B meson decays to charmless meson pairs containing eta or eta' mesons

We present updated measurements of the branching fractions for B0 meson decays to etaK0, etaeta, etaphi, etaomega, eta'K0, eta'eta', eta'phi, and eta'omega, and branching fractions and CP-violating charge asymmetries for B+ decays to etapi+, etaK+, eta'pi+ and eta'K+. The data represent the full dataset of 467 10^{6} BB pairs collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at the SLAC National Accelerator Laboratory. Besides large signals for the four charged B decay modes and for B0\to eta'K0, we find evidence for three B0 decay modes at greater than 3.0sigma significance. We find B(B0\to etaK0) = (1.15^{+0.43}_{-0.38} \pm0.09)x10^{-6}, B(B0\to etaomega) = (0.94^{+0.35}_{-0.30}\pm0.09)x10^{-6}, and B(B0\to eta'omega) = (1.01^{+0.46}_{-0.38}\pm0.09)x10^{-6}, where the first (second) uncertainty is statistical (systematic). For the B+\to etaK+ decay mode, we measure the charge asymmetry A_{ch}(B+\to etaK+) = -0.36 \pm 0.11 \pm 0.03.

The charge asymmetry is expected to be sizable in ηK + and suppressed in η ′ K + decays [6,9,19]. However, different approaches predict the two asymmetries to have the same [9] or opposite [6] signs; precise measurement of such asymmetries can discriminate between these models. Furthermore, the charge asymmetries in η ′ π + and ηπ + decays are expected to be sizable [6,9], with model-dependent predictions for their magnitudes.
The results presented here are based on the full dataset collected with the BABAR detector [20] at the PEP-II asymmetric-energy e + e − collider located at the SLAC National Accelerator Laboratory. An integrated luminosity of 426 fb −1 , corresponding to N BB = 467 × 10 6 BB pairs, was recorded at the Υ (4S) resonance (centerof-mass energy √ s = 10.58 GeV). A further 44 fb −1 was collected approximately 40 MeV below the resonance (off-peak) for the study of the e + e − → qq background, where q is a u, d, s, or c quark.
Charged particles are detected, and their momenta measured, by a combination of a vertex tracker, consisting 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. We identify photons and electrons using a CsI(Tl) electromagnetic calorimeter (EMC). Further charged-particle identification (PID) is provided by the average energy loss (dE/dx) measurements in the tracking devices and by the information provided by an internally reflecting ring-imaging Cherenkov detector (DIRC) covering the central region.
We select η, η ′ , φ, ρ 0 , K 0 S , ω, and π 0 candidates through the decays η → γγ (η γγ ), η → π + π − π 0 (η 3π ), , ω → π + π − π 0 , and π 0 → γγ. We do not study the decay B 0 → η ′ η ′ with both η ′ mesons decaying to ργ, because it suffers large backgrounds. Requirements applied to the photon energy E γ and to the invariant mass of the B daughters are listed in Table I. The requirements on the η and η ′ invariant masses depend on the decay mode. Branching fractions of charged B decays with η ′ in the final state and of B 0 → η ′ K 0 S are higher than those of the other neutral B modes. In neutral decay modes we apply a tighter requirement on η 3π invariant mass in order to prevent possible contamination from BB background. The different requirements on the η ′ mass increase the purity of the charged B and η ′ K 0 S modes and enhance the selection efficiency for the other neutral B decay modes. The energy (momentum) of the π 0 (η) candidates is required

State
Invariant mass ( MeV/c 2 ) Eγ ( MeV) π 0 120 < mγγ < 150 > 30 Prompt ηγγ 505 < mγγ < 585 > 100 Secondary ηγγ 490 < mγγ < 600 to exceed 200 MeV (200 MeV/c) in the laboratory frame. The prompt charged tracks in B + → η ′ π + and secondary charged tracks in η, η ′ , and ω candidates are required to have DIRC, dE/dx, and EMC signatures consistent with the pion hypothesis. After selection, we constrain the η, η ′ , and π 0 masses to their world average values [21]. The prompt charged track in B + → η ′ K + is required to be consistent with the kaon hypothesis. The signatures for the charged kaons from φ decays are required to be inconsistent with hypotheses for electrons, pions and protons. For the prompt charged track in B + decays to ηK + and ηπ + , we define the variables C K and C π as where θ meas K,π (θ exp K,π ) is the measured (expected) DIRC Cherenkov angle and σ meas K,π is its uncertainty, for the kaon and pion hypothesis, respectively. We require −3 < C K < 13 and −13 < C π < 3. For K 0 S candidates we require a vertex χ 2 probability larger than 0.001 and a reconstructed decay length greater than three times its uncertainty.
We reconstruct the B meson candidate by combining the four-momenta of the final state particles and imposing a vertex constraint. A B meson candidate is kinematically characterized by the energy-substituted mass is the B-meson four-momentum vector expressed in the Υ (4S) rest frame. For signal events, the m ES and ∆E distributions peak around 5.28 GeV/c 2 and zero, respectively. We require 5.25 < m ES < 5.29 GeV/c 2 and |∆E| < 0.2 GeV for all decay modes except B 0 → ηK 0 S , where we require −0.15 < ∆E < 0.2 GeV in order to suppress most of the background from radiative B decays.
Backgrounds arise primarily from random combinations of tracks and neutral clusters in e + e − → qq continuum events. We use large samples of Monte Carlo (MC) simulated [22] events and control samples to optimize criteria to suppress the background. We reject continuum events by using the angle θ T between the thrust axis of the B candidate in the Υ (4S) frame and that of the rest of the event. The thrust axis of the B candidate is given by the thrust axis of the B decay products. The distribution of | cos θ T | is sharply peaked near 1.0 for jet-like qq pair events and is nearly uniform for Υ (4S) → BB events. We require | cos θ T | < 0.9 (0.85 for η ′ ργ π + , 0.8 for η γγ ω and η ′ ργ ω). To discriminate against τ -pair and two-photon backgrounds, and to better describe the event shape, we require the event to contain at least three charged tracks, or one track beyond the minimum required for the signal decay topology, whichever is larger.
In η → γγ (φ) decays, we define H η (H φ ) as the cosine of the angle between the direction of a daughter γ (K) and the flight direction of the parent of η (φ) in the η (φ) rest frame; for η ′ ργ , H ρ is the cosine of the angle between the direction of a daughter pion and the flight direction of the η ′ in the ρ rest frame. For B decays containing an ω meson in the final state we define H ω as the cosine of the angle between the B recoil direction and the normal to the plane defined by the ω daughters in the ω rest frame. We require |H η | < 0.95 in B 0 → ηη decay modes. We reject candidate events if |H ρ | > 0.9 (> 0.75 in the To suppress this background, we search for π 0 candidates with a photon in common (overlapping) with the η candidate from the reconstructed signal B candidate. We require the π 0 mass not to be in the range (0.117, 0.152) GeV/c 2 for the B 0 → η γγ K 0 S decay mode, and (0.118, 0.150) GeV/c 2 for the B + → η γγ h + decay modes. Further suppression of this background is obtained with suitable requirements on |H η | and on the energy of the second (non-overlapping with η) π 0 photon (E 2nd γ ). We optimize these requirements by maximizing S/ √ S + B, where S (B) is the number of signal (background) events surviving the selection. We find the optimal criteria to be |H η | < 0.966 and E 2nd γ < 0.207 GeV for the B 0 → η γγ K 0 S decay mode, and |H η | < 0.977 and E 2nd γ < 0.143 GeV for the B + → η γγ h + decay modes.
We find a mean number of B candidates per event in the range 1.0-1.4, depending on the final state. Signal events are divided into two categories: correctly reconstructed (CR) signal where all candidate particles come from the correct signal B, and self cross-feed (SCF) signal where at least one candidate particle is exchanged with a particle coming from the rest of the event. Simula-tions show that the fraction of SCF candidates is in the range (3-7)% in charged B decay modes and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)% in neutral B decay modes. If an event has multiple B candidates, we select the candidate with the highest B vertex χ 2 probability, determined from a vertex fit that includes both charged and neutral particles [23]. This algorithm selects the correct candidate, if present, with an efficiency of (91-99)% and introduces negligible bias.
We obtain yields from unbinned extended maximumlikelihood (ML) fits. The main input observables are ∆E, m ES , and a Fisher discriminant F [24]. Where relevant, the invariant masses m res of the intermediate resonances and angular variables H are used. The Fisher discriminant F combines five variables: the angles with respect to the beam axis of the B momentum and B thrust axis, the zeroth and second angular moments L 0,2 of the energy flow about the B thrust axis, and the absolute value of the continuous output of a flavor-tagging algorithm. The first four variables are evaluated in the Υ (4S) rest frame. The moments are defined by L r = s p s ×|cos θ s | r , where θ s is the angle with respect to the B thrust axis of track or neutral cluster s with momentum p s , and the sum excludes the B candidate. Flavor tagging information is derived from an analysis of the decay products of the nonsignal candidate B meson (B tag ), using a neural network based technique [25]. The output value of the tagging algorithm reflects the different final states identified in B tag decay. In particular, the presence of a lepton in the final state usually results in a large tagging output value, for both B 0 B 0 and B + B − events. Since leptons are not generally present in continuum background events, the inclusion of the tagging algorithm output in F improves its discriminating power between continuum background and BB events. The coefficients of F are chosen to maximize the separation between the signal and the continuum background. They are determined from studies of MC signal events and off-peak data.
The set of probability density functions (PDF) used in the ML fits, specific to each decay mode, is determined on the basis of studies with MC samples. We estimate BB backgrounds using MC samples of B decays. Where needed, we add components to account for BB background events with a m ES or ∆E distribution that peaks in the signal region and for background from B meson decays with charmed particles in the final state.
The extended likelihood function is where N is the number of input events, n j is the number of events for hypothesis j (j = 1 for signal, j = 2 for continuum background, and j = 3 for BB background), and P j (x i ) is the corresponding PDF evaluated with the observables x i of the i th event. In the B 0 → η ′ ω, η ′ φ, and η ′ ργ ω decay modes the signal includes both the CR and SCF signal components with the SCF fraction fixed to the value estimated from simulation. Due to the similar kinematics and branching fractions of the ηK + and ηπ + decay modes, we perform a combined fit to extract the two signal yields and charge asymmetries. In this fit we use the C K and C π variables to discriminate the mass hypothesis of the prompt track. Since the correlations among the observables in the data are small, we assume each P j to be the product of the PDFs for the separate variables. Correlations between the ηK + and ηπ + signal yields (charge asymmetries) are below 5% (7%). We determine the PDF functional form and parameters from MC simulation for the signal and BB backgrounds, and from sideband data (5.25 < m ES < 5.27 GeV/c 2 ; 0.1 < |∆E| < 0.2 GeV) for the continuum background. For B + → ηh + decay modes, PDF functional form and parameters for the continuum background are determined using off-peak data. We parameterize each of the functions P 1 (m ES ), P 1 (∆E), P j (F ), and the peaking components of P j (m res ) with either a symmetric or a bifurcated Gaussian, the sum of two symmetric or bifurcated Gaussian shapes, a bifurcated Gaussian distribution with exponential tails [26] or a Crystal Ball function [27], as required to describe the distribution. Slowly varying distributions (m res and ∆E for the continuum background, and angular variables) are represented by linear or quadratic functions. For the continuum background, the m ES distribution is described by the ARGUS function [28]. Large data control samples of B decays to charmed final states of similar topologies are used to verify the simulated resolutions in m ES and ∆E. Where the control samples reveal differences between data and MC samples in mass (energy) resolution, we correct the mean and scale the width of the mass (energy) distribution used in the likelihood fits.
The validity of the fit procedure and PDF parameterization, including the effects of unmodeled correlations among observables, is checked with simulated experiments. This is done by embedding a number of signal and peaking BB background events from fully simulated MC samples and by drawing a number of qq and charm BB events from PDFs, according to the values found in the data. In each fit the free parameters are: the yields, the charge asymmetry for the signal and continuum background, and several parameters describing the ∆E, m ES , and F distributions of the continuum background. A systematic uncertainty due to fixing signal and background parameters in the fit is accounted. The charge asymmetry for BB background is fixed to zero in the fit. A systematic is evaluated to account for this restriction. Table II and Table III show, for B 0 and B + decays, respectively, the measured yields, fit biases, efficiencies, and products of daughter branching fractions for each decay mode. The efficiency is calculated as the ratio of the number of signal MC events after the event selection to the total generated, and is corrected for known differences between simulations and data. We compute the branching fractions from the fitted signal event yields, reconstruction efficiencies, daughter branching fractions, and the number of produced B mesons N BB , assum- II: Fitted signal event yield and fit bias in events (ev), detection efficiency ǫ, daughter branching fraction product Q Bi, significance S, and measured branching fraction B with statistical error for each B 0 decay mode. For the combined measurements we give the significance (with systematic uncertainties included) and the branching fraction with the statistical and systematic uncertainties (in parentheses the 90% CL upper limit). Significances greater than 7 standard deviations (σ) are omitted.

Mode
Yield (  TABLE III: Fitted signal event yield and fit bias, detection efficiency ǫ, daughter branching fraction product Q Bi, measured branching fraction B, charge asymmetry A ch with statistical error, and significance SA of the charge asymmetry for each charged decay mode. For the combined measurements we give the branching fraction, the charge asymmetry and the significance of the charge asymmetry with the statistical and systematic uncertainties.

Mode
Yield ( ing equal production rates of charged and neutral B pairs from Υ (4S) decays. We correct the yields for any bias measured with the simulations. We combine results from different sub-decays by adding the values of −2 ln (L/L max ) (parameterized in terms of the branching fraction or charge asymmetry), where L max is the value of L at its maximum, taking into account the correlated and uncorrelated systematic errors. We report the branching fractions for the individual decay channels and their significances S in units of standard deviations (σ). For B 0 → η ′ K 0 S and all charged decay modes, where the significance of the branching fraction is always greater than 7σ, the value of S is omitted. For the combined measurements we also report the 90% confidence level (CL) upper limits of the branching fraction for the B 0 modes where the significance is less than 5σ. For charged B decays we give the combined result for the charge asymmetry A ch and its significance S A in units of σ.
The statistical uncertainty on the signal yield and charge asymmetry is calculated as the change in the central value when the quantity −2 ln L increases by one from its minimum. The significance is calculated as the square root of −2 ln (L 0 /L max ), with systematic uncertainties included, where L 0 is the value of L for zero signal events or zero value for the charge asymmetry. We determine a Bayesian 90% CL upper limit on the branching fraction, assuming a uniform prior probability distribution, by finding the branching fraction below which lies 90% of the total of the likelihood integral in the positive branching fraction region. Figures 2 and 3 show the projections onto the m ES and ∆E variables for the four neutral decay modes that have a branching fraction significance greater than 3σ, and for the four charged decay modes, respectively. For each decay mode we optimize a requirement on the probability ratio P 1 /(P 1 + P 2 + P 3 ) in order to enhance the visibility of the signal. The probabilities P j are evaluated with-  out using the variable shown. The points show the data that satisfy such a requirement, while the solid curves show the total rescaled fit functions. In η ′ ω decays, a fit performed on ω mass sidebands m πππ < 735 MeV/c 2 or m πππ > 825 MeV/c 2 shows that contamination from possible B 0 → η ′ π + π − π 0 background is negligible. The main sources of systematic error include ML fit bias (0-14 events) and uncertainties in the PDF parameterization (0-12 events). The ML fit bias systematic error is taken to be half of the bias, summed in quadrature with its statistical uncertainty. The uncertainties related to the PDF parameterization are obtained by varying the PDF parameters within their errors. Published world averages [21] provide the uncertainties of the Bdaughter branching fractions (0-4)%. These uncertainties are the main contribution to the systematic errors of the B → η ′ K decay modes. The uncertainty on N BB is 1.1%. Other sources of systematic uncertainty are track (1%) and neutral particle (3-6%) reconstruction efficiencies; selection efficiency uncertainties are 1% each for the cos θ T and PID requirements. Using large inclusive kaon and B decay samples we estimate a systematic uncertainty for A ch of 0.005 due to the dependence of the reconstruction efficiency on the charge of the high momentum K ± . Other sources of systematic uncertainties for A ch are the fit bias (0-0.02) and the presence of a fit bias in the signal yield (0.02-0.03). The systematic uncertainty due to fixing the value of the charge asymmetry in BB background components is taken to be the largest deviation observed when varying this value of ±10%, and is in range (0-0.02).
In summary we present updated measurements of branching fractions for eight B 0 and four B + decays to charmless meson pairs. The results shown in Table II and  Table III are consistent with, but generally more precise than, previous measurements [2,3] and supersede our previous ones [2]. The branching fraction results are in agreement with predictions within the theoretical uncertainties that limit discrimination between different models [4,5,6,7,8,9,10]. We find evidence for three B 0 decay modes: ηK 0 (3.5σ), ηω (3.7σ) and η ′ ω (3.6σ). In the decay mode B + → ηK + we find evidence at 3.3σ for non-zero charge asymmetry, in agreement with theoretical predictions [6,9,19]. Discrimination between QCD factorization [6] and flavor SU(3) [9] symmetry models, based on the relative sign of the charge asymmetry in B + → ηK + and B + → η ′ K + decays, is limited by the accuracy of the latter measurement. The measurement of A ch for η ′ π + shows a slightly better agreement with the QCD factorization prediction [6] than with the flavor SU(3) symmetry based model [9], within large theoretical and experimental uncertainties.