Search for B0 ->K*+ K*-

We report the results of a search for the decay B0 ->K*+ K*- with a sample of 454 +/- 5 million BBbar pairs collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at the Stanford Linear Accelerator Center. We obtain an upper limit at the 90% confidence level on the branching fraction for Br(B0 ->K*+ K*-)<2.0 x 10^{-6}, assuming the decay is fully longitudinally polarized.

without a charm quark probes the dynamics of both weak and strong interactions, and plays an important role in understanding CP violation. Improved experimental measurements of these charmless decays, combined with theoretical developments, can provide significant constraints on the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters [1] and uncover evidence for physics beyond the standard model [2,3].
QCD factorization models predict the angular distribution of the decay of the B meson to two vector particles (VV), as measured by the longitudinal polarization fraction f L , to be ∼ 0.9 for both tree-and penguindominated decays [4]. Two measurements of the pure penguin V V decay B → φK * give f L = 0.52 ± 0.08 ± 0.03 and f L = 0.49 ± 0.05 ± 0.03 [5], while f L = 0.81 +0. 10 −0.12 ± 0.06 has recently been measured for the decay B 0 → K * 0 K * 0 [6]. Several attempts to understand the values of f L within or beyond the standard model have been made [7]. Further information about decays related by SU (3) symmetry may provide insights into this polarization puzzle and test factorization models.
The decay B 0 → K * + K * − is expected to occur through a b → u quark transition via W -exchange, as shown in Figure 1, or from final-state interactions. Its branching fraction is expected to be small, with Beneke, Rohrer and Yang [2] predicting (0.09 +0.05+0. 12 −0.03−0.10 ) × 10 −6 , while Cheng and Yang [3] quote (0.1 ± 0.0 ± 0.1) × 10 −6 , both based on QCD factorization. The current experimental upper limit on the branching fraction at the 90% confidence level (C.L.) is 141(89) × 10 −6 [8], assuming a fully longitudinally (transversely) polarized system. Searches for the related decay B 0 → K + K − have produced upper limits on the branching fraction at the 90% C.L. in the range (0.4 − 0.8) × 10 −6 [9] We report on a search for the decay mode B 0 → K * + K * − , where K * ± refers to the K * ± (892) resonance, without explicit consideration of interference from higher mass K * states, and place an upper limit on the branching fraction. Charge-conjugate modes are implied throughout and we assume equal production rates of This analysis is based on a data sample of 454 ± 5 million BB pairs, corresponding to an integrated luminosity of 413 fb −1 , collected with the BABAR detector at the PEP-II asymmetric-energy e + e − collider operated at the Stanford Linear Accelerator Center. The e + e − centerof-mass (c.m.) energy is √ s = 10.58 GeV, corresponding to the Υ (4S) resonance mass (on-resonance data). In addition, 41.2 fb −1 of data collected at 40 MeV below the Υ (4S) resonance (off-resonance data) are used for background studies.
The BABAR detector is described in detail in Ref. [10]. Charged particles are reconstructed as tracks with a 5layer silicon vertex detector (SVT) and a 40-layer drift chamber inside a 1.5-T solenoidal magnet. An electromagnetic calorimeter (EMC) comprising 6580 CsI(Tl) crystals is used to identify electrons and photons. A ringimaging Cherenkov detector (DIRC) is used to identify charged hadrons and to provide additional electron identification information. The average K-π separation in the DIRC varies from 12σ at a laboratory momentum of 1.5 GeV/c to 2.5σ at 4.5 GeV/c. Muons are identified by an instrumented magnetic-flux return (IFR).
The B 0 → K * + K * − candidates are reconstructed through the decay of both K * ± to K 0 S π ± or with one K * ± decaying to K 0 S π ± and the other to K ∓ π 0 . The differential decay rate, after integrating over the angle between the decay planes of the vector mesons, for which the acceptance is uniform, is where θ 1 and θ 2 are the helicity angles of the K * + and K * − , defined as the angle between the daughter kaon (K 0 S or K ± ) momentum and the direction opposite to the B meson in the K * ± rest frame [11].
The charged particles from the K * ± decays are required to have at least 12 hits in the drift chamber and a transverse momentum greater than 0.1 GeV/c. The particles are identified as either charged pions or kaons by measurement of the energy loss in the tracking devices, the number of photons recorded by the DIRC and the corresponding Cherenkov angle. These measurements are combined with additional information from the EMC and IFR detectors, where appropriate, to reject electrons, muons, and protons.
The K 0 S is reconstructed through its decay to π + π − . The K 0 S candidates are required to have a reconstructed mass within 0.01 GeV/c 2 of the nominal K 0 S mass [12], a decay vertex separated from the B meson decay vertex by at least twenty times the uncertainty in the measurement of the vertex position, a flight distance in the transverse direction of at least 0.3 cm, and the cosine of the angle between the line joining the B and K 0 S decay vertices and the K 0 S momentum greater than 0.999. We reconstruct the π 0 through the decay π 0 → γγ. In the laboratory frame, the energy of each photon from the π 0 candidate must be greater than 0.04 GeV, the energy of the π 0 must be greater than 0.25 GeV, and the reconstructed π 0 invariant mass is required to be 0.12 ≤ m γγ ≤ 0.15 GeV/c 2 .
We require the invariant mass of the K * + candidates to be 0.792 < m Kπ < 0.992 GeV/c 2 . A B meson candidate is formed from the K * ± candidates, with the condition that the K * ± candidates originate from the interaction region.
B meson candidates are characterized kinematically by the energy difference ∆E = E * B − √ s/2 and the beam energy-substituted mass (E B , p B ) are the four-momenta of the Υ (4S) and B meson candidate, respectively, and the asterisk denotes the Υ (4S) rest frame. For a final state with a π 0 , the total event sample is taken from the region −0.1 ≤ ∆E ≤ 0.2 GeV and 5.25 ≤ m ES ≤ 5.29 GeV/c 2 ; with no π 0 , the signal ∆E has a smaller width and the region −0.08 ≤ ∆E ≤ 0.15 GeV is used. The asymmetric ∆E criteria are applied to remove backgrounds from charm decays which occur in the negative ∆E region. In both cases, events outside the region |∆E| ≤ 0.07 GeV and 5.27 ≤ m ES ≤ 5.29 GeV/c 2 are used to characterize the background. We suppress the background from decays to charmed states by forming the invariant mass, m D , from combinations of three out of the four daughter particles' four-momenta. The event is rejected if 1.845 < m D < 1.895 GeV/c 2 and the charge and particle type of the tracks are consistent with a decay from a D meson. We reduce backgrounds from B 0 → φK * 0 by assigning the kaon mass to the pion candidate and rejecting the event if the combined invariant mass of the two charged tracks is between 1.00 and 1.04 GeV/c 2 . Finally, to reduce the continuum background and avoid the region where the reconstruction efficiency falls off rapidly for low momentum tracks, we require the cosine of the helicity angle of the K * ± candidates to be in the range −1.0 ≤ cos(θ) ≤ 0.9 for states without a π 0 and −0.9 ≤ cos(θ) ≤ 0.9 for decays with a π 0 .
To reject the dominant background consisting of lightquark qq (q = u, d, s, c) continuum events, we require | cos θ T | < 0.8, where θ T is the angle, in the c.m. frame, between the thrust axis [13] of the B meson and that formed from the other tracks and neutral clusters in the event. Signal events have a flat distribution in | cos θ T |, while continuum events peak at 1.
We use Monte Carlo (MC) simulations of the signal decay to estimate the number of signal candidates per event. After the application of the selection criteria, the average number of signal candidates per event is predicted to be 1.08 (1.02) for fully longitudinally (transversely) polarized decays with no π 0 in the final state and 1.18 (1.10) for decays with one π 0 in the final state. A single candidate per event is chosen as the one whose fitted decay vertex has the smallest χ 2 . MC simulations also show that up to 7% (2.4%) of longitudinally (transversely) polarized signal events with no π 0 are misreconstructed, with one or more tracks originating from the other B meson in the event. In the case of signal events with one π 0 , the number of misreconstructed candidates is 11% (4.3%) for longitudinally (transversely) polarized signal events.
We create a Fisher discriminant F to be used in the maximum-likelihood (ML) fit, constructed from a linear combination of five variables: the polar angles of the B meson momentum vector and the B meson thrust axis with respect to the beam axis, the ratio of the secondand zeroth-order momentum-weighted Legendre polynomial moments of the energy flow around the B meson thrust axis in the c.m. frame [14], the flavor of the other B meson as reported by a multivariate tagging algorithm [15], and the boost-corrected proper-time difference between the decays of the two B mesons divided by its variance. The second B meson is formed by creating a vertex from the remaining tracks that are consistent with originating from the interaction region. The Fisher discriminant is trained using MC for signal and qq continuum MC, off-resonance data and data outside the signal region for the background.
We use an extended unbinned ML fit to extract the signal yield and polarization simultaneously for each mode. The extended likelihood function is We define the likelihood L i for each event candidate i as the sum of n j P j ( x i ; α j ) over three hypotheses j (signal, qq background and BB backgrounds as discussed below), where P j ( x i ; α j ) is the product of the probability density functions (PDFs) for hypothesis j evaluated for the i-th event's measured variables x i , n j is the yield for hypothesis j, and N is the total number of events in the sample. The quantities α j represent parameters in the expected distributions of the measured variables for each hypothesis j. Each discriminating variable x i in the likelihood function is modeled with a PDF, where the parameters α j are extracted from MC simulation, off-resonance data, or (m ES , ∆E) sideband data. The seven variables x i used in the fit are m ES , ∆E, F , and the invariant masses and cosines of the helicity angle of the two K * ± candidates. Since the correlations among the fitted input variables are found to be on average ∼ 1%, with a maximum of 5%, we take each P j to be the product of the PDFs for the separate variables. The effect of neglecting correlations is evaluated by fitting ensembles of simulated experiments in which we embed signal and background events randomly extracted from fully-simulated MC samples. Any observed fit bias is then subtracted from the fitted yield.
For the final state with no π 0 , the two invariant mass and helicity angle distributions for each K * ± meson are indistinguishable and so we use the same PDF parameters for both K * ± candidates; for the final state with a π 0 , we use separate PDFs for K * ± → K 0 S π ± and K * ∓ → K ∓ π 0 . For the signal, we use a relativistic Breit-Wigner for the K * ± invariant mass and a sum of two Gaussians for m ES and ∆E. The longitudinal (transverse) helicity angle distributions are described with a cos 2 θ (sin 2 θ) function corrected for changes in efficiency as a function of helicity angle. The correction also accounts for the reduction in efficiency at a helicity of ∼ 0.78 introduced indirectly by the criteria used to veto D mesons. The BB backgrounds use an empirical non-parametric function for ∆E, the masses and helicity angles. The continuum and the BB background m ES shapes are described by the function and ξ a free parameter) [16] and a first-or third-order polynomial is used for ∆E and the helicity angles, respectively. The continuum invariant mass distributions contain real K * ± candidates; we model the peaking mass component using the parameters extracted from the fit to the signal invariant mass distributions together with a second-order polynomial to represent the non-peaking component. The Fisher distributions are modeled using an asymmetric Gaussian for all hypotheses. BB backgrounds that remain after the event selection criteria have been applied are identified and modeled using MC simulation based on the full physics and detector models [17]. There are no significant charmless BB backgrounds. The charm BB backgrounds are effectively suppressed by applying the veto on D meson mass described above. The remaining charm BB background events are mostly single candidates formed from the decay products of a D, D * or D * ± s , together with another track from the event. Given the uncertainty in the polarization and branching fractions of these backgrounds, we allow the BB background yield to float in the fit.
The continuum background PDF parameters that are allowed to vary are the F peak position, ξ for m ES , the slope of ∆E, and the polynomial coefficients and normalizations describing the mass and helicity angle distributions. We fit for the branching fraction B and f L directly and exploit the fact that B is less correlated with f L than is either the yield or efficiency taken separately. We validate the fitting procedure and extract fitting biases by applying the fit to ensembles of simulated experiments using the extracted fitted yields from data. The qq component is drawn from the PDF, and the signal and BB background events are randomly sampled from the fully simulated MC samples.
The total event sample consists of 602 and 1923 events for B 0 → K * + K * − with zero or one π 0 in the final state, respectively. The corresponding signal event yield is 1.8 +2.7 −1.7 and 4.1 +5.8 −3.2 and the longitudinal polarization f L is 0.0 ± 0.6 and 1.0 ± 1.0, respectively. Given the large errors on f L , we repeat the analysis with f L set to 1.0; this gives the most conservative 90% confidence level upper limit on the branching fractions. The results of the ML fits with f L = 1.0 are summarized in Table I. The BB background yield agrees with the MC prediction within the large statistical errors. We compute the branching fractions B by subtracting the ML fit bias from the fitted yield and dividing the result by the number of BB pairs and by the reconstruction efficiency, ǫ, times B(K 0 → K 0 S → π + π − ) = 0.5 × (69.20 ± 0.05)% and B(π 0 → γγ) = (98.80 ± 0.03)%. The significance S of the signal is defined as S = 2∆ ln L, where ∆ ln L is the change in likelihood from the maximum value when the number of signal events is set to zero, corrected for the systematic errors defined below.
The significance of the B 0 → K * + K * − branching fraction is 0.87σ, including statistical and systematic uncertainties. The 90% C.L. branching fraction upper limit (B UL ) is determined by combining the likelihoods from the two fits and integrating the total likelihood distribution (taking into account correlated and uncorrelated systematic uncertainties) as a function of the branching fraction from 0 to B UL , so that BUL 0 LdB = 0.9 ∞ 0 LdB. Figures 2 and 3 show the projections of the two fits onto m ES , ∆E, K * ± mass and cosine of the K * ± helicity angle for the final state with zero and one π 0 , respectively. The candidates in the figures are signal-enhanced with a requirement on the probability ratio P sig /(P sig + P bkg ), optimized to enhance the visibility of potential signal, where P sig and P bkg are the signal and the total background probabilities, respectively (computed without using the variable plotted). The dip in helicity at ∼ 0.78 is created by the criteria used to veto charm background. Bi, branching fraction B (B 0 → K * + K * − ), significance S, and 90% C.L. upper limit BUL. The first error is statistical and the second, if given, is systematic.  (c) K * ± mass; and (d) cosine of K * ± helicity angle for B 0 → K * ± (→ K 0 S π ± )K * ∓ (→ K 0 S π ∓ ) events selected with a requirement on the signal-to-total likelihood probability ratio, optimized for each variable, with the plotted variable excluded. The points with error bars show the data; the solid line shows signal-plus-background; the dashed line is the continuum background; the hatched region is the signal; and the shaded region is the BB background. (c) K * ± mass; and (d) cosine of K * ± helicity angle for B 0 → K * ± (→ K 0 S π ± )K * ∓ (→ K ∓ π 0 ). The same projection criteria and legend are used as in Fig. 2.
The systematic uncertainties are summarized in Table II. The errors on the branching fractions arise from the PDFs, fit biases and efficiencies. The PDF uncertainties are calculated by varying the PDF parameters that are held fixed in the original fit by their errors. The uncertainty from the fit bias includes its statistical uncertainty from the simulated experiments and half of the correction itself, added in quadrature. The uncertainties in PDF modeling and fit bias are additive in nature and affect the significance of the branching fraction results. Multiplicative uncertainties include reconstruction efficiency uncertainties from tracking and particle identification (PID), track multiplicity, MC signal efficiency statistics, and the number of BB pairs. In summary, we have measured the branching fraction B(B 0 → K * + K * − ) = [0.52 +0.83+0.08 −0.58−0.06 ] × 10 −6 , assuming the decay is fully longitudinally polarized. The 90% C.L. upper limit on the branching fraction B(B 0 → K * + K * − ) < 2.0×10 −6 is nearly two orders of magnitude more stringent than previous searches.