Limit on the B0->rho0rho0 Branching Fraction and Implications for the CKM Angle alpha

We search for the decay B0 ->rho0 rho0 in a data sample of about 227 million Upsilon(4S)->BBbar decays collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We find no significant signal and set an upper limit of 1.1*10^-6 at 90% CL on the branching fraction. As a result, the uncertainty due to penguin contributions on the CKM unitarity angle alpha measured in B ->rho rho decays is 11 degrees at 68% CL.

We search for the decay B 0 → ρ 0 ρ 0 in a data sample of about 227 million Υ (4S) → BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e + e − collider at SLAC. We find no significant signal and set an upper limit of 1.1 × 10 −6 at 90% CL on the branching fraction. As a result, the uncertainty due to penguin contributions on the CKM unitarity angle α measured in B → ρρ decays is 11 o at 68% CL.
PACS numbers: 13.25.Hw,11.30.Er,12.15.Hh Measurements of CP -violating asymmetries in the B 0 B 0 system provide tests of the standard model by overconstraining the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1] through the measurement of the unitarity angles. Measuring the time-dependent CP asymmetry in a neutral-B-meson decay to a CP eigenstate dominated by the tree-level amplitude b → uūd gives an approximation α eff to the CKM unitarity angle α ≡ arg [−V td V * tb /V ud V * ub ]. The correction ∆α = α − α eff , which accounts for the effects of penguin-amplitude contributions as an additional decay mechanism, can be extracted from an isospin analysis of the branching fractions of the B decays into the full set of isospin-related channels [2].
Measurements of branching fractions and timedependent CP asymmetries in B → ππ, ρπ, and ρρ have already provided information on α. Because the branching fraction for B 0 → π 0 π 0 is comparable to that for B + → π + π 0 and B 0 → π + π − , the limit on the correction is weak: |∆α ππ | < 35 o at 90% confidence level (CL) [3]. (Charge conjugate B decay modes are implied in this paper.) In contrast, the ρ 0 ρ 0 channel has a much smaller branching fraction than the channels with charged ρ's [4,5,6,7]. As a consequence, it is possible to set a tighter limit on ∆α ρρ . This makes the ρρ system particularly effective for measuring α in a modelindependent way.
In B → ρρ decays the final state is a superposition of CP -odd and CP -even states, and an isospin-triangle relation [2] holds for each of the three helicity amplitudes, which can be separated through an angular analysis. The measured polarizations in B + → ρ + ρ 0 [4,5] and B 0 → ρ + ρ − [6,7] modes indicate that the ρ's are nearly entirely longitudinally polarized. The current best limit on the B 0 → ρ 0 ρ 0 branching fraction was obtained by BABAR with a sample of 89 million Υ (4S) → BB decays [4].
In this Letter we present improved constraints on the B 0 → ρ 0 ρ 0 branching fraction and the penguin contribution to the measurement of the unitarity angle α. These results 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. A sample of 226.6 ± 2.5 million BB pairs, corresponding to an integrated luminosity of approximately 205 fb −1 , was recorded at the Υ (4S) resonance with We use a sample of 16 fb −1 taken 40 MeV below the Υ (4S) resonance to study background contributions from e + e − → qq (q = u, d, s, or c) continuum events.
To reconstruct B 0 → ρ 0 ρ 0 → (π + π − )(π + π − ) candidates, we select four charged tracks that are consistent with originating from a single vertex near the e + e − interaction point. Particle identification is provided by measurements of the energy loss in the silicon vertex tracker and the drift chamber and by the Cherenkov angle in an internally reflecting ring-imaging Cherenkov detector.
The angular distribution of the B 0 → ρ 0 ρ 0 decay products can be expressed as a function of the helicity angles (θ 1 , θ 2 , φ), which are defined by the directions of the two-body ρ 0 decay axes and the direction opposite the B in the ρ 0 rest systems, as shown in Fig. 1. Since the detector acceptance does not depend on φ, the resulting is the longitudinal polarization fraction and A λ=−1,0,+1 are the helicity amplitudes. The identification of signal B candidates is based on two kinematic variables: the beam-energy-substituted mass, where the initial total e + e − four-momentum (E i , p i ) and the B momentum p B are defined in the laboratory frame; and the difference between the reconstructed B energy in the c.m. frame and its known value ∆E = E cm B − √ s/2. The signal m ES and ∆E resolutions are 2.6 MeV/c 2 and 20 MeV, respectively. The selection requirements for m ES , ∆E, the two π + π − invariant masses m 1,2 , and the helicity angles are the following: 5.24 < m ES < 5.29 GeV/c 2 , |∆E| < 85 MeV, 0.55 < m 1,2 < 1.00 GeV/c 2 , and | cos θ 1,2 | < 0.99. The latter requirement removes a region with low reconstruction efficiency.
To reject the dominant continuum background we require | cos θ T | < 0.8, where θ T is the angle between the B-candidate thrust axis and that of the remaining tracks and neutral clusters in the event, calculated in the c.m. frame. Other discriminating variables include the polar angles of the B momentum vector and the B-candidate thrust axis with respect to the beam axis in the c.m. frame, and the two Legendre moments L 0 and L 2 of the energy flow around the B-candidate thrust axis [10]. These variables are combined in a neural network, the output of which is transformed into a variable E for which the signal and background distributions are approximately Gaussian.
We veto the background mode B 0 → D − π + → h + π − π − π + , where h + refers to a pion or kaon. We require the invariant mass of the three-particle combination that excludes the highest-momentum track in the candidate B rest frame to be inconsistent with being the D-meson mass (|m hππ − m D | > 13 MeV/c 2 ). After application of all selection criteria, N cand = 35740 events are retained, most of which are background events with candidates in the sidebands of the variables. On average each selected event has 1.05 candidates. When more than one candidate is present in the same event, one candidate is selected randomly.
The signal selection efficiency determined from Monte Carlo (MC) [11] simulation is 27% or 32% for longitudinally or transversely polarized events, respectively. MC simulation shows that 22% of longitudinally and 8% of transversely polarized signal events are misreconstructed with one or more tracks not originating from the B 0 → ρ 0 ρ 0 decay. These are mostly due to combinatorial background from low-momentum tracks from the other B. We treat these as part of the signal.
Further background separation is achieved by the use of multivariate B-flavor-tagging algorithms trained to identify primary leptons, kaons, soft pions and highmomentum charged particles from the other B in the event [12]. The discrimination power arises from the difference between the tagging efficiencies for signal and background in the five tagging categories c tag .
We use an unbinned extended maximum likelihood fit to extract the B 0 → ρ 0 ρ 0 event yield. The likelihood function is where n j is the number of events for each hypothesis j (signal, continuum, and six B-background classes), and P j ( x i ) is the corresponding probability density function (PDF), evaluated with the variables x i = {m ES , ∆E, E, m 1 , m 2 , cos θ 1 , cos θ 2 , c tag } of the ith event.
We use MC-simulated events to study the background from other B decays. The charmless modes are grouped into five classes with similar kinematic and topological properties: B 0 → a ± tracks come from a ρ 0 meson. The two ρ 0 candidates of some exclusive non-signal modes can have very different mass and helicity distributions. This occurs when one of the two ρ 0 candidates is real (e.g., ρ + ρ 0 , ρ 0 K * 0 ) or when one of the two ρ 0 candidates contains a high-momentum pion (a 1 π). In such cases, we use a four-variable correlated mass-helicity PDF.
The signal and B-background PDF parameters are extracted from MC simulation while the continuum background PDF parameters are obtained from data in m ES and ∆E sidebands. The MC parameters of m ES , ∆E, and E are adjusted by comparing data and MC in calibration channels with similar kinematics and topology, such as B 0 → D − π + with D − → K + π − π − . Finally, the B-flavor tagging PDFs for all categories are the discrete c tag distributions of tagging efficiencies. Large samples of fully reconstructed B-meson decays are used to obtain the B-tagging efficiencies for signal B decays and to study systematic uncertainties in the MC values of B-tagging efficiencies for the B backgrounds. Table I shows the results of the fit. No significant signal yield is observed. We obtain an upper limit by integrating the normalized likelihood distribution over the positive values of the branching fraction. The value of f L is fixed to 1 in the fit, as this assumption has been shown to give the most conservative upper limit and it approximates the values obtained in the B → ρρ decays dominated by the tree-level amplitude. The statistical significance is taken as the square root of the change in −2 ln L when the number of signal events is constrained to zero in the likelihood fit. In Fig. 2 we show the projections of the fit results onto m ES and ∆E.
Systematic errors in the fit originate from uncertainties in the PDF parameterizations, which arise from the limited number of events in the sideband data and signal control samples. The PDF parameters are varied by their respective uncertainties to derive the corresponding systematic errors (6.0 events). The event yields from the B-background modes fixed in the fit are varied according to the uncertainties in the measured or estimated branching fractions. This results in a systematic error on the  signal yield of 5.8 events. We also assign a systematic error of 3.0 events to cover a possible fit bias, evaluated with MC experiments. We estimate the systematic uncertainty due to signala ± 1 π ∓ interference using a simulation study in which the decay amplitudes for B 0 → ρ 0 ρ 0 are generated according to this measurement and those for B 0 → a ± 1 π ∓ correspond to a branching fraction of 4 × 10 −5 [15]. The relative phases between these are modeled with BW amplitudes for all ρ → ππ and a 1 → ρπ combinations, with additional constants. The values of the constants and the a ± 1 π ∓ CP asymmetries are varied over the allowed ranges. We take the rms variation of the average signal yield (7.5 events) as a systematic uncertainty.
Our measurement confirms the small value of the B 0 → ρ 0 ρ 0 branching fraction with the statistical uncertainty improved by approximately a factor of two over our previous result [4]. Since the tree contribution to the B 0 → ρ 0 ρ 0 decay is color-suppressed, the decay rate is sensitive to the penguin amplitude. Thus, this mode has important implications for constraining the uncertainty due to penguin contributions in the measurement of the CKM unitarity angle α with B → ρρ decays.
In the isospin analysis [2], we minimize a χ 2 that includes the measured quantities expressed as the lengths of the sides of the isospin triangles. We use the measured branching fractions and fractions of longitudinal polarization of the B + → ρ + ρ 0 [4,5] and B 0 → ρ + ρ − [6,7] decays, the CP -violating parameters S +− L and C +− L obtained from the time evolution of the longitudinally polarized B 0 → ρ + ρ − decay [7], and the branching fraction of B 0 → ρ 0 ρ 0 from this analysis. We neglect isospin- breaking effects, non-resonant, and I = 1 isospin contributions [16].
The error due to the penguin contribution may become the dominant uncertainty in the measurement of α using B → ρρ decays. However, if B 0 → ρ 0 ρ 0 decays are observed, time-dependent and angular analyses will allow us to measure the CP parameters S 00 L and C 00 L , analogous to S +− L and C +− L , resolving ambiguities inherent to isospin triangle orientations.
In summary, we have improved the precision on the measurement of the B 0 → ρ 0 ρ 0 branching fraction by approximately a factor of two. The limit on this branching fraction relative to those for B + → ρ 0 ρ + and B 0 → ρ + ρ − provides a tight constraint on the penguin uncertainty in the determination of the CKM unitarity angle α. The results summarized in Table I supersede our previous measurement [4].
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), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from CONACyT (Mexico), A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation.