Observation of B0 ->K*0 K*0bar and search for B0 ->K*0 K*0

We report the observation of the b ->d penguin-dominated decay B0 ->K*0 K*0bar with a sample of 383.2 +/- 4.2 million BBbar pairs collected with the BaBar detector at the PEP-II asymmetric-energy e^+e^- collider at the Stanford Linear Accelerator Center. The measured branching fraction is Br(B0 ->K*0 K*0bar) = [1.28^{+0.35}_{-0.30} +/- 0.11] x 10^{-6} and the fraction of longitudinal polarization f_L (B0 ->K*0 K*0bar) = 0.80^{+0.10}_{-0.12} +/- 0.06. The first error quoted is statistical and the second systematic. We also obtain an upper limit at the 90% confidence level on the branching fraction for Br(B0 ->K*0 K*0)<0.41 x 10^{-6}.

PACS numbers: 13.25.Hw,11.30.Er,12.15.Hh The study of the branching fractions and angular distributions of B meson decays to hadronic final states without a charm quark probes the dynamics of both weak and strong interactions, and plays an important role in understanding CP violation. Decays proceeding via electroweak and gluonic b → d penguin diagrams have only recently been measured in the decays B → ργ [1] and B 0 → K 0 K 0 [2]. On the other hand, the charmless decay B 0 → K * 0 K * 0 proceeds through both electroweak and gluonic b → d penguin loops to two vector particles (V V ). The Standard Model (SM) suppressed decay B 0 → K * 0 K * 0 could appear via an intermediate heavy boson.
Theoretical models in the framework of QCD factorization predict the angular distribution of the V V decays of the B meson, as measured by the longitudinal polarization fraction f L , to be ∼ 0.9 for both tree-and penguin-dominated decays [3]. However, recent measurements of the pure penguin V V decay B → φK * indicate f L ∼ 0.5 [4]. Several attempts to understand this unexpected value of f L within or beyond the Standard Model have been made [5]. Further information about decays related by SU (3) symmetry may provide insight into this polarization puzzle and test factorization models. A time-dependent angular analysis of B 0 → K * 0 K * 0 can distinguish between penguin annihilation and rescattering as mechanisms for the value of f L observed in B → φK * [6]. The B 0 → K * 0 K * 0 mode can also be used within the SM framework to help constrain the angles α and γ of the Unitarity Triangle [7].
We report measurements of the branching fraction and the fraction of longitudinal polarization for the decay mode B 0 → K * 0 K * 0 , with explicit consideration of non-resonant backgrounds and interference from K * 0 K * 0 (1430). We place an upper limit on the branching fraction of B 0 → K * 0 K * 0 , where we use the notation K * 0 K * 0 to also represent K * 0 K * 0 . Charge-conjugate modes are implied throughout and we assume equal production rates of B + B − and B 0 B 0 . This analysis is based on a data sample of 383.2 ± 4.2 million BB pairs, corresponding to an integrated luminosity of 348 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 − center-of-mass (c.m.) energy is √ s = 10.58 GeV, corresponding to the Υ (4S) resonance mass (on-resonance data). In addition, 36.6 fb −1 of data collected 40 MeV below the Υ (4S) resonance (off-resonance data) are used for background studies. The BABAR detector is described in detail in Ref. [11]. Charged particles are reconstructed as tracks with a 5layer silicon vertex detector and a 40-layer drift chamber inside a 1.5-T solenoidal magnet. An electromagnetic calorimeter is used to identify electrons and photons. A ring-imaging Cherenkov detector is used to identify charged hadrons and provides additional electron identification information. Muons are identified by an instrumented magnetic-flux return.
The B 0 → K * 0 K * 0 and B 0 → K * 0 K * 0 candidates are reconstructed through the decays K * 0 → K + π − and K * 0 → K − π + . 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 * 0 or K * 0 . The helicity angle of the K * 0 (K * 0 ) is defined as the angle between the K + (K − ) momentum and the direction opposite to the B meson in the K * 0 (K * 0 ) rest frame [12].
The charged tracks from the K * 0 decays are required to have at least 12 hits in the drift chamber and a transverse momentum greater than 0.1 GeV/c. The tracks are identified as either pions or kaons by measurement of the energy loss in the tracking devices, the number of photons measured by the Cherenkov detector and the corresponding Cherenkov angles. These measurements are combined with calorimeter information to reject electrons, muons, and protons. We require the invariant mass of the K * 0 candidates to be 0.792 < m Kπ < 1.025 GeV/c 2 . A B meson candidate is formed from two K * 0 candidates, with the constraint that the two K * 0 candidates originate from the interaction region.
B meson candidates are characterized kinematically by the energy difference ∆E = E * B − √ s/2 and the energy- are the four-momenta of the Υ (4S) and B meson candidate, respectively, and the asterisk denotes the Υ (4S) rest frame. The total event sample is taken from the region −0.08 ≤ ∆E ≤ 0.2 GeV and 5.25 ≤ m ES ≤ 5.29 GeV/c 2 . Events outside the region |∆E| ≤ 0.07 GeV and 5.27 ≤ m ES ≤ 5.29 GeV/c 2 are used to characterize the background. The average number of signal B meson candidates per selected data event is 1.03. A single B meson candidate per event is chosen as the one whose fitted decay vertex has the smallest χ 2 . MC simulations show that up to 4% (1.6%) of longitudinally (transversely) polarized signal events are misreconstructed, with one or more tracks originating from the other B meson in the event.
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 axes [13] of the B meson and that formed from the other tracks and neutral clusters in the event. 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 second-and 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.
We suppress background from decays to charmed states by removing candidates that have decays consistent with D − → K + π − π − and an invariant mass in the range 1.845 < m K + π − π − < 1.895 GeV/c 2 . 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, we require the cosine of the helicity angle of both K * 0 candidates to be less than 0.98 to reduce continuum background and avoid the region where the reconstruction efficiency falls off rapidly.
We use an extended unbinned ML fit to extract the signal yield and polarization simultaneously for each mode. The extended likelihood function is (2) We define the likelihood L i for each event candidate i as the sum of n j P j ( x i ; α j ) over four hypotheses j (signal, qq background, K * 0 (1430) 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 * 0 candidates. Since the correlations among the fitted input variables are found to be on average ∼ 1% with a maximum of 4%, 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.
The two invariant mass and helicity angle distributions for each K * 0 meson are indistinguishable and so we use the same PDF parameters for both K * 0 candidates. Peaking PDF distributions are described with an asymmetric Gaussian or a sum of two Gaussians. The transverse (longitudinal) 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 BB backgrounds use an empirical non-parametric function for ∆E, the masses and helicity angles. The continuum background m ES shape is 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 * 0 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.
We use the decay B 0 → D − π + (D − → K * 0 π − ) as a calibration channel to account for small differences between MC simulation and reconstructed data. This decay has a similar topology to the modes under study and is selected using the same criteria as for K * 0 K * 0 but requiring the reconstructed K * 0 π ± invariant mass to be in the range 1.845 < m K * 0 π ± < 1.895 GeV/c 2 . We predict 1860 ± 186 signal events and measure 1614 ± 47.
We use MC-simulated events to study backgrounds from other B meson decays. The major charmless BB background to B 0 → K * 0 K * 0 is B 0 → φK * 0 , while charm BB backgrounds are effectively suppressed by the requirement that the two pions (and kaons) have opposite charge. For B 0 → K * 0 K * 0 , B 0 → φK * 0 remains the major charmless BB background, but a number of charm decays contaminate the signal, dominated by decays of the type B 0 → D − K + and B − → D 0 K − . Given the uncertainty in the polarization and branching fractions of these backgrounds, we allow the BB background yield to float in the fit.
A possible background is the decay B 0 → K * 0 K * 0 (1430). We use the LASS parameterization for the K * 0 (1430) lineshape, which consists of the K * 0 (1430) resonance together with an effective-range non-resonant component [17]. We apply the same selection criteria used for K * 0 K * 0 but require one of the K * 0 candidates to have an invariant mass in the range 1.025 < m Kπ < 1.53 GeV/c 2 and perform an extended unbinned ML fit with the four variables m ES , ∆E, F , and the K * 0 mass. We fit the LASS parameterization to the selected sig-nal events in the K * 0 (1430) mass range and extrapolate to the K * 0 mass range. Interference effects between the K * 0 and the spin-0 final states (non-resonant and K * 0 (1430)) integrate to zero as the acceptance of the detector and analysis is uniform. Assuming no interference, we expect 6 ± 5 B 0 → K * 0 K * 0 (1430) events in the fitted B 0 → K * 0 K * 0 signal region. The uncertainty on the contribution is calculated from the statistical error and the large uncertainty in the fitted LASS parameters used to describe the K * 0 (1430) lineshape. We fix the yield in the final fit and vary the yield by its error to assess the systematic uncertainty.
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 normalization describing the mass and helicity angle distributions. We fit for 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.
The total event sample consists of 7363 and 1390 events for B 0 → K * 0 K * 0 and B 0 → K * 0 K * 0 , respectively. The results of the ML fits are summarized in Table I. The BB background yield agrees with the MC prediction within the statistical errors. 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 error defined below. The robustness of the significance estimate is cross-checked through fitting a series of toy MC ensembles generated from the fitted parameters. The significance of the B 0 → K * 0 K * 0 branching fraction is 6σ, including statistical and systematic uncertainties. For B 0 → K * 0 K * 0 , we compute the 90% C.L. upper limit as the branching fraction below which lies 90% of the total likelihood integral, taking into account the systematic uncertainty. Figure 1 shows the projections of the fits onto m ES , ∆E, K * 0 mass and cosine of the K * 0 helicity angle for B 0 → K * 0 K * 0 .
Systematic uncertainties in the branching fractions are dominated by our knowledge of the PDF modeling. Varying the PDF parameters by their errors results in changes in the yields of 6.5% and 19.0% for B 0 → K * 0 K * 0 and B 0 → K * 0 K * 0 , respectively. The largest contribution comes from the width of the K * 0 .
The reconstruction efficiency depends on the decay polarization. We calculate the efficiency using the measured polarization and assign a systematic error from the uncertainty on f L of 3.4% and 27.0% for B 0 → K * 0 K * 0 and B 0 → K * 0 K * 0 , respectively. Figure 2 shows the behavior of −2 ln L(B, f L ) for the B 0 → K * 0 K * 0 mode.
The uncertainties in PDF modeling and f L are additive in nature and affect the significance of the branching fraction results. Multiplicative uncertainties include reconstruction efficiency uncertainties from tracking (3.2%) and particle identification (4.4%), track multiplicity (1%), MC signal efficiency statistics (0.6%), and the number of BB pairs (1.1%). Variation of the expected yield from B 0 → K * 0 K * 0 (1430) events has a negligible effect on the signal. The systematic uncertainty in f L is dominated by the PDF shape variations, which contribute 7% for B 0 → K * 0 K * 0 and 20% for B 0 → K * 0 K * 0 . Other errors identified above for the branching fraction have a very small effect on f L and contribute in total 0.7%. The total systematic error is summarized in Table I. In summary, we have measured the branching fraction B(B 0 → K * 0 K * 0 ) = [1.28 +0.35 −0.30 (stat) ± 0.11(syst)]× 10 −6 with a significance of 6σ. We find the fraction of longitudinal polarization f L = 0.80 +0.10 −0.12 (stat) ± 0.06 (syst). Both results are in agreement with the upper range of theoretical predictions. The 90% C.L. upper limit on the branching fraction B(B 0 → K * 0 K * 0 ) < 0.41 × 10 −6 is I: Summary of results: signal yield nsig, the BB background yield n BB , signal reconstruction efficiency ε (taking into account that B(K * 0 → K + π − ) = 2/3), significance S (systematic uncertainties included), branching fraction B, 90% C.L. upper limit for B 0 → K * 0 K * 0 branching fraction, and the longitudinal polarization fL. The first error given is statistical and the second is systematic.

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K * 0 K * 0 K * 0 K * 0 nsig 33.5 +9. two orders of magnitude more stringent than previous measurements. 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 and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.