Measurements of CP-Violating Asymmetries and Branching Fractions in B Decays to omegaK and omegapi

We present measurements of CP-violating asymmetries and branching fractions for the decays omegapi+, omegaK+, and omegaK0. The data sample corresponds to 232 million BBbar pairs produced by e+e- annihilation at the Upsilon(4S) resonance. For the decay omegaKs, we measure the time-dependent CP-violation parameters S=0.51+0.35-0.39+/-0.02, and C=-0.55+0.28-0.26+/-0.03. We also measure the branching fractions, in units of 10^-6, B(omegapi+)=6.1+/-0.7+/-0.4, B(omegaK+)=6.1+/-0.6+/-0.4, and B(omegaK0)=6.2+/-1.0+/-0.4, and charge asymmetries Ach(omegapi+)=-0.01+/-0.10+/-0.01 and Ach(omegaK+)=0.05+/-0.09+/-0.01.

PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er Measurements of time-dependent CP asymmetries in B 0 meson decays through a Cabibbo-Kobayashi-Maskawa (CKM) favored b → ccs amplitude [1,2] have firmly established that CP is not conserved in such decays. The effect, arising from the interference between mixing and decay involving the CP -violating phase β = arg (−V cd V * cb /V td V * tb ) of the CKM mixing matrix [3], manifests itself as an asymmetry in the time evolution of the B 0 B 0 pair.
Decays to the charmless final states φK 0 , K + K − K 0 , η ′ K 0 , π 0 K 0 , f 0 (980)K 0 , and ωK 0 are all b → qqs processes dominated by a single penguin (loop) amplitude having the same weak phase β [4]. CKM-suppressed amplitudes and multiple particles in the loop complicate the situation by introducing other weak phases whose contributions are not negligible; see Refs. [5,6] for early quantitative work in addressing the size of these effects. We define ∆S as the difference between the time-dependent CP -violating parameter S (given in detail below) measured in these decays and S = sin2β measured in charmonium K 0 decays. For the decay B 0 → ωK 0 , these additional contributions are expected to give ∆S ∼0.1 [7,8], although this increase may be nullified when finalstate interactions are included [8]. A value of ∆S inconsistent with this expectation could be an indication of new physics [9].
We present an improved measurement of the timedependent CP -violating asymmetry in the decay B 0 → ωK 0 , previously reported by the Belle Collaboration based on a sample of ∼30 events [10]. We also measure branching fractions for the decays B 0 → ωK 0 , B + → ωπ + , and B + → ωK + (charge-conjugate decay modes are implied throughout), and for B + → ωπ + , and B + → ωK + , we measure the time-integrated charge asymmetry A ch = (Γ − − Γ + )/(Γ − + Γ + ), where Γ ± is the width for these charged decay modes. In the Standard Model A ch is expected to be consistent with zero within our experimental uncertainty; a non-zero value would indicate direct CP violation in this channel.
The data were collected with the BABAR detector [11] at the PEP-II asymmetric e + e − collider. An integrated luminosity of 211 fb −1 , corresponding to 232 million BB pairs, was recorded at the Υ (4S) resonance (center-ofmass energy √ s = 10.58 GeV). Charged particles are detected and their momenta measured by the combination of a silicon vertex tracker (SVT), consisting of five layers of double-sided detectors, and a 40-layer central drift chamber, both operating in a 1.5 T axial magnetic field. Charged-particle identification (PID) is provided by the energy loss in the tracking devices and by the measured Cherenkov angle from an internally reflecting ringimaging Cherenkov detector (DIRC) covering the central region. A K/π separation of better than four standard deviations (σ) is achieved for momenta below 3 GeV/c, decreasing to 2.5σ at the highest momenta in the B decay final states. Photons and electrons are detected by a CsI(Tl) electromagnetic calorimeter.
From a B 0 B 0 pair produced in an Υ (4S) decay, we reconstruct one of the B mesons in the final state f = ωK 0 S , a CP eigenstate with eigenvalue −1. For the time evolution measurement, we also identify (tag) the flavor (B 0 or B 0 ) and reconstruct the decay vertex of the other B. The asymmetric beam configuration in the laboratory frame provides a boost of βγ = 0.56 to the Υ (4S), which allows the determination of the proper decay time difference ∆t ≡ t f − t tag from the vertex separation of the two B meson candidates. Ignoring the ∆t resolution (about 0.5 ps), the distribution of ∆t is The upper (lower) sign denotes a decay accompanied by a B 0 (B 0 ) tag, τ is the mean B 0 lifetime, ∆m d is the mixing frequency, and the mistag parameters w and ∆w are the average and difference, respectively, of the probabilities that a true B 0 (B 0 ) meson is tagged as a B 0 (B 0 ). The parameter C measures direct CP violation. If C = 0, then S = sin2β + ∆S. The flavor-tagging algorithm [1] has seven mutually exclusive tagging categories of differing purities (including one for untagged events that we retain for yield determinations). The measured analyzing power, defined as efficiency times (1 − 2w) 2 summed over all categories, is (30.5 ± 0.6)%, as determined from a large sample of Bdecays to fully reconstructed flavor eigenstates (B flav ).
We reconstruct a B meson candidate by combining a π + , K + or K 0 S with an ω → π + π − π 0 . We select K 0 S → π + π − decays by requiring the π + π − invariant mass to be within 12 MeV of the nominal K 0 mass and by requiring a flight length greater than three times its error. We require the primary charged track to have a minimum of six Cherenkov photons in the DIRC. We require the π + π − π 0 invariant mass (m 3π ) to be between 735 and 825 MeV. Distributions from the data and from Monte Carlo (MC) simulations [12] guide the choice of these selection criteria. We retain regions adequate to characterize the background as well as the signal for those quantities taken subsequently as observables for fitting. We also use in the fit the angle θ H , defined, in the ω rest frame, as the angle of the direction of the boost from the B rest frame with respect to the normal to the ω decay plane. The quantity H ≡ | cos θ H | is approximately flat for background and distributed as cos 2 θ H for signal.
A B meson candidate is characterized kinematically by the energy-substituted mass m ES ≡ are four-momenta of the Υ (4S) and the B candidate, respectively, and the asterisk denotes the Υ (4S) rest frame. We require, assuming the B + → ωπ + hypothesis, |∆E| ≤ 0.2 GeV and 5.25 ≤ m ES ≤ 5.29 GeV.
To reject the dominant background from continuum e + e − → qq events (q = u, d, s, c), we use the angle θ T between the thrust axis of the B candidate and that of the rest of the tracks and neutral clusters in the event, calculated in the Υ (4S) rest frame. The distribution of cos θ T is sharply peaked near ±1 for jet-like qq pairs and is nearly uniform for the isotropic B decays; we require | cos θ T | < 0.9 (0.8 for the charged B decays).
From MC simulations of B 0 B 0 and B + B − events, we find evidence for a small (0.5%) BB background contribution for the charged B decays, so we have added a BB component to the fit described below for those channels.
We use an unbinned, multivariate maximum-likelihood fit to extract signal yields and CP -violation parameters. We use the discriminating variables m ES , ∆E, m 3π , H, and a Fisher discriminant F [13]. The Fisher discriminant combines five variables: the polar angles with respect to the beam axis in the Υ (4S) frame of the B candidate momentum and of the B thrust axis; the tagging category; and the zeroth and second angular moments of the energy flow, excluding the B candidate, about the B thrust axis [13]. We also use ∆t for the B 0 → ωK 0 S decay, while for the charged B decays we use the PID variables T π and T K , defined as the number of standard deviations between the measured DIRC Cherenkov angle and that expected for pions and kaons, respectively.
For the B 0 → ωK 0 S decay we define the probability density function (PDF) for each event i, hypothesis j (signal and qq background), and tagging category c where σ i ∆t is the error on ∆t for event i. We write the extended likelihood function as where Y j is the fit yield of events of species j, f j,c is the fraction of events of species j for each category c, and N c is the number of events of category c in the sample. We fix f sig,c to f B flav ,c , the values measured with the large B flav sample [1]. The same likelihood function is used for the charged decays except that the hypothesis j also includes BB background, the tagging category is not used and the PDF is slightly different, involving flavor k (primary π + or K + ): The PDF P sig (∆t, σ ∆t , c), is the convolution of F (∆t; c) (Eq. 1) with the signal resolution function (a sum of three Gaussians) determined from the B flav sample. The other PDF forms are: the sum of two Gaussians for all signal shapes except H, and the peaking component of the m 3π background; the sum of three Gaussians for P qq (∆t; c); an asymmetric Gaussian with different widths below and above the peak for P j (F ) (a small "tail" Gaussian is added for P qq (F )); Chebyshev functions of second to fourth order for H signal and the slowly-varying shapes of ∆E, m 3π , and H backgrounds; and, for P qq (m ES ), a phase-space-motivated empirical function [14], with a small Gaussian added for P BB (m ES ).
We determine the PDF parameters from simulation for the signal and BB background components. We study large control samples of B → Dπ decays of similar topology to verify the simulated resolutions in ∆E and m ES , adjusting the PDFs to account for any differences found. For the qq background we use (m ES , ∆E) sideband data to obtain initial PDF-parameter values but ultimately leave them free to vary in the final fit.
We compute the branching fractions and charge asymmetry from fits performed without ∆t or flavor tagging. The free fit parameters are the following: the signal and qq background yields (the BB yield, if present, is fixed); the three shape parameters of P qq (F ); the slope of P qq (∆E) and P qq (m 3π ); the fraction of the peaking component of P qq (m 3π ); ξ [14]; and, for the charged B decays, the signal and background A ch . Table I lists the quantities used to determine the branching fraction. Equal production rates of B + B − and B 0 B 0 pairs have been assumed. Small yield biases are present in the fit, due primarily to unmodeled correlations among the signal PDF parameters. In Table  I we include estimates of these biases, evaluated by fitting simulated qq experiments drawn from the PDF into which we have embedded the expected number of signal and BB background events randomly extracted from the 6.1 ± 0.7 6.1 ± 0.6 6.2 ± 1.0 Signal A ch −0.01 ± 0.10 0.05 ± 0.09 − fully simulated MC samples. The estimated purity in Table I is given by the ratio of the signal yield to the effective background plus signal, the latter being defined as the square of the error on the yield. Note that the ωK + signal in the ∆E plot is displaced from zero since ∆E is defined for the ωπ + hypothesis. Fig. 1 shows projections onto m ES and ∆E for a subset of the data (including 45-65% of signal events) for which the signal likelihood (computed without the variable plotted) exceeds a threshold that optimizes the sensitivity.
For the time-dependent analysis, we require |∆t| < 20 ps and σ ∆t < 2.5 ps. The free parameters in the fit are the same as for the branching fraction fit plus S, C, the fraction of background events in each tagging category, and the six primary parameters describing the ∆t back- ground shape. The parameters τ and ∆m d are fixed to world-average values [15]. Here we find a slightly smaller yield of 95±14 events and S = 0.51 +0.35 −0.39 , C = −0.55 +0.28 −0.26 . The errors have been scaled by ∼1.10 to account for a slight underestimate of the fit errors predicted by our simulations when the signal sample size is small. Fig. 2 shows the ∆t projections and asymmetry of the timedependent fit with events selected as for Fig. 1.
The major systematic uncertainties affecting the branching fraction measurements include the reconstruction efficiency (0.8% per charged track, 1.5% per photon, and 2.1% per K 0 S ) estimated from auxiliary studies. We take one-half of the measured yield bias (3-4%) as a systematic error. The uncertainty due to the signal PDF description is estimated to be < ∼ 1% in studies where the signal PDF parameters are varied within their estimated errors. The uncertainty due to BB background is also estimated to be 1% by variation of the fixed BB yield by its estimated uncertainty. The A ch bias is estimated to be −0.005 ± 0.010 from studies of signal MC, control samples, and calculation of the asymmetry due to particles interacting in the detector. We correct for this bias and assign a systematic uncertainty of 0.01 for A ch for both B + → ωπ + and B + → ωK + .
For the time-dependent measurements, we estimate systematic uncertainties in S and C due to BB background and PDF shape variation (0.01 each), modeling of the signal ∆t distribution (0.02), and interference between the CKM-suppressedb →ūcd amplitude and the favored b → cūd amplitude for some tag-side B decays [16] (0.02 for C, negligible for S). We also find that the uncertainty due to SVT alignment and position and size of the beam spot are negligible. The B flav sample is used to determine the errors associated with the signal