Searches for B meson decays to phiphi, phirho, phifzero(980), and fzero(980)fzero(980) final states

We present the results of searches for B decays to charmless final states involving phi, fzero(980), and charged or neutral rho mesons. The data sample corresponds to 384 million BBbar pairs collected with the babar detector operating at the PEP-II asymmetric-energy epem collider at SLAC. We find no significant signals and determine the following 90% confidence level upper limits on the branching fractions, including systematic uncertainties: B(B0->phiphi)<2.0 x 10^-7, B(B+->phirho+)<30 x 10^-7, B(B0->phirho0)<3.3 x 10^-7, B(B0-phif0) x B(f0->pi+pi-)<3.8 x 10^-7, and B(B0->f0f0) x B(f0->pi+pi-) x B(f0->K+K-)<2.3 x 10^-7

The B decays to φφ and φρ are complicated by the presence of one amplitude with longitudinal polarization and two amplitudes with transverse polarization. The fraction of longitudinally polarized events is denoted by f L . Integrating over the angle between the vector meson decay planes, the angular distribution where the indices 1, 2 label the two vector mesons in the final state, and the helicity angles θ 1,2 are the angles between the direction opposite to that of the B 0 (B + ) and the K + or π + (π 0 ) momentum in the φ or ρ 0 (ρ + ) rest frame. We define the angles θ 1,2 for f 0 mesons in an analogous way. The expected values of f L range from 0.6 to 0.8 [3,4,6,7] for B 0 → φφ, φρ 0 , and B ± → φρ ± . The presence of NP could lead to enhancements of the transverse polarization amplitudes [2,3,6]. The current upper limit on the B 0 → φφ branching fraction, obtained from a data sample of 82 fb −1 , is 1.5×10 −6 [10]. The upper limits on B 0 → φρ 0 and B + → φρ + , determined using 3.1 fb −1 of data, are 1.3×10 −5 and 1.6×10 −5 [11], respectively. Using a data sample of 349 fb −1 , BABAR recently reported an upper limit of 1.6×10 −7 for B 0 → f 0 f 0 [12]. This last result relies on the assumption that the f 0 → π + π − branching fraction is 100%. In this analysis, we make the complimentary assumption that one f 0 decays to π + π − and the other to K + K − and search for B 0 → f 0 f 0 in a cleaner final state than Ref. [12]. All these limits correspond to a confidence level (C.L.) of 90%.
The results presented here are based on an integrated luminosity of 349fb −1 , corresponding to (384 ± 4) million BB pairs. These data were recorded at the Υ (4S) resonance with a center-of-mass (CM) energy √ s = 10.58 GeV. The BABAR detector is described in detail elsewhere [13], and is situated at the interaction region of the PEP-II asymmetric energy e + e − collider located at the Stanford Linear Accelerator Center (SLAC). We use Monte Carlo (MC) simulated events generated using the GEANT4 based [14] BABAR simulation.
Photons are reconstructed from localized deposits of energy greater than 50 MeV in the electromagnetic calorimeter that are not associated with a charged track. We require γ candidates to have a lateral shower profile [15] that is consistent with the expectation for photons. π 0 candidates are reconstructed from two γ candidates with invariant mass 0.10 < m γγ < 0.16 GeV/c 2 .
We use information from the vertex detector, drift chamber and detector of internally reflected Cherenkov light to select charged tracks that are consistent with kaon or pion signatures in the detector [16]. We reconstruct φ (ρ 0 ) candidates from pairs of oppositely charged kaon (pion) candidates with invariant mass 0.99 < m KK < 1.05 GeV/c 2 (0.55 < m ππ < 1.05 GeV/c 2 ). For ρ 0 candidates we require the helicity angles to satisfy | cos θ i | < 0.98 since signal efficiency falls off near | cos θ i | = 1. Charged ρ candidates are reconstructed from a charged track consistent with the pion signature and a π 0 candidate. The invariant mass m ππ 0 of the ρ + candidate is required to lie between 0.5 and 1.0 GeV/c 2 . We also require that the helicity angles satisfy −0.8 < cos θ i < 0.98 as signal efficiency is asymmetric because of the π 0 meson, and falls off near cos θ i = ±1, and background peaks near −1. We select f 0 candidates from two charged tracks that are both either consistent with the kaon or the pion signature in the detector. We apply the same selection criteria to f 0 → π + π − candidates as for ρ 0 mesons. Similarly we apply the same selection criteria to f 0 → K + K − candidates as for φ mesons as the minimum m KK we can reconstruct in the detector is 0.99 GeV/c 2 .
We reconstruct signal B candidates (B rec ) from combinations of two φ mesons, one φ and one ρ or f 0 , and two f 0 mesons. The f 0 f 0 mode is required to have one f 0 decaying into π + π − , and the other decaying into K + K − . We require the f 0 in φf 0 to decay into π + π − .
We use two kinematic variables, m ES and ∆E, in order to isolate the signal: is the beam-energy substituted mass and ∆E = E * B − √ s/2 is the difference between the B candidate energy and the beam energy in the e + e − CM frame. Here the B rec momentum p B and four-momentum of the initial state (E i , p i ) are defined in the laboratory frame, and E * B is the B rec energy in the e + e − CM frame. The distribution of m ES (∆E) peaks at the B mass (near zero) for signal events and does not peak for background. We require m ES > 5.25 GeV/c 2 . For the φφ final state we require |∆E| < 0.15 GeV. To reduce background from non-signal B meson decays we apply the more stringent cut of −0.07 < ∆E < 0.15 GeV for all other modes.
The angle in CM frame between the thrust axis of the rest of the event (ROE) and that of the B candidate is required to satisfy | cos(θ TB,TR )| < 0.8 in order to reduce background from e + e − → qq (q = u, d, s, c) continuum events. The variable | cos(θ TB,TR )| is strongly peaked near 1 for qq events, whereas BB events are more isotropic because the B mesons are produced close to the kinematic threshold. Additional separation between signal and continuum events is obtained by combining several kinematic and topological variables into a Fisher discriminant F , which we use in the maximum-likelihood fit described below. The variables | cos(θ TB,TR )|, |∆t|/σ(∆t), | cos(θ B,Z )|, | cos(θ TB,Z )|, and the output of a multivariate tagging algorithm [17] are used as inputs to F . The time interval ∆t is calculated from the measured separation distance ∆z between the decay vertices of B rec and the other B in the event (B ROE ) along the beam axis (z). The vertex of B rec is reconstructed from the tracks that come from the signal candidate; the vertex of B ROE is reconstructed from tracks in the ROE, with constraints from the beam spot location and the B rec momentum. The uncertainty on the measured value of ∆t is σ(∆t). The variable θ B,Z is the angle between the direction of B rec and the z axis in the CM frame. This variable follows a sine squared distribution for BB events, whereas it is almost uniform for qq. The variable θ TB,Z is the angle between the B thrust direction and the z axis in the laboratory frame.
The decay modes studied are classified into three groups according to the final state particles: (i) B 0 → φφ, (ii) B + → φρ + , and (iii) B 0 → φρ 0 , B 0 → φf 0 , and B 0 → f 0 f 0 . We find that 6% of events for the mode in group (ii) and 3% of events for the modes in group (iii) have more than one candidate that passes our selection criteria. For such events we retain the candidate with the smallest χ 2 for the B rec vertex for use in the fits described below. The numbers of selected candidates are given in Table I.
The dominant background for all modes comes from continuum events. The yield of this background component is determined from the fit to data. The dominant B backgrounds for group (i) are B 0 → φK * 0 and f 0 K * 0 , which are estimated to contribute 1.4 and 0.6 events to the data, respectively. The B backgrounds for group (ii) are events from B decays to final states including charm and B + → φK * + . These are estimated to contribute 107 and 5.5 events to the data. The B backgrounds for group (iii) are events from B decays to final states including charm, B 0 decays to φK * 0 , f 0 K * 0 , φK * 0 2 (1430), and B + decays to φK + and φK * + estimated to contribute 249, 25.9, 9.1, 2.3, 4.7, and 1.8 events to the data. The branching fractions for the B backgrounds are taken from Ref. [18], except for B 0 → f 0 K * 0 , which has not yet been measured, and φρ + where we use the results obtained here. The current upper limit on the B 0 → f 0 K * 0 branching fraction is 4.3×10 −6 and we assume a branching fraction of (2 ± 2)×10 −6 . We obtain yields for each mode from extended unbinned maximum likelihood (ML) fits with the input observables m ES , ∆E, and cos θ 1,2 . In addition, for all modes except φφ, we include m 1,2 and F in the likelihood, where m 1,2 is m ππ or m KK for the φ, ρ or f 0 candidates. A total of three fits are performed, one for each group of signal modes. We include event hypotheses for signal events and the aforementioned backgrounds in each of the fits. For each event i and hypothesis j, the likelihood function is where N is the number of input events, N j is the number of hypotheses, n j is the number of events for hypothesis j and P j (x i ) is the corresponding probability density function (PDF) evaluated for the observables x i of the i th event. The correlations between input observables are small and are assumed to be negligible. Possible biases due to residual correlations are evaluated as described below. We compute the combined PDFs P j (x i ) as the product of PDFs for each of the input observables. These combined PDFs are used in the fit to the data. For B decays to φφ and φρ, the m ES distribution is parametrized with the sum of a Gaussian and a Gaussian with a low-side exponential component. The ∆E distribution is described by the sum of two Gaussian distributions, and the cos θ 1,2 distributions are described by Eq. (1) multiplied by an acceptance function. The acceptance function is a polynomial for all cos θ 1,2 , with the exception of the ρ + helicity angle distribution for longitudinally polarized φρ + , which uses a polynomial multiplied by the sigmoid function 1/(1 + exp[α(cos θ 1,2 + β)]), where the parameters α and β are determined from MC simulated data. For the φρ final states we use a Gaussian to describe the F distribution, and the sum of a relativistic Breit-Wigner (BW) with two Gaussians for m 1,2 . The continuum background m ES distribution is described by an ARGUS function [19]. We parameterize the continuum ∆E distribution using a second-order polynomial and use polynomials to describe cos θ 1,2 . Where appropriate, we parameterize the F distributions for the continuum background using a Gaussian, and we parameterize the m 1,2 distributions using the sum of a BW and a polynomial. We use smoothed histograms of MC simulated data as the PDFs for all other signal and background modes. We generate B 0 → φf 0 assuming that the I: Number of events N in the data sample, signal yield YS (corrected for fit bias), fit bias, detection efficiency ǫ, daughter branching fraction product ( Q Bi), significance σ (including additive systematic uncertainties, taken to be zero if the fitted yield is negative), measured branching fraction where the first error is statistical, and the second systematic (see text), and the 90% C.L. upper limit on this branching fraction (including systematic uncertainties). For B decays to φφ and φρ, two efficiencies are reported, one for longitudinally and one for transversely polarized events. The reported branching fractions for φf0 and f0f0 are product branching fractions that are not corrected for the probability of f0 decaying into π + π − or K + K − . φ is longitudinally polarised, and we use phase space distributions for B 0 → f 0 f 0 . Before fitting the data, we validate the fitting procedure using the methods described in Ref. [20]. We determine a bias correction on our ability to correctly determine the signal yield using ensembles of simulated experiments generated from samples of MC simulated data for the signal and exclusive backgrounds and from the PDFs for the other backgrounds.
Our results are summarized in Table I where we show the measured yield, fit bias, efficiency, and the product of daughter branching fractions for each decay mode. We compute the branching fractions from the fitted signal event yields corrected for the fit bias, reconstruction efficiency, daughter branching fractions, and the number of produced B mesons, assuming equal production rates of charged and neutral B pairs. As we do not know the value of f L for the φφ and φρ modes, we fit the data for different physically allowed values of f L in steps of 0.1. We find no evidence for any of the signal modes and calculate 90% C.L. branching fraction upper limits x UL such that where L(Y S , f L ) is the likelihood as a function of signal yield Y S and f L multiplied by a uniform prior. We report the most conservative (largest) upper limits for each mode, for which f L = 0.5, 0.7, and 0.2 for groups (i), (ii), and (iii), respectively. The central values of the branching fractions given in Table I correspond to these values of f L . Figure 1 shows the m ES distributions in subsamples of the data where |∆E| < 0.05 GeV for B + → φρ + , and |∆E| < 0.025 GeV for all other modes.
We estimate the systematic uncertainty related to the parameterization of the PDF by varying each parameter by its estimated uncertainty, and by substituting smoothed histograms by un-smoothed ones. The total contribution of all variations in signal yields, when added in quadrature, gives an error between 0.2 and 5.6 events, depending on the mode. We account for possible differences between data and MC events from studies of a control sample of B → Dπ events, yielding an uncertainty of 0.1 to 12.2 events depending on the mode. The uncertainty from fit bias is taken to be half the correction listed in Table I. Incorporating the statistical uncertainty of the bias has a negligible effect. The uncertainty on B-daughter branching fractions is in the range (1.2 to 4.9)% [18]. The modes in group (iii), φρ 0 , φf 0 , and f 0 f 0 have systematic uncertainties from the f 0 lineshape [21] of 0.2, 3.1, and 15.9 events, respectively. The mode B + → φρ + has a fractional systematic uncertainty of 3.0% from the reconstruction efficiency of π 0 mesons.