longitudinal K * polarization. The average efficiency is The values of a and b are shown in Table III. When no signal is observed, as is the case here, the polarization is unknown. We assume an unpolarized decay and we estimate the efficiency as (a + 0.5b) ± (|b|/ √ 12). The branching fraction measurements reported here are b Efficiency K * 0 (K + π − ) 8.68 -1.40 7.98± 0.40 K * 0 (K 0 S π 0 ) 4.25 -1.66 3.43± 0.48 K * + (K + π 0 ) 5.05 -1.79 4.16± 0.52 K * + (K 0 S π + ) 7.83 -1.84 6.92± 0.53 affected by the systematic uncertainties described in what follows. The relative uncertainty on the number of BB events is 1.1%. The secondary branching fractions and their uncertainty are taken from Ref. [8]. Other estimated uncertainties are: tracking efficiency, 1.3% per track added linearly; K 0 S reconstruction, 2.5%; selection of the γ from the χ c decays, 2.5%; π 0 selection, 5.0%; PID efficiency, 3.0%. For each mass peak and for ∆E, the uncertainty of the central value and of the width of the peaks are measured with the χ c1 channels. These quantities are used to estimate the efficiency uncertainty from this source. The ratio of B 0 to B + production in Υ (4S) decays is assumed to be unity. The related uncertainty is small [11] and is neglected here. A summary of the multiplicative contributions to the systematics can be found in Table IV. In addition to these multiplicative contributions there is a small contribution from the uncertainty on r for the NR background subtraction.
Combining the measurements of the K * sub-modes, and with the approximation that the multiplicative efficiencies for each K * sub-mode are fully correlated, we obtain the branching fractions for the factorizationsuppressed modes listed in Table V. As a cross check, the results for the allowed χ c1 are found to be compatible with those of a recent analysis [12] optimized for that IV: Summary of the multiplicative systematic uncertainties in percent. The first eight rows are in common to decays to χc0 and χc2. decay. We obtain upper bounds on the BFs at 90% confidence level (C.L.) assuming Gaussian statistics for the statistical uncertainties and taking into account the systematic uncertainties. We have used a Bayesian method with uniform prior for positive BF values in the derivation of these limits. The upper limits obtained for decays to χ c0 are larger than for χ c2 due to the smaller χ c0 radiative BF. For B + → χ c0 K + they are compatible with the previous measurements [4,5]. B → χ c(0,2) K ( * ) production requires non-factorizable contributions. B + → χ c0 K + decays have been previously observed. Colangelo et al. [7] explain this with rescattering effects and predict a similar rate for B → χ c2 K. This is not observed. The upper limits obtained for decays to χ c2 are approximately one order of magnitude lower than the branching fractions of the observed B + → χ c0 K + decays. Furthermore, we find no evidence for the decays B → χ c(0,2) K * . χc2 χc0 K * 0 0.36 (0.14 ± 0.11 ± 0.14) 7.7 (3.8 ± 2.6 ± 1.5) K * + 0.12 (-0.15 ± 0.05 ± 0.14) 28.6 (13.5 ± 9.6 ± 5.3) K + 0.30 (0.09 ± 0.10 ± 0.11) 8.9 (4.4 ± 3.3 ± 0.7) K 0 0.41 (0.21 ± 0.11 ± 0.13) 12.4 (5.3 ± 5.0 ± 0.8) 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 CONACyT (Mexico), A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation.