Branching Fractions and CP Asymmetries in B0 ->pi0pi0, B+ ->pi+pi0 and B+ ->K+pi0 Decays and Isospin Analysis of the B ->pipi System

Based on a sample of 227 million BBbar pairs collected by the BaBar detector at the PEP-II asymmetric-energy B Factory at SLAC, we measure the branching fraction B(B0 ->pi0pi0) = (1.17 +- 0.32 +- 0.10) x 1e-6, and the asymmetry C(pi0pi0) = -0.12 +- 0.56 +- 0.06. The B0 ->pi0pi0 signal has a significance of 5.0 sigma. We also measure B(B+ ->pi+pi0) = (5.8 +- 0.6 +- 0.4) x 1e-6, B(B+ ->K+pi0) = (12.0 +- 0.7 +- 0.6) x 1e-6, and the charge asymmetries A(pi+pi0) = -0.01 +- 0.10 +- 0.02 and A(K+pi0) = 0.06 +- 0.06 +- 0.01. Using isospin relations we find an upper bound on the angle difference |alpha - alpha(eff)| of 35 degrees at the 90% C.L.

PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er In the Standard Model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix V qq ′ [1] describes the chargedcurrent couplings in the quark sector. The Unitarity Triangle is a useful representation of relations between CKM matrix elements, and measurements of its sides and angles provide a stringent test of the SM. Following the success in measuring the CKM angle β [2], an important challenge for the B Factories is the determination of the remaining angles. The extraction of the CKM angle α ≡ arg [−V td V * tb /V ud V * ub ] from the time-dependent CPviolating asymmetry in the B 0 → π + π − decay mode [3] is complicated by the interference of competing amplitudes ("tree" and "penguin") with different weak phases. The difference between α and α eff , where α eff is derived from the time-dependent B 0 → π + π − CP asymmetry, may be evaluated using the isospin-related decays B 0 → π 0 π 0 and B + → π + π 0 [4]. Here and throughout this Letter, charge conjugate reactions are included implicitly. For B 0 → π 0 π 0 the asymmetry may deviate from zero if the tree and penguin amplitudes have different weak and strong phases. In the SM the decay B + → π + π 0 is governed by a pure tree amplitude since penguin diagrams cannot contribute to the I = 2 final state; as a result no charge asymmetry is expected. The B → Kπ system is a rich source of information on the understanding of CP violation, as has been illustrated by the recent observation of direct CP asymmetry in B 0 → K + π − decays [5]. Both the rate and asymmetry of the B + → K + π 0 decay may be used to extract constraints on penguin contributions to the B → Kπ amplitudes [6].
In this Letter, we report a constraint on δ ππ ≡ α eff − α, using the measurement of the asymmetry C π 0 π 0 and updated measurements of the branching fractions for B 0 → π 0 π 0 and B + → π + π 0 and the charge asymmetry A π + π 0 . We also measure the branching fraction for the B + → K + π 0 decay and its charge asymmetry A K + π 0 . The asymmetry C π 0 π 0 is defined as amplitude. This study is based on 227×10 6 Υ (4S) → BB decays (on-resonance), collected with the BABAR detector. We also use 16 fb −1 of data recorded 40 MeV below the BB production threshold (off-resonance). The BABAR detector is described in Ref. [7]. The pri-mary components used in this analysis are a tracking system consisting of a five-layer silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) surrounded by a 1.5 T solenoidal magnet, an electromagnetic calorimeter (EMC) comprising 6580 CsI(Tl) crystals, and a ring imaging Cherenkov counter (DIRC).
Candidate π 0 mesons are reconstructed as pairs of photons, spatially separated in the EMC, with an invariant mass m γγ satisfying 110 < m γγ < 160 MeV/c 2 . The mass resolution is 8 MeV/c 2 for high energy (above 2 GeV) π 0 's [7]. Photon candidates are required to be consistent with the expected lateral shower shape, not to be matched to a track, and to have a minimum energy of 30 MeV. To reduce the background from false π 0 candidates, the angle θ γ between the photon momentum vector in the π 0 rest frame and the π 0 flight direction is required to satisfy | cos θ γ | < 0.95. Candidate tracks are required to be within the tracking fiducial volume, to originate from the interaction point, to consist of at least 12 DCH hits, and to be associated with at least 6 Cherenkov photons in the DIRC.
B meson candidates are reconstructed by combining a π 0 with a charged pion or kaon (h + ) or by combining two π 0 mesons. Two variables, used to isolate the B 0 → π 0 π 0 and B + → h + π 0 signal events, take advantage of the kinematic constraints of B mesons produced at the Υ (4S). The first is the beam-energy-substituted mass is the four-momentum of the initial e + e − system, p B is the B candidate momentum, both measured in the laboratory frame, and √ s is the e + e − center-of-mass (CM) energy.
The primary source of background is e + e − → qq (q = u, d, s, c) events where a π 0 or h + from each jet randomly combine to mimic a B decay. This jet-like qq background is suppressed by requiring that the angle θ S between the sphericity axis of the B candidate and that of the remaining tracks and photons in the event, in the CM frame, satisfy | cos θ S | < 0.7 (0.8) for B 0 → π 0 π 0 (B + → h + π 0 ). The other sources of background are B decays to final states containing one vector meson and one pseudoscalar meson, where one pion is produced almost at rest in the B rest frame and the remaining decay products match the kinematics of a B 0 → π 0 π 0 or B + → h + π 0 decay. For the B 0 → π 0 π 0 analysis we restrict the m ES -∆E plane to the region with m ES > 5.2 GeV/c 2 and |∆E| < 0.4 GeV. For the on-resonance sample we define the signal region as the band in the plane with |∆E| < 0.2 GeV and the sideband region as the rest of the plane excluding the region which is also populated with B + → ρ + π 0 events. The entire plane for the off-resonance data and the sideband region for the on-resonance data are kept in the fit in order to constrain the qq background parameters. B + → h + π 0 candidates are selected in the region with m ES > 5.22 GeV/c 2 and −0.11 < ∆E < 0.15 GeV.
For B 0 → π 0 π 0 candidates, the other tracks and clusters in the event are used to determine whether the other B meson (B tag ) decays as a B 0 or B 0 (flavor tag). We use a multivariate technique [8] to determine the flavor of the B tag meson. Events are assigned to one of several mutually exclusive categories based on the estimated mistag probability and on the source of tagging information.
The number of signal B candidates is determined with an extended, unbinned maximum-likelihood fit. The probability density function (PDF) P i ( x j ; α i ) for a signal or background hypothesis is the product of PDFs for the variables x j given the set of parameters α i . The likelihood function is a product over the N events of the M signal and background hypotheses: For B 0 → π 0 π 0 the coefficients c ij are defined as where s j refers to the sign of the flavor tag of the other B in the event j and is zero for untagged events. The fit parameters n i and A i are the number of events and raw asymmetry for B 0 → π 0 π 0 signal, B + → ρ + π 0 background, and continuum background components. The average of branching fraction measurements [9] is used to fix n(B + → ρ + π 0 ) to 32 ± 6. The raw asymmetry for signal is (1 − 2χ)(1 − 2ω)C π 0 π 0 , where χ = 0.186 ± 0.004 [10] is the neutral B mixing probability, and ω is the mistag probability.
For B + → h + π 0 the probability coefficients are c ij = 1 2 (1 − q j A i )n i , where q j is the charge of the track h in the event j. The fit parameters n i and A i are the number of events and asymmetry for B + → π + π 0 and B + → K + π 0 signal, continuum, and B background components. The B background yields are fixed to the expected number of events using the current world averages of branching ratios [11], which are 18 ± 4 for B 0 → ρ + π − and B + → ρ + π 0 combined, and 3±1 events for B 0 → ρ − K + . Uncertainties on these numbers are dominated by the uncertainty on selection efficiencies, due to the sensitivity to the tight requirement in ∆E.
The variables x j used for B 0 → π 0 π 0 are m ES , ∆E, and a Fisher discriminant F . The Fisher discriminant is an optimized linear combination of i p i and i p i cos 2 θ i , where p i is the momentum and θ i is the angle with respect to the thrust axis of the B candidate, both in the CM frame, for all tracks and neutral clusters not used to reconstruct the B meson. For both the B 0 → π 0 π 0 signal and the B + → ρ + π 0 background the m ES and ∆E variables are correlated and therefore a two-dimensional PDF from a smoothed, simulated distribution is used. For the continuum background, the m ES distribution is modeled as a threshold function [12], and the ∆E distribution as a second-order polynomial. The PDF for the F variable is modeled as a parametric step function (PSF) [13] for all event components. A PSF is a variable width binned distribution whose parameters are the heights of each bin. The limits of the ten bins F PSF are chosen so that each bin contains 10% of the signal sample. For B 0 → π 0 π 0 and B + → ρ + π 0 the F PSF parameters are correlated with the flavor tagging, and the PSF parameters are different for each tagging category. Simulated events are used to determine the PSF distributions for both B 0 → π 0 π 0 and B + → ρ + π 0 . For qq background, the F PSF parameters are free in the fit.
An additional discriminating variable for B + → h + π 0 is the Cherenkov angle θ c of the h + track. The PDF parameters for m ES , ∆E, θ c , and F for the background are determined using the data, while the PDFs for signal are found from a combination of simulated events and data. The m ES and ∆E distributions for qq events are treated as in the B 0 → π 0 π 0 case, with parameters allowed to vary freely in the fit. For the signal, the m ES and ∆E distributions are both modeled as a Gaussian distribution with a low-side power law tail whose parameters are determined from simulation. The means of the Gaussian components are determined from the fit to the B + → h + π 0 sample and their values used to tune the π 0 energy scale in the B 0 → π 0 π 0 analysis. The mean of ∆E for the B + → K + π 0 mode is a function of the kaon laboratory momentum, since a pion mass hypothesis is used. The distribution of F is modeled as a Gaussian function with an asymmetric variance for the signal, whose parameters are obtained from simulation, and as a double Gaussian for the continuum background, whose parameters are determined in the likelihood fit. The difference of the measured and expected values of θ c for the pion or kaon hypothesis, divided by the uncertainty on θ c , is modeled as a double Gaussian function, whose parameters are obtained from a control sample of kaon and pion tracks, from D * + → D 0 π + , D 0 → K − π + decays.
The result of the maximum-likelihood fit for B 0 → π 0 π 0 is n(B 0 → π 0 π 0 ) = 61 ± 17 (see Table I), with a corresponding statistical significance of 5.2σ. The asymmetry is C π 0 π 0 = −0.12 ± 0.56. Shown in Fig. 1 are distributions of m ES and F , for signal-enriched samples of B 0 → π 0 π 0 candidates. The projections contain 25% and 68% of the signal, 14% and 17% of the ρ + π 0 background, and 2.2% and 4.4% of the continuum background, for m ES and F respectively. The results for the modes B 0 → π 0 π 0 and B + → h + π 0 are summarized. For each mode, the sample size N , number of signal events NS, total detection efficiency ε, branching fraction B, asymmetry A or C π 0 π 0 , and the 90% confidence interval for the asymmetry are shown. For C π 0 π 0 the confidence interval is obtained inferring minimum coverage inside the physical region [−1, 1]. The first errors are statistical, the second systematic, with the exception of ε whose error is purely systematic.
For B + → h + π 0 the likelihood fit results are summarized in Table I. Using the event-weighting technique described in Ref. [14] we show signal and background projections in Fig. 2. For each event, a weight to be signal or background is assigned based on a fit performed without the specific variable that is plotted. The resulting distributions are normalized to the event yields, and are compared to the PDFs used in the full fit.
Systematic uncertainties on the event yields and CP asymmetries are evaluated on data control samples, or by varying the fixed parameters and refitting the data. In order of decreasing importance, the dominant systematics on the B 0 → π 0 π 0 branching fraction arise from the uncertainty on the ∆E resolution, the efficiency of the π 0 reconstruction, and the uncertainty on B background event yields. The significance of the B 0 → π 0 π 0 signal yield, taking systematic effects into account, is 5.0σ. The systematic uncertainty on C π 0 π 0 is dominated by the uncertainties on the B background asymmetry and tagging

efficiency.
For B + → h + π 0 the dominant systematic uncertainties arise from the F signal PDF parameters, selection efficiencies, and the ∆E resolution. Additional systematics arise from uncertainties on the B background event yields and particle identification. The systematic uncertainty on the charge asymmetries is dominated by the 1% upper limit on the charge bias in the detector [15].