Search for B+ ->phi pi+ and B0 ->phi pi0 Decays

A search has been made for the decays B+ ->phi pi+ and B0->to phi pi0 in a data sample of approximately 232 x 10^6 B Bbar pairs recorded at the Upsilon(4S) resonance with the BaBar detector at the PEP-II B-meson Factory at SLAC. No significant signals have been observed, and therefore upper limits have been set on the branching fractions: BR(B+ ->phi pi+)<2.4 x 10^{-7} and BR(B0->phi pi0)<2.8 x 10^{-7} at 90% probability.

A search has been made for the decays B + → φπ + and B 0 → φπ 0 in a data sample of approximately 232 ×10 6 BB pairs recorded at the Υ (4S) resonance with the BABAR detector at the PEP-II B-meson Factory at SLAC. No significant signals have been observed, and therefore upper limits have been set on the branching fractions: B(B + → φπ + ) < 2.4×10 −7 and B(B 0 → φπ 0 ) < 2.8×10 −7 at 90% probability.
PACS numbers: 13.25.Hw, 12.15.Hh,11.30.Er The measurements of B → φK and B → φπ decay rates are important because they are sensitive to contributions beyond the Standard Model (SM). In particular, the latter is strongly suppressed in the SM, and a measurement of B(B → φπ) > ∼ 10 −7 would be evidence for new physics, for example supersymmetric contributions [1]. The study of the processes B + → φπ + [2] and B 0 → φπ 0 is also important to understand the theoretical uncertainties associated with measurements of CP asymmetries in B 0 → φK 0 decays. The B → φπ decay amplitudes are related to the sub-leading terms of the B 0 → φK 0 decay amplitude [3] and can therefore provide stringent bounds on possible contributions to the time-dependent CP asymmetry in B 0 → φK 0 [4], another probe of new physics effects in B decays.
In Fig. 1 we show the leading order Feynman diagram for the B → φπ decay and a sub-leading diagram for B → φK decay. Previous searches for these decay modes have been reported by BABAR and CLEO [5,6,7]. The results presented here are based on data collected with the BABAR detector [8] at the PEP-II asymmetric-energy e + e − collider [9] located at the Stanford Linear Accelerator Center. An integrated luminosity of 211 fb −1 , corresponding to (231.8±2.6)×10 6 BB pairs, was recorded at the Υ (4S) resonance (center-of-mass energy √ s = 10.58 GeV). Charged particles from the e + e − interactions are detected, and their momenta measured, by a combination of five layers of double-sided silicon microstrip detectors (SVT) and a 40-layer drift chamber (DCH), both operating in the 1.5-T magnetic field of a superconducting solenoid. Photons and electrons are identified with a CsI(Tl) electromagnetic calorimeter (EMC). Further charged particle identification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring imaging Cherenkov detector (DIRC) covering the central region.
Monte Carlo simulation is used to evaluate background contamination and selection efficiency. Signal and background Monte Carlo samples are generated with EvtGen [10]. The detector response is simulated with GEANT4 [11] and all simulated events are reconstructed in the same manner as data.
We reconstruct B meson candidates through the decays φπ + or φπ 0 , with φ → K + K − and π 0 → γγ. All kaon candidate tracks in the reconstructed decay chains must satisfy a set of loose kaon identification criteria based on the response of the DIRC and the dE/dx measurements in the DCH and SVT. In both decay modes, all the tracks coming from the fully reconstructed B are required to originate from the interaction point. A pair of oppositely-charged kaon candidates is considered as a φ candidate if its invariant mass is within 15 MeV/c 2 of the nominal φ mass value (1019.5 MeV/c 2 [12]). This is about three times the observed width in the K + K − invariant mass spectrum. A pair of energy deposits in the EMC, each of which is isolated from any charged track and has the lateral shower shape expected for photons, is considered as a π 0 candidate if both the deposits exceed 40 MeV in the laboratory frame and the associated invariant mass of the pair is between 110 MeV/c 2 and 160 MeV/c 2 (about three times the observed width in the γγ invariant mass spectrum). B meson candidates are made by combining φ candidates with a charged track or a π 0 candidate. We do not apply any particle identification criteria on the track which comes directly from B meson decay (primary track) at this stage, so for the charged mode we reconstruct B + → φh + (h + = π, K) events. This allows us to study the B + → φK + signal, which is the largest background coming from B decays.
Two kinematic variables are used to discriminate between signal B decays and combinatorial background: the invariant mass of the reconstructed B meson candidate, m B and m miss = (q e + e − −q B ) 2 , where q e + e − is the four momentum of the initial e + e − system and q B is the mass-constrained four momentum of the reconstructed B meson candidate. By construction, the linear correlation between m miss and m B vanishes. Compared to the kinematic variables ∆E = E * B − 1 2 √ s and e + e − and the asterisk denotes the e + e − rest frame), which were used in the previous BABAR analysis of these modes [6], the present combination of variables has less correlation and better background suppression. The distribution of m B peaks at the nominal B mass value [12], with a width of about 20 MeV/c 2 for φπ + , and about 40 MeV/c 2 for φπ 0 , with a low-side tail due to energy leakage from the EMC. The resolution on m miss is about 5 MeV/c 2 , dominated by the beam-energy spread. We require m B to be within 150 MeV/c 2 of the nominal B mass and 5.11 GeV/c 2 < m miss < 5.31 GeV/c 2 . The region m miss < 5.2 GeV/c 2 is used for background characterization.
The dominant background comes from combinatorial e + e − → qq (q = u, d, s, c) continuum events. They tend to be jet-like in the center-of-mass (CM) frame, while B decays tend to be spherical. To exploit this characteristic for discriminating against continuum background, we use the ratio L 2 /L 0 , where L i is defined as where p k is the momentum of particle k, and θ k is the angle between p k and the thrust axis of the reconstructed B meson evaluated in the CM frame. The sum runs over the charged and neutral particles of the event not assigned to the B meson. We require L 2 /L 0 < 0.55, which suppresses the continuum background by more than a factor of 3, while retaining about 90% of the signal. We require | cos θ * B | < 0.9, where θ * B is the angle between the B candidate momentum and the e + momentum in the CM frame. For B candidates the probability density function of θ * B is proportional to sin 2 θ * B , whereas for continuum events it is nearly uniform after acceptance. We select events for which one B is reconstructed as B + → φh + or B 0 → φπ 0 and the other B is only partially reconstructed [13]. We define ∆t to be the difference between the proper decay times of the B mesons and σ ∆t the uncertainty associated with it. We require, in the case of B 0 → φπ 0 only, |∆t| < 20 ps and σ ∆t < 2.5 ps. These requirements on ∆t and σ ∆t retain about 92% of the signal, while removing about 15% of the continuum events. The r.m.s. ∆t resolution is 1.1 ps for the events that satisfy these requirements. After the application of these selection criteria on Monte Carlo simulated events, the efficiencies for φπ + and φπ 0 signal are (37.1 ± 0.1)% and (29.5 ± 0.8)% respectively. The average candidate mul-tiplicity in events with at least one candidate is ∼ 1.005 for both decay modes. If more than one B candidate is reconstructed in an event, we choose the one with the φ → K + K − invariant mass closest to the nominal φ mass value [12], for B + → φπ + decays. For B 0 → φπ 0 decays, we choose the candidate with the π 0 → γγ invariant mass closest to the nominal π 0 mass value [12]. These criteria produce no bias in the shape of the other event variables used in the maximum likelihood fit described below. We select 10990 and 2732 events in the φh + and φπ 0 analyses respectively.
A possible background to the φ → K + K − decays comes from the S-wave production of the K + K − system (B → (K + K − ) S−wave π decays) with contributions coming predominantly from resonances such as f 0 (980) and a 0 (980). Using samples of simulated decays of B mesons equivalent to nearly five times the size of the data sample, we found that all the other B decay modes give negligible sources of background. To discriminate against S-wave background in the maximum likelihood fit, we use the helicity of the K + K − system, in terms of the cosine of the angle θ H between the K + candidate and the parent B meson flight direction in the K + K − rest frame. The helicity probability density function is proportional to cos 2 θ H for the signal, and is uniformly distributed for the S-wave background. Further discrimination is provided by the K + K − invariant mass distribution, m KK , which peaks at the φ mass for the signal, while it peaks at lower values for the S-wave background.
In the case of charged B decays, we exploit the Cherenkov angle θ c measured in the DIRC for the primary track, in order to determine simultaneously the yields of B + → φπ + and B + → φK + decays and the yields of the two corresponding B + → (K + K − ) S−wave h + (h = π, K) background components.
Signal and background yields N i , where i denotes signal, continuum, and S-wave background, are extracted using an extended maximum likelihood fit with the likelihood function: where N is the total number of events entering the fit. The probabilities P i are products of Probability Density Functions (PDF) for each of the independent variables x = {m miss , m B , L 2 /L 0 , m KK , cos θ H }. In the case of B + → φh + the variable θ c is also used in the fit. The α i are the parameters of the PDFs for x. The continuum parameters are allowed to vary, except for the m miss end-point. All other parameters α i are fixed to their values derived from data control samples. These are varied within their uncertainties to evaluate the systematic error. By minimizing the quantity − ln L in two separate fits, we determine the yields for φπ + and φπ 0 .
There are three B backgrounds to B + → φπ + decay (B + → (K + K − ) S−wave h + and B + → φK + ), while only B 0 → (K + K − ) S−wave π 0 contributes to the B 0 → φπ 0 mode. All the yields in Eq. 2 are allowed to fluctuate to negative values in the fits. The distributions of L 2 /L 0 and cos θ H are described by a parametric step function [14] and a second-order polynomial respectively. We use a Gaussian for the m miss distribution for φπ + signal and S-wave components, a Gaussian with exponential tails for the m B distribution for φπ + signal and S-wave components, and for both m miss and m B for φπ 0 signal and S-wave components. For the continuum m miss distribution we use the function , with x ≡ 2m miss / √ s and ξ a floating parameter. The m KK invariant mass distribution is described by a relativistic Breit-Wigner function for signal, a relativistic Breit-Wigner plus exponential for the continuum background and a Flatté [15,16] function for the S-wave background. The Flatté function takes into account the coupling of the scalar resonances to the π + π − and K + K − channels [17].
The Cherenkov angle θ c PDFs are obtained from a large data sample of D * + → D 0 π + (D 0 → K − π + ) decays where K ∓ /π ± tracks are identified through the charge correlation with the π ± from the D * ± decay. The PDFs are constructed separately for K + , K − , π + and π − tracks as a function of momentum and polar angle using the expected values of θ c , and its uncertainty.
Using a large number of simulated experiments, we find that the usual maximum likelihood fitting technique does not provide an unbiased estimate of the true values of signal and S-wave yields (N S and N S−wave ) because of the non-Gaussian shape of the likelihood function when the yield is very small. Therefore we use a Bayesian statistical approach to obtain a modified likelihood function L(N S ): where the normalization N 0 is such that The two dimensional likelihood L(N S , N S−wave ) is given at each point on the N S -N S−wave plane by the function defined in Eq. 2, maximized with respect to all of the other fit variables. When seeking the central value for the branching fraction we take the median of L, with the lower limit replaced by −∞ and N S unrestricted. This is because we find from simulations that in the case of very low yields, the median provides a less biased estimator of the true value of N S than the maximum of L. We correct the central value of the branching fractions for the residual biases. When calculating upper limits, we impose the a priori constraints N S > 0 and N S−wave > 0. Fig. 2 shows the m miss and m B distributions for data, with the PDF corresponding to the maximum likelihood fit overlaid. We do not observe evidence for either B + → φπ + or B 0 → φπ 0 decays. I: Signal yield (evaluated as the median of the likelihood), detection efficiency ε (the uncertainty includes both statistical and systematic effects), measured branching fraction B with statistical error, after the correction for the fit bias has been applied, for the two decay modes considered and upper limit at 90% probability.
The signal yields, extracted from the median of the likelihood L(N S ) (Eq. 3), are reported in Table I. In the case of B + → φh + , we also measure the N φK + yield, which is found to be compatible with the expectation from published branching fractions [5].
The branching fraction B is calculated from the observed number of signal events as where N BB is the number of BB pairs produced and ε is the reconstruction efficiency for the B candidates. In Eq. 4 we assume equal branching fractions for Υ (4S) decays to charged and neutral B-meson pairs [18]. The systematic uncertainties are summarized in Table II. The uncertainty arising from the lack of knowledge of continuum background PDFs is part of the statistical error since the background parameters are free to vary in the fit. The uncertainty on the signal PDFs represents the dominant error. We estimate it by using simulated and high-statistics data control samples of B + → π + D 0 (D 0 → K + π − ) and B 0 → π + D − (D − → K 0 S π − ) events. In order to estimate the systematic uncertainty on m B for B 0 → φπ 0 we use a data control sample of  B + → h + π 0 events. The control channels have event topologies similar to those of B + → φh + and B 0 → φπ 0 . We use them to determine the signal PDF parameters and take the difference in yields found by varying these parameters within one standard deviation as the systematic error. The second most important error comes from the uncertainty on the efficiency ε. The track detection efficiency uncertainty is estimated to be 0.8% per track from a study of a variety of control samples, such as τ → 3-track decays. We assign 0.5% uncertainty on the kaon identification efficiency. The uncertainty on the reconstruction efficiency for the π 0 is 3%, as measured in a large sample of τ − → ρ − ν τ , ρ − → π − π 0 decays coming from e + e − → τ + τ − . We assign a 1.8% uncertainty on the L 2 /L 0 cut efficiency, estimated by the difference between Monte Carlo and data control samples, 1.1% on the total number of Υ (4S) → BB decays in the sample and 1.2% on the knowledge of B(π 0 → γγ) and B(φ → K + K − ). We estimate the systematic error introduced by the approximation of ignoring interference effects between the φ and the K + K − S-wave components by varying the relative strong phases and taking the largest observed variation as the error. In this study we include the f 0 (980) resonance and a non-resonant component, whose contribution is taken from a B + → K + K − K + Dalitz plot measurement by the Belle Collaboration [19]. The resulting uncertainty is 4.4% for both modes.
Under the assumption that N BB and ε are distributed as Gaussians, we obtain a likelihood function, L B , for the branching fraction, B, based on Eq. 4, by convolving the likelihood (L in Eq. 3) with the distributions of N BB and ε. We also include the additional uncertainty coming from the systematic error on the signal yield. The resulting likelihood is shown in Fig. 3 for each of the two decay modes. In the plots, the upper boundary of the dark region represents the 90% probability Bayesian upper limit B UL , defined as: We determine B(B + → φπ + ) < 2.4 × 10 −7 and B(B 0 → φπ 0 ) < 2.8 × 10 −7 . We compute the central values for the branching fractions by correcting the fitted signal yields for the fit bias, estimated using a large number of simulated experiments, and including a systematic uncertainty equivalent to half the fit bias. This error corresponds to a shift of −0.8 and −0.4 events in the signal yield, and −1.9 × 10 −8 and −1.2 × 10 −8 in the branching fraction for B + → φπ + and B 0 → φπ 0 , respectively. Without taking into account the a priori knowledge of N S > 0 and N S−wave > 0, and integrating the likelihood in Eq. 3 around the median, we obtain as 68%-probability regions B(B + → φπ + ) = (−0.04 ± 0.17) × 10 −6 and  Table I.
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. This work is supported by DOE