Measurement of branching fractions and charge asymmetries in B+ decays to etapi+, etaK+, etarho+ and eta'pi+, and search for B0 decays to etaK0 and etaomega

We present measurements of branching fractions and charge asymmetries for six B-meson decay modes with an eta or eta' meson in the final state. The data sample corresponds to 232 million BBbar pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- B Factory at SLAC. We measure the branching fractions (in units of 10^-6): B(B->etapi+)=5.1+/-0.6+/-0.3, B(B->etaK+)=3.3+/-0.6+/-0.3, B(B->etaK0)=1.5+/-0.7+/-0.1 (<2.5 at 90% C.L.), B(B->etarho+)=8.4+/-1.9+/-1.1, B(B->etaomega)=1.0+/-0.5+/-0.2 (<1.9 at 90% C.L.), and B(B->eta'pi+)=4.0+/-0.8+/-0.4, where the first uncertainty is statistical and second systematic. We also determine the charge asymmetries for the charged modes: Ach(B->etapi+)=-0.13+/-0.12+/-0.01, Ach(B->etaK+)=-0.20+/-0.15+/-0.01, Ach(B->etarho+)=0.02+/-0.18+/-0.02, and Ach(B->eta'pi+)=0.14+/-0.16+/-0.01.

PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er Charmless B decays are becoming increasingly useful to test the accuracy of theoretical predictions, for example based on QCD factorization [1,2] or flavor SU (3) symmetry [3,4]. In this Letter we present measurements of branching fractions and, when applicable, charge asymmetries for six charmless B decays: B + → ηπ + , B + → ηK + , B 0 → ηK 0 , B 0 → ηω, B + → ηρ + and B + → η ′ π + , of which the last four were not observed before [5,6,7,8]. Some of these decays may proceed through CKM-suppressed b → u and loop ("penguin") b → s transitions with amplitudes of comparable size. Interference between these amplitudes can lead to direct CP violation measurable in charge asymmetries A ch [2]. The measured branching fractions and charge asymmetries may also be sensitive to the effect of non-Standardmodel heavy particles entering the loop [9].
Charmless B decays with kaons are usually expected to be dominated by b → s loop amplitudes, while b → u tree amplitudes are typically larger for the decays with pions and ρ mesons. However, the B → ηK decays are especially interesting since they are suppressed relative to the abundant B → η ′ K decays due to destructive interference between two penguin amplitudes [10]. The CKM-suppressed b → u tree amplitudes may interfere significantly with b → s penguin amplitudes of similar sizes, possibly leading to large direct CP violation in B + → ηρ + , B + → ηπ + and B + → η ′ π + [11]; numerical estimates are available in a few cases [2,3,12]. We search for such direct CP violation by measuring the charge asymmetry Finally, phenomenological fits to the branching fractions and charge asymmetries of charmless B decays can be used to understand the relative importance of tree and penguin contributions and may provide sensitivity to the CKM angle γ [3,4].
The results presented here are obtained from extended unbinned maximum likelihood (ML) fits to data collected with the BABAR detector [13] at the PEP-II asymmetric e + e − collider [14] located at the Stanford Linear Accel-erator Center. The analysis uses an integrated luminosity of 211 fb −1 , corresponding to 232 million BB pairs, recorded at the Υ (4S) resonance (center-of-mass energy √ s = 10.58 GeV).
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 central 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). Charged particle identification (PID) is provided by an internally reflecting ring imaging Cherenkov detector (DIRC) covering the central region of the detector, the average energy loss (dE/dx) in the tracking devices and by the EMC. A K/π separation better than two standard deviations (σ) is achieved for all momenta.
All tracks from resonance candidates are required to have PID consistent with pions. For the B + decays to ηπ + , ηK + and η ′ π + , the primary charged track must have an associated DIRC Cherenkov angle within 3.5σ of the expected value for either a π or K hypothesis. The discrimination between primary π and K is performed in the ML fits.
A B-meson candidate is characterized kinematically by the energy-substituted mass Backgrounds arise primarily from random combinations in continuum e + e − → qq (q = u, d, s, c) events. To reject these events we make use of 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 clusters in the event. The distribution of | cos θ T | is sharply peaked near 1 for combinations drawn from jetlike qq pairs, and nearly uniform for the almost isotropic B-meson decays; we require | cos θ T | < 0.9 (< 0.65 for η ′ ργ π + ). Further discrimination from continuum in the ML fit is obtained from a Fisher discriminant F that is described in detail elsewhere [6].
Where necessary, we use additional event selection criteria to reduce BB backgrounds from several charmless final states. Specifically, we require that photons have energies in ranges uncharacteristic of these backgrounds and, in η γγ ω and η γγ K 0 S , we eliminate η γγ candidates that share a photon with any π 0 candidate having momentum between 1.9 and 3.1 GeV in the Υ (4S) frame.
Multiple candidates are found in less than 30% of the events, in which case we choose the candidate with the smallest value of a χ 2 constructed from the deviations of the daughter resonance masses from their nominal values.
We use Monte Carlo (MC) simulation [15] for an initial estimate of the residual BB background and to identify the few (mostly charmless) decays that may survive the candidate selection and have characteristics similar to the signal. We find these contributions to be negligible for several of our modes. Where they are not negligible, namely for η γγ π + , η γγ K + , ηρ + and η ′ ργ π + , we include a component in the ML fit to account for them.
We obtain yields and A ch for each decay chain from a ML fit with the following input observables: ∆E, m ES , F , and m res (the mass of the η, η ′ , ρ + , or ω candidate).
For ω and ρ + decays we also use H and, for charged modes with a primary charged track, the PID variables S π and S K , defined as the number of standard deviations between the measured DIRC Cherenkov angle and that expected for pions and kaons, respectively.
For each event i, hypothesis j (signal, continuum background, BB background), and flavor k (primary π + or K + ), we define the probability density function (PDF) The bracketed variables S and H pertain to modes with a primary charged track or vector resonance daughters, respectively. Known correlations between ∆E k and S k , and between m res and H, are included in the PDF. The likelihood function is where Y jk is the yield of events of hypothesis j and flavor k, to be found by maximizing L. N is the number of events in the sample. Free parameters of the fit are the signal and background yields, qq background PDF parameters (see below), and for charged modes the signal and qq background charge asymmetries.
For the signal and BB background components we determine the PDF parameters from simulation. For background from continuum (and non-peaking combinations from B decays) we obtain the PDF from (m ES , ∆E) sideband data for each decay chain, before applying the fit to data in the signal region; we refine this PDF by letting as many of its parameters as feasible free to vary in the final fit. We parameterize each of the functions P sig (m ES ), P sig (∆E k ), P j (F ), P(S k ) and the peaking components of P j (m res ) with either a Gaussian, the sum of two Gaussians or an asymmetric Gaussian function as required to describe the distribution. Slowly varying distributions (mass, energy or helicity-angle for combinatorial background) are represented by one or a combination of linear, quadratic and phase-space motivated functions [6]. The peaking and combinatorial components of the ω and ρ + mass spectra each have their own H shapes. Control samples with similar topologies as our signal modes (e.g. B → D(Kππ)π) are used to verify or adjust the simulated resolutions evaluated from MC.
Before applying the fitting procedure to the data we subject it to several tests. In particular we evaluate possible biases in the yields from our neglect of small residual correlations among discriminating variables in the PDFs. This is achieved by fitting ensembles of 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 fully simulated MC samples. The measured biases are listed in Table I.
The branching fraction for each decay is obtained from the measured yield, corrected for the fit bias and for the selection efficiency, and the number of BB pairs. We assume equal decay rates of the Υ (4S) to B + B − and B 0 B 0 . In Table I we show for each decay mode the measured branching fraction together with the event yield and efficiency, and A ch when applicable. The purity is the ratio of the signal yield (Y S ) to the effective background plus signal (Y eff B + Y S ), which we estimate as the square of the uncertainty in the signal yield (Y eff B + Y S ≡ σ 2 YS ). The statistical uncertainties in the signal yield and A ch are taken as the change in the central value when the quantity −2 ln L increases by one unit from its minimum value. The significance is taken as the square root of the difference between the value of −2 ln L (with systematic uncertainties included) for zero signal and the value at its minimum.
For each mode the measurements for separate daughter decays are combined by adding the values of −2 ln L as functions of branching fraction, taking proper account of the correlated and uncorrelated systematic uncertainties described below [6]. For ηω and ηK 0 we quote 90% confidence level (C.L.) upper limits, taken to be the branching fraction below which lies 90% of the total of the likelihood integral in the positive branching fraction region.
In Fig. 1 we show projections onto m ES and ∆E of subsamples enriched with a mode-dependent threshold requirement on the signal likelihood (computed without of the variable plotted) that optimizes the sensitivity.
Most of the uncertainties arising from lack of knowledge of the PDFs have been included in the statistical uncertainty since most background parameters are free in the fit. For the signal the uncertainties in PDF parameters are estimated from the consistency of fits to MC and data in control modes with similar final states. Varying the signal PDF parameters within these errors, we estimate the mode-dependent uncertainties due to the signal PDFs to be 1-8 events. We verify the validity of 5.25 5.26 5.27 5.28 5.29 Events / 2MeV the fit procedure and PDF shapes by demonstrating that the likelihood for each fit is consistent with the distribution found in simulation.
The uncertainty in the fit bias correction is taken to be half of the correction itself. Similarly we estimate the uncertainty from modeling the BB backgrounds by taking half of the difference between the signal yield fitted with and without the BB background component.
Uncertainties in our knowledge of the reconstruction efficiency, found from auxiliary studies on inclusive control samples [6], include 0.6% per primary track, 0.8% per track from a resonance, 1.5% per photon, and 2.1% for a K 0 S . Our estimate of the systematic uncertainty in the number of BB pairs is 1.1%. Published data [16] provide the uncertainties in the B-daughter product branching fractions (1-3%). The uncertainties in the efficiency of the event selection are 1% (4% in B + → η ′ ργ π + ) for the requirement on cos θ T and 1% for PID. Using several large inclusive kaon and B-decay samples, we find a systematic uncertainty for A ch of 1.1%, due mainly to the dependence of reconstruction efficiency on the charge, for the high momentum pion from B + → ηπ + , ηK + and η ′ π + . The corresponding number for the softer charged pion from the ρ + in B + → ηρ + is 2%.
In this Letter, we have presented improved measurements of branching fractions for six charmless Bmeson decays. All branching fractions are in agreement with theoretical predictions. The previously unobserved B + → ηρ + and B + → η ′ π + decay modes are seen with significance 4.7σ and 5.4σ, respectively. For the charged modes, we also determine the charge asymmetries. These are found to be consistent with zero within their uncertainties.
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. We wish to acknowledge support from the University of Colorado Undergraduate Research Opportunities Program. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and