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Evidence for the decay B0 -->omega omega and search for B0 -->omega phi

We describe searches for B meson decays to the charmless vector-vector final states omega omega and omega phi with 471 x 10^6 B Bbar pairs produced in e+ e- annihilation at sqrt(s) = 10.58 GeV using the BABAR detector at the PEP-II collider at the SLAC National Accelerator Laboratory. We measure the branching fraction B(B0 -->omega omega) = (1.2 +- 0.3 +0.3-0.2) x 10^-6, where the first uncertainty is statistical and the second is systematic, corresponding to a significance of 4.4 standard deviations. We also determine the upper limit B(B0 -->omega phi)<0.7 x 10^-6 at 90% confidence level. These measurements provide the first evidence for the decay B0 -->omega omega, and an improvement of the upper limit for the decay B0 -->omega phi.

We describe searches for B meson decays to the charmless vector-vector final states ωω and ωφ with 471×10 6 BB pairs produced in e + e − annihilation at √ s = 10.58 GeV using the BABAR detector at the PEP-II collider at the SLAC National Accelerator Laboratory. We measure the branching fraction B(B 0 → ωω) = (1.2 ± 0.3 +0. 3 −0.2 ) × 10 −6 , where the first uncertainty is statistical and the second is systematic, corresponding to a significance of 4.4 standard deviations. We also determine the upper limit B(B 0 → ωφ) < 0.7 × 10 −6 at 90% confidence level. These measurements provide the first evidence for the decay B 0 → ωω, and an improvement of the upper limit for the decay B 0 → ωφ.
PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er Charmless decays of B mesons to two vector mesons have been of significant recent interest, in part because of the unexpectedly small value of the longitudinal polarization component observed in B → φK * decays [1,2]. The resulting large transverse spin component could be due either to unanticipated large Standard Model (SM) contributions [3] or to non-SM effects [4]. Further information and SM constraints on these decays can be obtained from measurements of, or limits on, the branching fractions of related decays, such as B 0 → ωω and B 0 → ωφ [5]. These latter decays are also important because they contain relatively unstudied b → d quark transitions (B 0 → ωω however is expected to be dominated by b → u transitions) and are sensitive to the phase angles α and γ of the Cabibbo-Kobayashi-Maskawa quark mixing matrix [6]. Deviations of the observed branching fractions from their SM expectations could provide evidence for physics beyond the SM.
Due to the limited size of the data sample, there is insufficient precision to determine the decay polarization in B 0 → ωω or B 0 → ωφ. We therefore integrate over the angular distributions, correcting for detector acceptance and efficiency. The angular distribution is where V 1,2 = ({ω, ω} or {ω, φ}) are vector mesons, θ V1,2 are helicity angles, and f L is the fraction of events with longitudinal spin polarization. For the φ meson, θ φ is the angle in the φ rest frame between the positively charged kaon and the boost from the B rest frame, whereas for the ω, θ ω is the angle in the ω rest frame between the normal to the ω decay plane and the boost from the B rest frame. For both B 0 → ωω and B 0 → ωφ, f L is predicted to be 80% or larger [10]. The data were collected with the BABAR detector [11] at the PEP-II asymmetric-energy e + e − collider located at the SLAC National Accelerator Laboratory. An integrated luminosity of 429 fb −1 [12], corresponding to N BB = (471 ± 3) × 10 6 BB pairs, was recorded at the Υ (4S) resonance (center-of-mass energy √ s = 10.58 GeV). Charged particles are detected, and their momenta measured, by 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. Charged particle identification (PID) is provided by energy loss measurements in the tracking detector and by a ring-imaging Cherenkov detector.
We reconstruct the vector-meson decays through the ω → π + π − π 0 and φ → K + K − channels, with π 0 → γγ. The minimum laboratory energy (momentum) required for photons (charged kaons) is 50 MeV (100 MeV). There is no specific minimum momentum requirement for charged pions but they generally respect p T > 50 MeV. Charged pion and kaon candidates are rejected if their PID signature satisfies tight consistency with protons or electrons, and the kaons must have a kaon signature, while the pions must not. We require all charged particle products associated with the B meson candidate decay to be consistent with having originated at a common vertex.
We apply the invariant mass requirements listed in Table I for the π 0 , ω, and φ mesons. After selection, the π 0 is constrained to its nominal mass [13], which improves the ω mass resolution. The restrictions on the ω and φ meson masses are loose enough to incorporate sideband regions.
A B meson candidate is characterized kinematically by the energy-substituted mass m ES = are the four-momenta of the Υ (4S) and the B candidate, respectively, and the asterisk denotes the Υ (4S) rest frame (quantities without asterisks are measured in the laboratory frame).
For correctly reconstructed signal candidates, ∆E and m ES peak at values of zero and m B , respectively, with resolutions of about 30 MeV and 3.0 MeV. Thus, signal events for this analysis mostly fall in the regions |∆E| ≤ 0.1 GeV and 5.27 ≤ m ES ≤ 5.29 GeV.
To incorporate sideband regions, we require |∆E| ≤ 0.2 GeV and 5.24 ≤ m ES ≤ 5.29 GeV. The average number of candidates found per selected event is 1.3 for B 0 → ωφ decays and 1.7 for B 0 → ωω decays. We choose the candidate with the smallest χ 2 value constructed from the deviations of the ω and φ resonance masses from their nominal values [13].
Backgrounds arise primarily from random combinations of particles in continuum events (e + e − → qq, with q = u, d, s, c). We reduce this background by using the angle θ T in the Υ (4S) rest frame between the thrust axis [14] of the B candidate and the thrust axis of the other charged and neutral particles in the event. The distribution of | cos θ T | is sharply peaked near 1.0 for qq jet pairs, and nearly uniform for B meson decays. We require | cos θ T | < 0.9 for B 0 → ωφ and | cos θ T | < 0.8 for B 0 → ωω.
We employ a maximum-likelihood fit, described below, to determine the signal and background yields. For the purposes of this fit, we construct a Fisher discriminant [15] F that combines four variables defined in the Υ (4S) frame: the polar angles with respect to the beam axis of the B meson momentum and B thrust axis, and the zeroth and second angular moments L 0 and L 2 of the energy flow about the B thrust axis. The moments are defined by L j = i p i × |cos θ i | j , where θ i is the angle with respect to the B thrust axis of a charged or neutral particle i, p i is its momentum, and the sum excludes the B candidate daughters.
From simulated event samples produced with Monte Carlo (MC) event generators [16], we identify the most important backgrounds that arise from other BB decay modes. Most of the BB background does not peak in m ES or ∆E and is grouped with continuum events into a "combinatoric" background category. Other BB decay modes, such as B 0 → ωωπ 0 , B 0 → ωφπ 0 , B 0 → ωρπ, B 0 → ωa 1 , etc., peak in m ES and/or ∆E and are referred to as "peaking" background. All peaking modes are grouped together into a single background component, with a broad peak centered at negative values of ∆E, and which is fitted in data simultaneously with the signal and combinatoric background components.
We obtain signal and background yields from extended unbinned maximum-likelihood fits with input observables ∆E, m ES , F , and, for the vector meson V = ω or φ, the mass m V and the cosine of the helicity angle cos θ V . For each ω meson, there is an additional helicity angle input observable, cos Φ ω , provided by the polar angle, with respect to the ω flight direction, of the π 0 in the π + π − rest frame. This angle is uncorrelated with the other input observables and has a distribution that is proportional to sin 2 Φ ω for signal. For background, the angular distribution is nearly flat in cos Φ ω , and its deviation from flatness is parameterized by separate thirdorder polynomials for combinatoric and for peaking BB backgrounds. For each event i and component j (signal, combinatoric background, peaking BB background) we define the probability density function (PDF) where the last of the P j terms is not present for B 0 → ωφ. The likelihood function is where Y j is the event yield for component j and N is the number of events in the sample. For signal events, the PDF factor takes the form where Q corresponds to the right-hand side of Eq.
(1) after modification to account for detector acceptance. For combinatoric background events, the PDF factor is given for each vector meson independently by distinguishing between genuine resonance (P peak ) and combinatorial (P cont ) components. The background PDFs P peak (cos θ i V ) and P cont (cos θ i V ) are given by separately fitted third-order polynomials. For the peaking BB background, we assume that all four mass and helicity angle observables are independent.
To describe the PDFs for signal, we use the sum of two Gaussians for P sig (m ES ) and for P sig (∆E). An asymmetric Gaussian is used for P sig (F ), i.e., two half-Gaussian distributions (one on the right side of the mean and one on the left side) with different values for the standard deviation, summed with a small additional Gaussian component to account for misreconstructed signal events. The m ES , ∆E, and F PDFs for peaking BB background have the same functional form as for signal events, but their parameters are determined separately. The genuine resonance components of P j (m V ) are both described by relativistic Breit-Wigner distributions, each convolved with the sum of two Gaussians to account for detector resolution, while the combinatoric components of P j (m V ) are described by third-order polynomials. For the combinatoric background category, the m ES distribution is described by an ARGUS function [17], the ∆E distribution by a second-order polynomial, and the F distribution by an asymmetric Gaussian summed with an additional Gaussian. The background PDF parameters that are allowed to vary in the fit are the ARGUS function parameter ξ for m ES , the polynomial coefficients describing the combinatorial and the peaking BB components for ∆E and m V , and the BB peak position and the two standard-deviation parameters of the asymmetric Gaussian for F .
For signal events, the PDF parameters are determined from simulation. We study large control samples of B → D ( * ) X events with similar topology to the signal modes, such as B 0 → D − ρ + , to verify the simulated resolutions in m ES and ∆E. We make (small) adjustments to the signal PDFs to account for any differences that are found.
In the fit to data, 13 parameters (out of around 130) are allowed to vary for each mode including the yields Y j of the signal, total peaking BB background, and total combinatoric background, and ten parameters of the continuum background PDFs. For both modes, we set f L to 0.88, a value consistent with theoretical expectation [10]. The event yields with their statistical uncertainties are presented in Table II.
We evaluate possible biases in the signal yields, which might arise as a consequence of neglected correlations between the discriminating variables, by applying our fit to an ensemble of simulated experiments. The numbers of signal and peaking BB background events in these samples are Poisson-distributed around the observed values and are extracted randomly from MC samples that include simulation of the detector. The largest of the correlations (approximately 15%) is between the analysis variables m ES and ∆E. The signal yield bias Y bias sig we find for each mode is provided in Table II. The resulting branching fractions are calculated as where the signal efficiencies ǫ are evaluated using MC and data control samples. The total number of BB pairs in data N BB is evaluated using a dedicated analysis [18]. The systematic uncertainties on the branching fractions are summarized in Table III. The uncertainty attributed to the yield-bias correction is taken to be the quadrature sum of two terms: half of the bias correction and the statistical uncertainty on the bias itself. The uncertainties of PDF parameters that are fixed in the fit are evaluated by taking the difference between the respective parameter values determined in fits to simulated and observed B → D ( * ) X events. Varying the signal PDF parameters within these uncertainties, we estimate yield uncertainties for each mode. Similarly, the uncertainty due II: Fitted signal yield Ysig and its statistical uncertainty, signal yield bias Y bias sig , peaking BB and combinatoric background yields Y peak and Y comb and their statistical uncertainties, signal detection efficiency ǫ and its statistical uncertainty, daughter branching fraction product Bi and its total uncertainty, significance S (with systematic uncertainties included), measured branching fraction B (bold if evidence for signal is seen), and 90% CL upper limit (UL, bold if no evidence) for the B 0 → ωω and B 0 → ωφ decay modes.

Mode
Ysig  +26. 3 -9.7 +31.5 -69.5 to the modeling of the peaking BB background is estimated as the change in the signal yield when the number of peaking BB background events is fixed (to within one standard deviation) of the expectation from simulation. We evaluate an uncertainty related to the constraint that all charged particles in the B candidate emanate from a common vertex by the change in signal yield when this requirement is removed. The uncertainty associated with f L is evaluated by the change relative to the standard result when f L is varied between the extreme values of 0.58 (the value of f L in B → φK * decays) and 1.0. Systematic uncertainties associated with the selection efficiency, evaluated with data control samples, are 0.8% × N t and 3.0% × N π 0 , where N t is the number of tracks and N π 0 the number of π 0 mesons [19]. The uncertainty of N BB is 0.6% [18]. World averages [13] provide the uncertainties in the B-daughter product branching fractions (1-2%). The uncertainty associated with the requirement on cos θ T is 1-2% depending on the decay mode.
Table II also presents the measured branching fractions, total associated uncertainties, and significances. The significance, which we denote in terms of the analogous number of Gaussian standard deviations, is taken as the square root of the difference between the value of −2 ln L (with systematic uncertainties included) for zero signal events and the value at its minimum. The behavior of −2 ln L(B) for the two modes is shown in Fig. 1. We find evidence for B 0 → ωω decays at the level of 4.4 standard deviations including systematic uncertainties. For each mode we also quote a 90% CL upper limit, taken to be the branching fraction below which lies 90% of the total of the likelihood integral in the positive branching fraction region. In calculating branching fractions we assume that the decay rates of the Υ (4S) to B + B − and B 0 B 0 are equal [13].
and | cos θ T | < 0.8, with |∆E| < 30 MeV for the two m ES plots and m ES > 5.274 GeV for the two ∆E plots. These criteria retain 23% (40%) of B 0 → ωω (B 0 → ωφ) signal events, and in both modes reject over 99% of the background events.
In summary, we have performed searches for B 0 → ωω and ωφ decays. We establish the following branching . The solid curve gives the total PDF (computed without the variable plotted), the dashed curve is the signal contribution, and the dot-dashed curve is the background contribution, which includes both combinatoric and peaking BB backgrounds.
For the branching fraction, the first uncertainty is statistical and the second is systematic. These results provide the first evidence for B 0 → ωω decays and improve the constraint on the B 0 → ωφ branching fraction. Our results are in agreement with theoretical estimates [7,10].
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