B-meson decays to eta' rho, eta' f0, and eta' K*

We present measurements of B-meson decays to the final states eta'rho, eta'f0, and eta'K*, where K* stands for a vector, scalar, or tensor strange meson. We observe a significant signal or evidence for eta'rho+ and all the eta'K* channels. We also measure, where applicable, the charge asymmetries, finding results consistent with no direct CP-violation in all cases. The measurements are performed on a data sample consisting of 467 x 10^6 B-Bbar pairs, collected with the BaBar detector at the PEP-II e+e- collider at the SLAC National Accelerator Laboratory. Our results favor the theoretical predictions from perturbative QCD and QCD Factorization and we observe an enhancement of the tensor K_2*(1430) with respect to the vector K*(892) component.

We present measurements of B-meson decays to the final states η ′ ρ, η ′ f0, and η ′ K * , where K * stands for a vector, scalar, or tensor strange meson. We observe a significant signal or evidence for η ′ ρ + and all the η ′ K * channels. We also measure, where applicable, the charge asymmetries, finding results consistent with no direct CP violation in all cases. The measurements are performed on a data sample consisting of 467 × 10 6 BB pairs, collected with the BABAR detector at the PEP-II e + e − collider at the SLAC National Accelerator Laboratory. Our results favor the theoretical predictions from perturbative QCD and QCD Factorization and we observe an enhancement of the tensor K * 2 (1430) with respect to the vector K * (892) component. Charmless two-body decays of B mesons are a powerful probe for testing the standard model (SM) and searching for new physics phenomena [1]. Decays to final states containing η or η ′ mesons exhibit a distinctive pattern of interference among the dominant amplitudes and are also sensitive to a potentially large flavor-singlet contribution [2]. B meson decays to the final states η ′ ρ and η ′ K * (892) have been investigated theoretically within the SM by means of perturbative QCD (pQCD) [3], QCD Factorization (QCDF) [4], Soft Collinear Ef-fective Theory (SCET) [5], and SU (3) flavor symmetry [6]. The predicted branching fractions to the final states η ′ K * (892) + and η ′ K * (892) 0 are in the range of a few times 10 −6 , whereas the branching fraction for B 0 → η ′ ρ 0 is suppressed to 10 −7 − 10 −8 . There is some disagreement on the predictions of the branching fraction for B + → η ′ ρ + : SCET calculations give a value of 0.4×10 −6 , whereas pQCD and QCDF predict a branching fraction of (6 − 9) × 10 −6 . There are no theoretical predictions for the branching fraction of B 0 → η ′ f 0 .
In this paper, we report measurements of the branching fractions of B mesons decaying to the final states η ′ ρ, η ′ f 0 , and η ′ K * . Where applicable, we also measure the charge asymmetry A ch ≡ (Γ − − Γ + )/(Γ − + Γ + ), where the superscript to the decay width Γ refers to the charge of the B ± meson or to the charge of the kaon in the neutral B decays.
For this analysis we use the full BABAR dataset, collected at the PEP-II asymmetric-energy e + e − collider located at the SLAC National Accelerator Laboratory, consisting of 467 × 10 6 BB pairs originating from the decay of the Υ (4S) resonance, produced at a center-ofmass (CM) energy √ s = 10.58 GeV. The BABAR detector is described in detail elsewhere [12].
We reconstruct B-daughter candidates through their S → π + π − , and π 0 → γγ. We use both η ′ → ηπ + π − and η ′ → ρ 0 γ for η ′ K * , but due to the larger backgrounds affecting the η ′ ργ channel, we do not use the η ′ → ρ 0 γ decay mode for the η ′ ρ and η ′ f 0 final states. We require the invariant masses of the B-daughter candidates to satisfy the following requirements: 910 < m(η ′ ) < 1000 MeV, 510 < m(η) < 580 MeV, 510 < m(ρ/f 0 ) < 1060 MeV, 750 < m(K * ) < 1550 MeV, 488 < m(K 0 S ) < 508 MeV, and 120 < m(π 0 ) < 150 MeV; these mass intervals are chosen to include sidebands to estimate the background levels. We require the photon energy of the π 0 candidates to be greater than 30 MeV in the laboratory frame, while the minimum energy is 100 MeV for the photons of η candidates and 200 MeV for the photons from the η ′ → ρ 0 γ decay. A fit constraining the two pion tracks from the K 0 S decay to originate from the same decay vertex is performed and a K 0 S candidate is selected if its flight length exceeds three times its uncertainty. Daughter particles from η ′ , η, ρ, f 0 , and K * decays are rejected if their particle identification signatures are consistent with those of electrons or protons; K + candidates are required to be positively identified as kaons, and pions must fail this criterion. Unless otherwise stated, charge-conjugate reactions are always implied.
A B-meson candidate is characterized by two kinematic variables, whose small correlation is accounted for in the correction of the fit bias: the energy substituted mass m ES ≡ s/4 − p 2 B and the energy difference is the B-meson fourmomentum vector in the Υ (4S) rest frame. Signal events peak at 0 in ∆E and at the B mass [14] in m ES , with a resolution in ∆E (m ES ) of 20-35 MeV (3 MeV). We select events with 5.25 < m ES < 5.29 GeV and |∆E| < 0.2 GeV.
The dominant backgrounds arise from random combinations of particles in continuum e + e − → qq events (q = u, d, s, c). The angle θ T between the thrust axis [15] of the B candidate in the Υ (4S) rest frame and that of the remaining particles in the event is used to suppress this background. Jet-like continuum events peak at | cos θ T | close to 1, while spherical B decays exhibit a flat distribution for this variable. Further rejection is achieved by restricting the range of the helicity angle of the ρ or K * meson. The helicity angle θ H is defined in the rest frame of the ρ or K * and corresponds to the angle between two vectors: one is the momentum of the daughter pion and the other is the direction of the boost into this rest frame from the B meson rest frame; for the ρ + candidate we use the positively charged pion. Table I summarizes the requirements we apply on | cos θ T | and cos θ H . After the selection criteria have been applied, the average number of combinations per event in data is between 1.1 and 1.3, and we select the candidate with the highest χ 2 probability in a geometric fit to a common B-decay vertex. In this way the probability of selecting the correctly reconstructed event is a few percent higher with respect to a random selection.
Further signal/background separation is provided by a Fisher discriminant F exploiting four variables sensitive to the production dynamics and event shape: the polar angles, with respect to the beam axis in the e + e − CM frame, of the B candidate momentum and of the B thrust axis; and the zeroth and second angular moments L 0,2 of the energy flow, excluding the B candidate. The moments are defined by L j = i p i × |cos θ i | j , where i labels a track or neutral cluster, θ i is its angle with respect to the B thrust axis, and p i is its momentum. The mean of F is shifted so that it is independent of the B-flavor tagging category [16] for qq background. The Fisher variable provides about one standard deviation discrimination between B-decay events and continuum background.
We obtain the yields and the charge asymmetries A ch from extended maximum-likelihood (ML) fits to the six observables: ∆E, m ES , F , the masses of the two resonance candidates m η ′ and m ρ/f0/K * , and cos θ H . The fits distinguish among several categories: qq background, BB background, and signal component(s) (one for η ′ ρ + , two for η ′ ρ 0 /f 0 , and three for the η ′ K * modes). For each event i and category j we define the probability density functions (PDFs) P j (x) for the variable x, with the resulting likelihood L: where Y j is the yield for category j and N is the number of events entering the fit. Where applicable, we split the yields by the flavor of the decaying B meson in order to measure A ch . We find correlations among the observables to be significant in the BB components, whereas those are small in the data samples, which contain mostly qq background. An exception occurs in the B + → η ′ ργ K * + K + π 0 mode, for which the correlation between m K * and cos θ H , if not taken into account, may cause large biases in the yield of the different K * components. In this case the factors for m i K * and cos θ i H in Eq. 1 are replaced with a two-dimensional non-parametric PDF [17]. We discuss below our treatment of the somewhat larger correlations found in simulated signal events.
The signal component is studied from the Monte Carlo (MC) simulation [18] of the decay process and the response of the detector and reconstruction chain. Signal events selected in simulation contain both properly reconstructed and incorrectly reconstructed B-meson candidates, which are labeled as "self-crossfeed" (SXF). SXF occurs either when some particles from the correct parent B meson are incorrectly assigned to intermediate resonances or when particles from the rest of the event are used in the signal B reconstruction. The fraction of SXF events ranges between 14% and 32% and we do not separate correctly reconstructed events from SXF in the fit. For the scalar Kπ component, we use the LASS model [19,20], which consists of the K * 0 (1430) resonance together with an effective-range nonresonant component. Backgrounds arising from BB decays to charmless final states are modeled from the simulation. We select the channels (20-40 for each final state) which have a high probability of passing our selection and build a sample of simulated specimens of these, weighting each component by its branching fraction, either measured or estimated. We model from this sample the PDFs for the BB background component and fix its yield (25-350 events, depending on the final state) to the MC prediction. Backgrounds arising from b → c transitions have distributions very similar to those of qq events and thus they are absorbed by the continuum component. For the η ′ ρ modes, we estimate the contribution of the nonresonant η ′ ππ with a fit of the data, selecting only the central region (which excludes the region across the ρ and f 0 resonances) of the η ′ ππ Dalitz plot. The expected nonresonant component is then included in the charmless BB background PDF. This procedure is not necessary for the η ′ K * fits, since the nonresonant η ′ Kπ component is already included in the LASS model. PDF shapes for the signals and BB background are determined from fits to MC samples, while for the qq component we use data sidebands, which we obtain excluding the signal region 5.27 < m ES < 5.29 GeV and |∆E| < 0.075 GeV. The calibration of m ES and ∆E is checked by means of large data control samples of B decays to charmed mesons with topology similar to the decays under study (e.g. B + → D 0 (K + π − π 0 )π + , B + → D 0 (K + π − π 0 )ρ + ).
We use a combination of Gaussian, exponential, and polynomial functions to parameterize most of the PDFs. For the m ES distribution of the qq background component, we use a parameterization motivated by phasespace arguments [21]. The following are free to vary in the fit: the signal and qq background yields and charge asymmetries A ch , along with the parameters that most strongly influence the shape of the continuum background.
We perform fits to ensembles of simulated experiments in order to evaluate the potential bias Y 0 on the fitted signal yield, which originates from our neglect of the correla- Color online: the solid curve is the fit function, black long-dash-dotted is the total background, and the blue dashed curve is the total signal contribution. In (a) we separate the ρ 0 component (red dashed) from the f0 (green dotted). In (c,d) we separate the K * (892) (red dashed), the (Kπ) * 0 (green dotted), and K * 2 (1430) (magenta dot-dashed) components.
tions among the variables. Each such experiment has the same number of signal and background candidates as the data; given that correlations among fit variables are negligible for qq events, these are generated from the PDFs, while signal and BB background events are taken from fully simulated MC samples. In computing the branching fraction B for each mode, we subtract Y 0 from the fitted signal yield Y and divide by the selection efficiency ε for signal events, the number of B mesons in our sample, and the product of the branching fractions of the intermediate resonances, B i . We assume the branching fraction of Υ (4S) to B + B − and B 0 B 0 to be the same and equal to 50%, consistent with the measurements [14]. The efficiency ε is evaluated from the simulation.
The different submodes of η ′ K * 0 and η ′ K * + are combined by adding their −2 ln L curves. For the significance of observation S we take the difference between the value of −2 ln L for the zero signal hypothesis and the value at its minimum. For modes with a significance below five standard deviations, we quote a 90% confidence level (C.L.) upper limit, corresponding to the branching fraction below which lies 90% of the total of the likelihood integral, in the region where the branching fraction is positive. The correlated and uncorrelated systematic uncertainties are taken into account in the above eval-uations by convolving the likelihood function given by the fitter with a Gaussian function representing the systematic uncertainties. The results are collected in Table  II. We show in Fig. 1 the data and the fit functions projected over the variable m ES , while in Fig. 2 we do the same for the ππ and Kπ invariant masses and for cos θ H . In these plots the signals are enhanced by the imposition of cuts on ln L and the fit variables, which retain 40-65% of the signal events.
We evaluate the systematic uncertainties due to the modeling of the signal PDFs by varying the relevant parameters by their uncertainty, derived from the consistency of fits to the above mentioned data control samples. The fit bias arises mostly from correlations among the fit variables, which are modeled by the MC; the associated uncertainty is the sum in quadrature of half the correction itself and its statistical uncertainty; this is the dominant source in most cases (2.1 -15.4 events), especially for the η ′ → ρ 0 γ modes. We verify that the correlations among the variables in SXF events are the major source of bias by performing a dedicated study on simulated experiments in which the SXF component is not embedded. The uncertainty for the SXF fraction is estimated by varying the fraction predicted by the MC by 2.5% (5%) relative for each photon (π 0 ) in the final state (most of this uncertainty originates from the simulation of neutral particles). We estimate the uncertainty on the charmless BB background by repeating the fit with the yield of this component varied by its estimated uncertainty (±20%). For the S-wave Kπ components, we vary the LASS parameters by the uncertainties found in [19] (the resulting uncertainties vary from 0.1 to 14.9 events).
Multiplicative systematic uncertainties (which do not affect the signal significance) account for imperfect knowledge of the luminosity, tracking efficiency, π 0 and K 0 S reconstruction efficiencies, and the uncertainty on the measured branching fractions of intermediate resonances.
In the nominal fit we do not account for interference among the different spin K * components. We estimate in a separate calculation, which takes into account the acceptance functions of our analysis, the potential impact of interference when the relative strong phases between the components are varied over the full range; we find that the uncertainties range from 1.5% to 14.1%.
From the analysis of a variety of data control samples, the bias on A ch is found to be negligible for pions and -0.01 for kaons, due to differences of K + and K − interactions in the detector material. We correct the fitted A ch by +0.01 in the modes where a charged kaon is present and assign a systematic uncertainty of 0.02, mainly due to the bias correction.
In conclusion, we have measured the branching fraction of B mesons to nine different final states; we claim observation of four of these, while we obtain robust ev- and mKπ for (c) η ′ K * 0 , (d) η ′ K * + ; on the bottom row we plot the cosine of the helicity angle θH for (e) η ′ ρ 0 /η ′ f0, (f) η ′ ρ + , (g) η ′ K * 0 , and (h) η ′ K * + . Color online: the solid curve is the fit function, black long-dash-dotted is the total background, and the blue dashed curve is the total signal contribution.
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. Roma, Italy § Now at University of South Alabama, Mobile, Alabama 36688, USA ¶ Also with Università di Sassari, Sassari, Italy II: Signal yield Y and its statistical uncertainty, bias Y0, detection efficiency ǫ, daughter branching fraction product Bi, significance S (with systematic uncertainties included), measured branching fraction B with statistical and systematic errors, 90% C.L. upper limit (U.L.), and charge asymmetry A ch . In the case of η ′ f0, the quoted branching fraction is the product of B(B 0 → η ′ f0) with B(f0 → ππ), which is not well known.