Search for B0->phiK+pi- Decays with Large K+pi- Invariant Mass

Motivated by the polarization anomaly in the B->phi(1020)K*(892) decay, we extend our search for other K* final states in the decay B0->phi(1020)K^*0 with the K*0->K+pi- invariant mass above 1.6 GeV. The final states considered include the K*(1680)0, K3*(1780)0, K4*(2045)0, and a Kpi spin-zero nonresonant component. We also search for B0->phiDbar0 decay with the same final state. The analysis is based on a sample of about 384 million BBbar pairs recorded with the BABAR detector. We place upper limits on the branching fractions BR(B0->phiK*(1680)0)<3.5*10^-6, BR(B0->phiK3*(1780)0)<2.7*10^-6, BR(B0->phiK4*(2045)0)<15.3*10^-6, and BR(B0->phiDbar0)<11.7*10^-6 at 90% C.L. The nonresonant contribution is consistent with the measurements in the lower invariant mass range.

PACS numbers: 13.25.Hw,13.88.+e,11.30.Er Recent measurements of polarization in rare vectorvector B meson decays, such as B → φK * and ρK * , have revealed a large fraction of transverse polarization [1,2,3,4,5]. This indicates a significant departure from the expected predominance of the longitudinal amplitude [6]. The rate, polarization, and CP measurements of B meson decays to particles with nonzero spin are sensitive to both strong and weak interaction dynamics and are discussed in a recent review [7,8].
In particular, the B → φK * decays are potentially sensitive to physics beyond the standard model in the b → s penguin transition, shown in Fig. 1 (a) [6]. The polarization anomaly in vector-vector B meson decays suggests other contributions to the decay amplitude, previously neglected. This has motivated a number of proposed contributions from physics beyond the standard model [9]. In addition, there are new mechanisms within the standard model which have been proposed to address the anomaly, including new weak dynamics [10], such as annihilation or electroweak penguin, or strong dynamics [11], such as QCD rescattering.
In order to distinguish the models, the BABAR experiment extended the study of the B 0 → φK * 0 decays with the tensor (J P = 2 + ), vector (J P = 1 − ), and scalar (J P = 0 + ) K * 0 [5]. The vector-tensor results are in agreement with quark spin-flip suppression [6] and A 0 amplitude dominance, whereas the vector-vector mode contains substantial A +1 amplitude, corresponding to anomalously large transverse polarization, where A λ corresponds to helicity states λ = −1, 0, +1 of the φ and K * mesons. In this paper, we extend our search for B 0 → φK * 0 to the higher-mass and higher-spin resonances K * (1680) 0 , K * 3 (1780) 0 , and K * 4 (2045) 0 . Charge conjugate reactions are implied throughout this paper. The respective quantum numbers for these states J P = 1 − , 3 − , and 4 + are allowed in the K * 0 → K + π − decay. Moreover, we extend our study of the B 0 → φ(Kπ) * 0 0 decay, where (Kπ) * 0 0 is the J P = 0 + Kπ component, to a Kπ invariant mass up to 2.15 GeV. We also search for the decay B 0 → φD 0 , which is expected to be significantly suppressed relative to the observed B 0 → ωD 0 due to a negligible uū + dd quark admixture in the φ meson [8].
The analysis follows closely our recent study [5] where we fully reconstruct the decay B 0 → φ(1020)K * 0 → (K + K − )(K + π − ). The Kπ invariant mass m Kπ window is now moved to the range from 1.60 to 2.15 GeV to cover the above mentioned resonances. In Fig. 2 we show the m Kπ distribution extended from our previous study in Ref. [5] to the mass range from 0.75 to 2.15 GeV.
The angular distribution of the B → φK * decay can be expressed as a function of H i = cos θ i and Φ shown in Fig. 1  GeV from the study of B 0 → φ(K + π − ) decays in Ref. [5]. The data distribution is shown with a requirement to enhance the signal as discussed in regard to Fig. 3 in text. The solid (dashed) line shows the signal-plus-background (background) expected distributions. The arrows indicate the higher mass range, 1.60 to 2.15 GeV, used in this analysis. I: Fit results for each decay mode: the reconstruction efficiency ε long and εtrans obtained from MC simulation for longitudinally and transversely polarized events; the total efficiency ε, including the daughter branching fractions [8] and assuming the smaller reconstruction efficiency; the number of signal events nsig; significance (S) of the signal; the branching fraction B; and the upper limit (UL) on the branching fraction at 90% C.L. The branching fraction B(B 0 → φ(Kπ) * 0 0 ) refers to the nonresonant J P = 0 + Kπ components quoted for 1.60 < mKπ < 2.15 GeV. The systematic errors are quoted last and are included in the S and UL calculations. The negative event yield (or B) for B 0 → φK * 3 (1780) 0 is extrapolated from the likelihood distribution in the physical range. Mode the direction of the K meson from the K * → Kπ (θ 1 ) or φ → KK (θ 2 ) and the direction opposite the B in the K * or φ rest frame, and Φ is the angle between the decay planes of the two systems. For each decay mode, the differential decay width has three complex amplitudes A J λ corresponding to the spin of the Kπ system J ≥ 1: where Y λ J are the spherical harmonics with J = 1 for K * (1680), J = 3 for K * 3 (1780), and J = 4 for K * 4 (2045). The angular distribution is simplified when averaged over the azimuthal angle Φ and becomes a function of the fraction of longitudinal polarization f J L = . The angular distribution has only one contributing amplitude with J = λ = 0 for each φ(Kπ) * 0 and φD final state. We use data collected with the BABAR detector [12] at the PEP-II e + e − collider. A sample of 383.6±4.2 million Υ (4S) → BB events was recorded at the center-of-mass energy √ s = 10.58 GeV. Charged-particle momenta are measured in a tracking system consisting of a silicon vertex tracker with five double-sided layers and a 40-layer drift chamber, both within the 1.5-T magnetic field of a solenoid. Charged-particle identification is provided by measurements of the energy loss in the tracking devices and by a ring-imaging Cherenkov detector.
We use two kinematic variables: is the e + e − initial state four-momentum, and (E B , p B ) is the four-momentum of the B candidate. We require |∆E| < 0.1 GeV and m ES > 5.25 GeV. The requirements on the invariant masses are 1.60 < m Kπ < 2.15 GeV and 0.99 < m KK < 1.05 GeV.
To reject the dominant e + e − → quark-antiquark continuum background, we use event-shape variables calculated in the center-of-mass frame. We require | cos θ T | < 0.8, where θ T is the angle between the B-candidate thrust axis and that of the rest of the event. We construct a Fisher discriminant, F , that combines the polar angles of the B-momentum vector and the B-candidate thrust axis with respect to the beam axis, and two moments of the energy flow around the B-candidate thrust axis [13].
We remove signal candidates that have decay products with invariant mass within 12 MeV of the nominal mass values for D + s or D + → φπ + . In about 8.8% of events more than one candidate is reconstructed and we select the one whose four-track vertex has the lowest χ 2 .
We use an unbinned, extended maximum-likelihood fit [5] to extract the event yields n j and the probability density function (PDF) parameters, denoted by ζ= {f 1 L , f 3 L , f 4 L } for the polarization parameters and ξ for the remaining parameters. The data model has eight event categories j: B 0 → φ(Kπ) * 0 0 , φK * (1680) 0 , φK * 3 (1780) 0 , φK * 4 (2045) 0 , φD 0 , f 0 (980)K * 0 , f 0 (980)D 0 , and combinatorial background. The f 0 (980)K * 0 and f 0 (980)D 0 categories are included to account for both the resonant and nonresonant K + K − contribution in exclusive B decays, while the combinatorial background PDF is found to account well for both the dominant quark-antiquark background and the random tracks from the B decays.
The likelihood L i for each candidate i is defined as L i = j n j P j (x i ; ζ; ξ), where each of the P j is the PDF for variables x i = {∆E, m ES , m Kπ , m KK , H 1 , H 2 , F }. We do not allow CP -violation in the decay amplitudes and ignore interference between the final states B → φ(Kπ) J with different J because no significant signal is observed. Since our acceptance in the decay angles is nearly uniform, the event yields are almost completely unaffected by interference among states of different J.
The PDF P j (x i ; ζ; ξ) for a given candidate i is a joint PDF for the helicity angles, and the product of the PDFs for each of the remaining variables. The helicity part of the exclusive B decay PDF is the ideal angular distribution from Eq. (1)  the amplitudes A J λ are expressed in terms of the polarization fractions ζ, multiplied by an empirically-determined acceptance function G (H 1 , H A relativistic spin-J Breit-Wigner amplitude parameterization is used for the resonance mass [8,14], except for the nonresonant (Kπ) * 0 0 contribution which has no m Kπ amplitude dependence beyond the phase-space factor. In the previous analysis with the Kπ mass below 1.6 GeV, we parameterized the (Kπ) * 0 0 m Kπ amplitude with the LASS function [5,15], which includes the K * 0 (1430) 0 resonance together with a nonresonant component. However, above 1.6 GeV the validity of the LASS parameterization is not certain and we use the phase-space model for the nonresonant (Kπ) * 0 0 parameterization. The parameters ξ describe the background or the remaining signal PDFs. They are left free to vary in the fit for the combinatorial background or are fixed to the values extracted from Monte Carlo (MC) simulation [16] and calibration of B-decay channels for the exclusive B decays. We use a sum of Gaussian functions for the parameterization of the signal PDFs for ∆E, m ES , F , and of the D 0 meson m Kπ distribution. For the combinatorial background, we use polynomial functions, except for m ES and F distributions which are parameterized by an empirical phase-space function [17] and by Gaussian functions, respectively. The φ and D 0 meson production can occur in the background, and we take this into account in the PDF.
In the mass range 1.60 < m Kπ < 2.15 GeV, we do not find significant signal in any of the four decays B 0 → φ(K + π − ) with K * (1680) 0 , K * 3 (1780) 0 , K * 4 (2045) 0 , or D 0 → K + π − and we place limits on their branching fractions as shown in Table I. We see evidence for the nonresonant φ(Kπ) * 0 0 contribution consistent with extrapolation (33 events) from the lower mass range studied in Ref. [5]. Due to large correlation among various signal yields of the decay modes with broad Kπ distributions, the errors on individual decay modes are relatively large.
However, the significance of the B 0 → φ(K + π − ) decay with (Kπ) * 0 0 , K * (1680) 0 , K * 3 (1780) 0 , and K * 4 (2045) 0 combined is larger than 5σ. The significance is defined as the square root of the change in 2 ln L when the yield is constrained to zero in the likelihood L.
Since we do not determine the flavor of the neutral B meson, our limits refer to the sum of two flavor final states, such as φD 0 and φD 0 . We assume equal production of B + B − and B 0 B 0 pairs in Υ (4S) decays. In Fig. 3 we show projections onto the variables. Data distributions are shown with a requirement on the signal-tobackground probability ratio calculated with the plotted variable excluded. This requirement is optimized to enhance the signal and results in signal selection efficiency between 60% and 90%.
In the fit, we constrain both event yields and polarization fractions f J L to the physically allowed ranges. The negative event yield in the B 0 → φK * 3 (1780) 0 decay is obtained by using the likelihood in the positive event region and fitting its shape with a parabolic function whose mininum is in the negative event region. For the three B 0 → φK * 0 J decay modes with J ≥ 1, the f J L fit results are consistent with any allowed value between 0 and 1 and we assume polarization which gives the smallest reconstruction efficiency in the branching fraction calculation. We integrate the likelihood distributions in the physically allowed ranges to compute the upper limits on the branching fractions.
The nonresonant K + K − contribution under the φ is accounted for with the B 0 → f 0 K * 0 category with the broad f 0 invariant mass distribution [14]. Its yield is consistent with zero for any of the K * 0 spin assumptions. We find evidence for a nonzero event yield in this nonresonant K + K − region under the φ with a D 0 of (31 +9 −8 ) events, with statistical errors only quoted. However, due to the broad K + K − invariant mass distribution, we cannot distinguish between f 0 , a 0 , or any other broad K + K − contribution under the φ. The uncertainties due to m KK parameterization are estimated with variation of the shape model from the resonant f 0 to phase-space and account for the errors between 3 and 11 events in different channels.
We vary those parameters in ξ not used to model combinatorial background within their uncertainties and derive the associated systematic errors between one and three events. The signal PDF model excludes the fake combinations originating from misreconstructed events. The biases from the dilution due to the presence of fake combinations, the finite resolution of the angle measurement, or other imperfections in the signal PDF model are estimated with MC simulation and generated samples. This results in an uncertainty between 1 and 11 events.
Additional systematic uncertainty originates from B background, where we estimate that only a few events can fake the signal. The systematic errors in selection efficiencies are dominated by those in particle identification (4%), track finding (2%), and uncertainty due to the K * resonance parameters [8] of 2-13%. Other systematic effects arise from event-selection criteria, φ, K * 0 , or D 0 branching fractions [8], and number of B mesons.
Our results place stringent limits on the B 0 → φK * 0 branching fractions with the higher-mass and spin resonances K * (1680) 0 , K * 3 (1780) 0 , and K * 4 (2045) 0 when compared with the lower-mass states [1,2,5]. The decay rate suppression may serve as an additional tool to study the mechanism of the anomalous transverse amplitude in the B → φK * (892) decay. We find the B 0 → φ(Kπ) * 0 0 rate with scalar (Kπ) * 0 0 to be consistent for Kπ invariant mass above and below 1.6 GeV. Our limit on the B 0 → φD 0 decay provides a test of the B decay mechanisms involving φ mesons in the final state.
In summary, we have searched for the B 0 → φK * 0 decays with the tensor K * 3 (1780) 0 and K * 4 (2045) 0 , vector K * (1680) 0 , and scalar nonresonant (Kπ) * 0 0 contributions with K * 0 → K + π − invariant mass above 1.6 GeV. Our results are summarized in Table I. We do not find significant signal with the above resonances and place upper limits on these and B 0 → φD 0 decays.
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