Study of B0 ->pi0 pi0, B ->pi pi0, and B ->K pi0 Decays, and Isospin Analysis of B ->pipi Decays

We present updated measurements of the branching fractions and CP asymmetries for B0 ->pi0 pi0, B+ ->pi+ pi0, and B+ ->K+ pi0. Based on a sample of 383 x 10^6 Upsilon(4S) ->B Bbar decays collected by the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC, we measure B(B0 ->pi0 pi0) =(1.47 +/- 0.25 +/- 0.12) x 10^-6, B(B+ ->pi+ pi0)= (5.02 +/- 0.46 +/- 0.29) x 10^-6, and B(B+ ->K+ pi0) = (13.6 +/- 0.6 +/- 0.7) x 10^-6. We also measure the CP asymmetries C(pi0 pi0) = -0.49 +/- 0.35 +/- 0.05, A(pi+ pi0) = 0.03 +/- 0.08 +/- 0.01, and A(K+ pi0) = 0.030 +/- 0.039 +/- 0.010. Finally, we present bounds on the CKM angle $\alpha$ using isospin relations.

PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er In the Standard Model (SM) of particle physics, the charged-current couplings of the quark sector are described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements V qq ′ [1]. The consistency of multiple measurements of the sides and angles of the CKM Unitarity Triangle provides a stringent test of the SM, and also provides constraints on non-SM physics. The CKM angle α ≡ arg [−(V td V * tb )/(V ud V * ub )] can be measured from the interference between b → u quark decays with and without B 0 ↔ B 0 mixing. In the limit of one (tree) amplitude, sin 2α can be extracted from the CP asymmetries in B 0 → π + π − decays [2]. However, the size of the branching fraction of B 0 → π 0 π 0 , relative to B ± → π ± π 0 and B 0 → π + π − , indicates that there is another significant (penguin) amplitude, with a different CP -violating (weak) phase, contributing to the decay. The deviation of the asymmetry obtained from B → ππ decays, sin 2α eff , from sin 2α can be measured using the isospin-related decays B ± → π ± π 0 and B 0 → π 0 π 0 [3,4,5]. In the SM, the charge asymmetry is expected to be very small in the decay B ± → π ± π 0 since penguin diagrams cannot contribute to the I = 2 final state. However, a non-zero time-integrated CP asymmetry in the decay B 0 → π 0 π 0 is expected if penguin and tree amplitudes have different weak and CP -conserving (strong) phases.
The B → Kπ system also exhibits interesting CPviolating features, including direct CP violation in B 0 → K + π − decays [6,7]. Sum rules derived from U-spin symmetry and parameters from the B → ππ system relate the branching fraction and charge asymmetry of B ± → K ± π 0 decays to other decays in the Kπ system [8,9]. The CP asymmetry in B ± → K ± π 0 is expected to have the same sign and roughly the same magnitude as the CP asymmetry in B 0 → K + π − in the absence of color-suppressed tree and electroweak-penguin amplitudes.
Based on a sample of 383×10 6 Υ (4S) → BB decays, we report updated measurements of the branching fraction for B 0 → π 0 π 0 and the time-integrated CP asymmetry, C π 0 π 0 , defined as where A 00 (A 00 ) is the B 0 (B 0 ) → π 0 π 0 decay amplitude. We also measure the branching fractions for B ± → h ± π 0 (h ± = π ± , K ± ) and the corresponding charge asymme- The BABAR detector is described in Ref. [10]. Charged particle momenta are measured with 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 is used to measure photon energies and positions. The photon energy resolution in the EMC is σ E /E = 2.3( GeV) 1/4 /E 1/4 ⊕ 1.9 %, and the angular resolution from the interaction point is σ θ = 3.9 o / E/ GeV. Charged hadrons are identified with a detector of internally reflected Cherenkov light (DIRC) and ionization measurements in the tracking detectors. The average Kπ separation in the DIRC varies from 12σ at a laboratory momentum of 1.5 GeV/c to 2σ at 4.5 GeV/c.
For the reconstruction of B ± → h ± π 0 events, we require the track from the B candidate to have at least 12 hits in the DCH and be associated with at least 5 photons in the DIRC. The measured Cherenkov opening angle θ C must be within 4σ of the expectation for the pion or kaon hypothesis and θ C must be greater than 10 mrad from the proton hypothesis. Electrons are removed from the sample by vetoing candidates based on their energy loss in the SVT and DCH and a comparison of the track momentum and deposited energy in the EMC.
While π 0 meson candidates are mostly formed from two EMC clusters, we increase our π 0 efficiency compared to Ref. [4] by ∼ 10% by including π 0 candidates consisting of two overlapping photon clusters ("merged" π 0 ) and candidates with one photon cluster and two tracks consistent with being a photon conversion inside the detector. Photon conversions are selected from pairs of oppositely charged tracks with an invariant mass less than 30 MeV/c 2 , a vertex that lies within the detector, and a total momentum vector that points back to the beamspot. EMC clusters are required to have energies greater than 0.03 GeV and a transverse shower shape consistent with a photon. To reduce the background from random photon combinations, the cosine of the angle between the direction of the decay photons in the center-of-mass system of the parent π 0 and the π 0 flight direction in the lab frame must be less than 0.95. For candidates consisting of two EMC clusters or one cluster and a converted photon, the reconstructed π 0 mass is required to be between 110 and 160 MeV/c 2 , and the candidates are then kinematically fit with their mass constrained to the π 0 mass. We distinguish merged π 0 candidates from single photons and other neutral hadrons using the second transverse moment, S = i E i × (∆α i ) 2 /E, where E i is the energy deposited in each CsI(Tl) crystal, and ∆α i is the angle between the cluster centroid and the crystal. Because merged π 0 s are caused by two overlapping photon clusters, they have a larger S than solitary photons. We use a large sample of π 0 s from τ ± → ρ ± ν decays to validate that our Monte Carlo simulation (MC) accurately simulates merged π 0 s and photon conversions, as well as our overall π 0 efficiency. We use two kinematic variables to isolate B 0 → π 0 π 0 and B ± → h ± π 0 candidates from the large background of e + e − → qq (q = u, d, s, c) continuum events. The first is the beam-energy-substituted mass We define the main signal region in the B 0 → π 0 π 0 analysis as m ES > 5.20 GeV/c 2 and |∆E| < 0.20 GeV.
To further discriminate the signal from qq backgrounds, we exploit the event topology variable θ S : the angle in the CM frame between the sphericity axis of the B candidate's decay products and that of the remaining neutral clusters and charged tracks in the rest of the event. Since the distribution of | cos θ S | peaks at 1 for qq events, we require | cos θ S | < 0.8 (0.7) for events with a B ± → h ± π 0 (B 0 → π 0 π 0 ) candidate. To further improve background separation, we construct a Fisher discriminant F from the sums i p i and i p i cos 2 θ i , where p i is the CM momentum and θ i is the angle with respect to the thrust axis of the B candidate's daughters, in the CM frame, of all tracks and clusters not used to reconstruct the B meson.
We use an extended, unbinned maximum likelihood (ML) fit to determine the number of signal events and the associated asymmetries. The probability density function (PDF) P i ( x j ; α i ) for event j and signal or background hypothesis i is the product of PDFs for the variables x j , given the set of parameters α i . The likelihood function L is where N is the number of events, n i is the PDF coefficient for hypothesis i, and M is the total number of signal and background hypotheses.
In the B 0 → π 0 π 0 fit, the variables x j are m ES , ∆E, and F . In addition to the signal and qq background, we expect background events from the charmless decays B ± → ρ ± π 0 and B 0 → K 0 S π 0 (K 0 S → π 0 π 0 ) to contribute 61 ± 7 events in the signal region, as determined from MC, so we include an additional component in the fit to account for this BB background. For the B 0 → π 0 π 0 signal and the BB background, we observe a correlation coefficient between m ES and ∆E of ∼ 0.2, so a two-dimensional PDF, derived from MC simulation, is used to parameterize these distributions. The qq background PDF is described by an ARGUS threshold function [11] in m ES and a polynomial in ∆E. We divide the F distribution from signal MC into ten equally-populated bins, and use a parametric step function to describe the distribution for all of the signal and background hypotheses. We fix the relative size of the F bins for the signal and BB background to values taken from MC. These values are verified with a sample of fully reconstructed B meson decays. Continuum F parameters are free in the fit.
In order to measure the time-integrated CP asymmetry C π 0 π 0 , we use the remaining tracks and clusters in a multivariate technique [12] to determine the flavor (B 0 or B 0 ) of the other B meson in the event (B tag ). Events are assigned to one of seven mutually exclusive categories k (including untagged events with no flavor information) based on the estimated mistag probability w k and on the source of the tagging information. The PDF coefficient for B 0 → π 0 π 0 is given by where N π 0 π 0 is the total number of B 0 → π 0 π 0 decays, χ d = 0.188 ± 0.004 [13] is the time-integrated mixing probability, and s j = +1(−1) when the B tag is a B 0 (B 0 ). The fraction of events in each category, f k , and the mistag rate are determined from a large sample of B 0 → D ( * ) (nπ)π decays.
For the B ± → h ± π 0 fit, along with m ES , ∆E, and F , we include the Cherenkov angle θ C to measure the B ± → π ± π 0 and B ± → K ± π 0 yields and asymmetries simultaneously. The difference between the expected and measured Cherenkov angle, divided by the uncertainty, is described by two Gaussian distributions. The values for m ES and ∆E are calculated assuming the track is a pion, so a B ± → K ± π 0 event will have ∆E shifted by a value dependent on the track momentum, typically −45 MeV. For the signal, the m ES and ∆E distributions are modeled as Gaussian functions with low-side power-law tails. The means of these distributions and the m ES width are determined in the fit, while the ∆E width is determined by MC simulation. We expect 69 ± 3 background events in the B ± → π ± π 0 signal region from other B meson decays, mainly from the same B decays as in the B 0 → π 0 π 0 case. For the B ± → K ± π 0 signal region we expect 9±2 events from B → X s γ and B 0 → ρ + K − . The PDFs for the BB backgrounds, the qq background, and the signal F are all treated the same as in the B 0 → π 0 π 0 case. The PDF coefficient for B ± → h ± π 0 is given by where A i is the charge asymmetry, and q j = ±1 is the charge of the B candidate.
The results from the B 0 → π 0 π 0 and B ± → h ± π 0 ML fits are summarized in Table I. In a total of 17,881 events we find 154 ± 27 B 0 → π 0 π 0 decays and an asymmetry C π 0 π 0 = −0.49 ± 0.35. For the B ± → h ± π 0 fit, we find 627 ± 58 B ± → π ± π 0 and 1364 ± 57 B ± → K ± π 0 events in a total of 85,895 events. All of the correlations among the signal variables are less than 5%. In Fig. 1 we use the event weighting and background subtraction method described in Ref. [14] to show signal and background distributions for B 0 → π 0 π 0 events. Signal and background distributions for B ± → h ± π 0 events are shown in Fig. 2 using the same method.
In order to account for a small bias in the B ± → h ± π 0 asymmetries arising from the difference in the π + and π − reconstruction efficiencies and the K + and K − hadronic interaction cross-sections in the BABAR detector, the B ± → π ± π 0 asymmetry is corrected by +0.005 ± 0.004 and the B ± → K ± π 0 asymmetry is corrected by +0.008 ± 0.008. We determine the π ± π 0 bias from a study of τ ± → ρ ± ν decays and verify it using the continuum background in data. For the B ± → K ± π 0 charge asymmetry bias, we use the continuum background and combine the results of the π ± π 0 asymmetry study and the K ± π ∓ asymmetry study in Ref. [6]. After the bias correction we find A π ± π 0 = 0.03 ± 0.08 and A K ± π 0 = 0.030 ± 0.039.
We evaluate the systematic errors on the branching fractions and asymmetries either using data control samples or by varying fixed parameters and refitting. The systematic uncertainties on the branching fraction and asymmetry measurements are summarized in Tables II and III, respectively. The largest systematic errors for the B 0 → π 0 π 0 and B ± → h ± π 0 branching fractions are from uncertainties in the π 0 reconstruction efficiency, signal selection efficiencies, F parameters, and BB background yields. We simulate radiative effects using the PHOTOS simulation package [15] and assign a systematic error equal to the difference between PHOTOS and the scalar QED calculation in Ref. [16]. For the B ± → h ± π 0 analysis, we also include as a systematic a small (< 2%) fit bias due to correlation among fit variables. The largest systematic uncertainties in the measurement of C π 0 π 0 are from the uncertainty on the B background CP content, tag-side interference, and the tagging fractions and asymmetry of B tag . The major contributions to the systematic error on A h ± π 0 are from the detector charge asymmetry and the ∆E and F PDF parameterization. We extract information on ∆α ≡ α eff − α and α using isospin relations [3] that relate the decay amplitudes of B → ππ decays and measurements of the branching fraction and time-dependent CP asymmetries in the decay B 0 → π + π − from BABAR [6]. For each of the six observable quantities required to calculate α [B(B 0 → π + π − ), B(B ± → π ± π 0 ), B(B 0 → π 0 π 0 ), S π + π − , C π + π − , and C π 0 π 0 ], we generate an ensemble of simulated experiments with uncorrelated Gaussian distributions where the width on each distribution is the sum in quadrature of the statistical and systematic errors of that measurement. Sets of generated experiments that result in an unphysical asymmetry or violate isospin are removed from the sample. Using the resulting distributions for ∆α and α, we calculate a confidence level (C.L.) for each solution and plot the maximum value of 1-C.L. of the various solutions in Fig. 3. One can further constrain α by using the fact that the penguin amplitude contribution to B → ππ decays must be very large if α is near 0 or π. We obtain a bound on the magnitude of the penguin amplitude from the branching fraction of the penguin-dominated decay B s → K + K − [17] by making the conservative assumption of SU (3) breaking at less than ∼ 100% [18]. In Fig. 3 we also show bounds on α when the size of the penguin amplitude is constrained by this assumption.
In summary, we measure the branching fractions and CP asymmetries in B 0 → π 0 π 0 , B ± → π ± π 0 , and The results for the B 0 → π 0 π 0 and B ± → h ± π 0 decays. For each mode we show the number of signal events, NS, number of continuum events, Ncont, number of B-background events, N Bbkg , total detection efficiency ε, branching fraction B, and asymmetry A h ± π 0 or C π 0 π 0 . Uncertainties are statistical for NS and Ncont, while for the branching fractions and asymmetries they are statistical and systematic, respectively.
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. α expressed as one minus the confidence level as a function of angle. We find an upper bound on ∆α of 39 • at the 90% confidence level. In (b) the curve shows the bounds on α using the isospin method alone, while the shaded region shows the result with the SU (3) requirement as discussed in the text.