Observation of B-meson decays to b_1 pi and b_1 K

We present the results of searches for decays of B mesons to final states with a b_1 meson and a charged pion or kaon. The data, collected with the BaBar detector at the Stanford Linear Accelerator Center, represent 382 million B-Bbar pairs produced in e+e- annihilation. The results for the branching fractions are, in units of 10^{-6}, B(B+ ->b1^0 pi+) = 6.7 +/- 1.7 +/- 1.0 (4.0 sigma), B(B+ ->b1^0 K+ = 9.1+/- 1.7+/- 1.0 (5.3 sigma), B(B0 ->b1^-/+ pi^+/-) = 10.9 +/- 1.2 +/- 0.9 (8.9 sigma), and B(B0 ->b1^-K+) = 7.4 +/- 1.0 +/- 1.0 (6.1 sigma), with the assumption that B(b_1 ->omega pi)=1. We also measure charge and flavor asymmetries Ach(B+ ->b1^0 pi+) = 0.05 +/- 0.16 +/- 0.02, Ach(B+ ->b1^0 K+ = -0.46 +/- 0.20 +/- 0.02, Ach(B0 ->b1^-/+ pi^+/-) = -0.05 +/- 0.10 +/- 0.02, C(B0 ->b1^-/+ pi^+/-) = -0.22 +/- 0.23 +/- 0.05, deltaC(B0 ->b1^-/+ pi^+/-) = -1.04 +/- 0.23 +/- 0.08, and Ach(B0 ->b1^-K+) = -0.07 +/- 0.12 +/- 0.02, The first error quoted is statistical, the second systematic, and for the branching fractions, the significance is given in parentheses.

The mass and width of the b 1 are 1229.5±3.2 MeV and 142 ± 9 MeV, respectively, and the dominant decay is to ωπ [3]. In the quark model the b 1 is the I G = 1 + member of the J P C = 1 +− , 1 P 1 nonet, whereas the a 1 is the I G = 1 − state in the J P C = 1 ++ , 3 P 1 nonet. The available theoretical estimates of the branching fractions of B mesons to b 1 π and b 1 K come from calculations based on naive factorization [4,5], and on QCD factorization [6]. The latter incorporate light-cone distribution amplitudes evaluated from QCD sum rules. Expected branching fractions lie in the range 5-10×10 −6 [6]; estimates as large as 26×10 −6 are found in the calculations of [4], and 40×10 −6 in those of [5].
The four modes B + → b 0 1 π + , B + → b 0 1 K + , B 0 → b − 1 π + , and B 0 → b − 1 K + can be mediated by external tree amplitudes in which the weak current produces the pion (kaon) with a Cabibbo-favored (suppressed) coupling. Alternatively, a "penguin" loop amplitude is favored for the kaon modes, and suppressed for the pion modes. The fifth mode, B 0 → b + 1 π − , requires a coupling of the current to the b + 1 , which is forbidden for this G = +1 state [7], leading to the expectation B( . Direct CP violation would be indicated by a non-zero value of the asymmetry A ch ≡ (Γ − − Γ + )/(Γ − + Γ + ) in the rates Γ ± (B ± → F ± ) for decay of a charged B meson, or Γ + (B 0 → b − 1 K + ) and its charge conjugate. For the decays B 0 → b ∓ 1 π ± we define A ch and two additional asymmetries C and ∆C through where the signal B meson flavor f = +1 for B 0 , −1 for B 0 , and q is the sign of charge of the b 1 . To measure C and ∆C we use the flavor η (+1 for B 0 and −1 for B 0 ) of the second meson B tag produced in Υ (4S) decay [8].
The yields are given by where Y S is the total signal yield, χ d = 0.188 ± 0.003 the time-integrated mixing probability [3], w the mistag fraction, and ∆w and µ the B − B differences in the mistag rate and tagging efficiency, respectively. The data were collected with the BABAR detector [9] at the PEP-II asymmetric e + e − collider located at the Stanford Linear Accelerator Center. Charged particles from the e + e − interactions are detected, and their momenta measured, by a combination of five layers of double-sided silicon microstrip detectors and a 40-layer drift chamber, both operating in the 1.5 T magnetic field of a superconducting solenoid. Photons and electrons are identified with a CsI(Tl) electromagnetic calorimeter (EMC). Further charged particle identification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring imaging Cherenkov detector (DIRC) covering the central region. A detailed Monte Carlo program (MC) is used to simulate the B production and decay sequences, and the detector response [10].
The b 1 candidates are reconstructed through the decay sequence b 1 → ωπ, ω → π + π − π 0 , and π 0 → γγ. The invariant mass of the photon pair is required to lie between 120 and 150 MeV, i.e., within about two standard deviations of the nominal mass [3]. For the b 1 and ω whose masses are observables in the maximum likelihood (ML) fit described below, we accept a range that includes wider sidebands (see Fig. 1). Secondary charged pions in b 1 and ω candidates are rejected if classified as protons, kaons, or electrons by their DIRC, dE/dx, and EMC PID signatures. For the primary pion (kaon) from the B-meson decay we define the PID variable S π (S K ) as the number of standard deviations between the measured DIRC Cherenkov angle and that expected for a pion (kaon), requiring −2 < S π < 5 (−5 < S K < 2).
We reconstruct the B-meson candidate by combining the 4-momenta of a pair of daughter mesons, using a fit that constrains all particles to a common vertex and the π 0 mass to its nominal value. From the kinematics of Υ (4S) decay we determine the energy-substituted is the B-meson 4-momentum vector, and all values are expressed in the Υ (4S) rest frame. The resolution in m ES is 2.4 − 2.7 MeV and in ∆E is 25-32 MeV, depending on the decay mode. We require 5.25 GeV < m ES < 5.29 GeV and −0.13 GeV < ∆E < ∆E max , with ∆E max = 0.1 (0.13) GeV for b 0 1 (b + 1 ), where the tighter restriction serves to limit the number of combinatorial candidates per event.
We also impose restrictions on resonance decay angles to exclude the most asymmetric decays where softparticle backgrounds accumulate and the acceptance changes rapidly. We require cos θ b1 ≤ 1.1 − 0.5| cos θ ω |, where θ b1 is the angle between the momenta of the pion from b 1 → ωπ and its parent B meson, measured in the b 1 rest frame, and θ ω is the angle between the normal to the ω → 3π decay plane and the momentum of its parent b 1 , measured in the ω rest frame. Backgrounds arise primarily from random combinations of particles in continuum e + e − → qq events (q = u, d, s, c). We reduce these with a requirement on the angle θ T between the thrust axis of the B candidate in the Υ (4S) frame and that of the rest of the charged tracks and neutral calorimeter clusters in the event. The distribution is sharply peaked near | cos θ T | = 1 for qq jet pairs, and nearly uniform for Bmeson decays. The requirement, which optimizes the expected signal yield relative to its background-dominated statistical error, is | cos θ T | < 0.7. The average number of candidates found per selected event is in the range 1.3 to 1.4 (1.4 to 1.6 in signal MC), depending on the final state. We choose the candidate with ωπ invariant mass closest to the nominal value of the b 1 mass [3]. In the ML fit we discriminate further against qq background with a Fisher discriminant F that combines several variables which characterize the energy flow in the event [11]. It provides about one standard deviation of separation between B decay events and qq background.
We obtain yields for each channel from an extended ML fit with the input observables ∆E, m ES , F , and the resonance masses m b1 and m ω . The selected data sample sizes are given in Table I. Besides the signal events these samples contain qq (dominant) and BB with b → c combinatorial background, and a fraction of cross feed from other charmless BB modes, which we estimate from the simulation to be (0.5-0.8)%. The last include nonresonant ωπ(π, K), and modes that have final states different from the signal, but with similar kinematics so that broad peaks near those of the signal appear in some observables, requiring a separate component in the probability density function (PDF). The likelihood function is where N is the number of events in the sample, and for each component j (signal, combinatorial background, or charmless BB cross feed), Y j,qη is the yield of events (Eq. 2) and P j (x i ) the PDF for observable x in event i. The signal component is further separated into two components (with proportions fixed in the fit for each mode) representing the correctly and incorrectly reconstructed candidates in events with true signal, as determined with MC. The factored form of the PDF indicated in Eq. 3 is a good approximation, particularly for the combinatorial qq component, since we find correlations among observables in the data (which are mostly qq background) to be small. The effects of this approximation are determined in simulation and included in the bias corrections and systematic errors discussed below. We determine the PDFs for the signal and BB background components from fits to MC samples. We calibrate the resolutions in ∆E and m ES with large data control samples of B decays to charmed final states of similar topology (e.g. B → D(Kππ)π). We develop PDFs for the combinatorial background with fits to the data from which the signal region (5.27 GeV < m ES < 5.29 GeV and |∆E| < 0.1 GeV) has been excluded.
The functions P j are constructed as linear combinations of Gaussian and polynomial functions, or in the case of m ES for qq background the threshold function s and parameter ξ. These functions are discussed in more detail in [11], and are illustrated in Fig. 1.
We allow the parameters most important for the determination of the combinatorial background PDFs to vary in the fit, along with the yields for all components, and the signal and qq background asymmetries. Specifically, the free background parameters are: ξ for m ES , linear and quadratic coefficients for ∆E, and the mean, width, and width difference and polynomial fraction parameters for F .
We validate the fitting procedure by applying it to ensembles of simulated experiments with the qq component drawn from the PDF, into which we have embedded the expected number of signal and BB background events randomly extracted from the fully simulated MC samples. Biases obtained by this procedure with inputs that reproduce the yields found in the data are reported, along with the signal yields, in Table I. In Fig. 1 we show the projections of the PDF and data for each fit. The data plotted are subsamples enriched in signal with a threshold requirement on the ratio of signal to total likelihood (computed without the plotted variable) that retains (29-53)% of the signal, depending on the mode.
We compute the branching fraction by subtracting the fit bias from the measured yield, and dividing the result by the efficiency times B(ω → π + π − π 0 ) = 89.1±0.7% [3], and by the number of produced BB pairs. We assume Γ(Υ (4S) → B + B − )/Γ(Υ (4S) → B 0 B 0 ) = 1, consistent with measurements [3]. The results are given in Table I,     along with the significance, computed as the square root of the difference between the value of −2 ln L (with additive systematic uncertainties included) for zero signal and the value at its minimum.
Systematic uncertainties on the branching fractions arise from the PDFs, BB backgrounds, fit bias, and efficiency. PDF uncertainties not already accounted for by free parameters in the fit are estimated from the consistency of fits to MC and data in control modes. Varying the signal-PDF parameters within these errors, we estimate yield uncertainties of (2.4-3.3)%, depending on the mode. The uncertainty from fit bias (Table I) includes its statistical uncertainty from the simulated experiments, and half of the correction itself, added in quadrature. For the BB backgrounds we vary the fixed fit component by 100% and include in quadrature a term derived from MC studies of the inclusion of a b → c component with the dominant qq background. Uncertainties in our knowledge of the efficiency include 0.5% × N t and 1.5% × N γ , where N t and N γ are the numbers of tracks and photons, respectively, in the B candidate. The uncertainties in the efficiency from the event selection are below 0.5%.
We study asymmetries from the track reconstruction (found negligible), and from imperfect modeling of the interactions with material in the detector, by measuring the asymmetries in the qq background in the data and control samples mentioned previously, in comparison with MC [12]. We apply corrections, and assign systematic errors, to A ch equal to −0.010 ± 0.005 for modes with a primary kaon and 0.000 ± 0.005 for those with a primary pion. The leading systematic errors on C and ∆C come from the fit bias.
The first error quoted is statistical and the second systematic. The QCD factorization estimates [6] for the branching fractions and charge asymmetries agree with these measurements within experimental and theoretical errors. The authors of [6] note that the observation B(B + → b 0 1 K + )/B(B 0 → b − 1 K + ) > 0.5, if confirmed with higher precision, would indicate the presence of a weak annihilation contribution to these modes. The value of the CP -conserving ∆C near −1 for B 0 → b ∓ 1 π ± agrees with the expected suppression of B 0 → b + 1 π − ; our results imply the ratio Γ(B 0 → b + 1 π − )/Γ(B 0 → b ∓ 1 π ± ) = −0.01 ± 0.12. We find no evidence for direct CP violation in these decays.
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), MES (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (Euro-pean Union) and the A. P. Sloan Foundation.