Observation of B0 Meson Decay to a1(1260)+- pi-+

We present a measurement of the branching fraction of the decay B0 -->a1(1260)^{+-} pi^{-+} with a1(1260)^{+-} -->pi^{-+} pi^{+-} pi^{+-}. The data sample consists of 218 million B B-bar pairs collected at the Y(4S) resonance and recorded by the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC. The analysis is based on unbinned multivariate maximum likelihood fit. The measured branching fraction is: (16.6 +/- 1.9 +/- 1.5) 10^{-6}. The decay mode, observed for the first time, is seen with a significance of 9.2 sigma (systematic uncertainties included).

The data were collected with the BABAR detector [7] at the PEP-II asymmetric e + e − collider [8]. An integrated luminosity of 198 fb −1 , corresponding to 218 million BB pairs, was recorded at the Υ(4S) resonance ("onresonance", center-of-mass energy √ s = 10.58 GeV). An additional 15 fb −1 were taken about 40 MeV below this energy ("off-resonance") for the study of continuum background in which a light or charm quark pair is produced instead of an Υ(4S).
Charged particles are detected and their momenta measured by the combination of a silicon vertex tracker, consisting of five layers of double-sided silicon detectors, and a 40-layer central drift chamber, both operating in the 1.5-T magnetic field of a superconducting solenoid. The tracking system covers 92% of the solid angle in the center-of-mass frame.
Charged-particle identification (PID) is provided by the average energy loss (dE/dx) in the tracking devices and by an internally reflecting ring-imaging Cherenkov detector (DIRC) covering the central region. A K/π separation of better than four standard deviations (σ) is achieved for momenta below 3 GeV/c, decreasing to 2.5 σ at the highest momenta in the B decay final states.
Monte Carlo (MC) simulations of the signal decay modes, continuum, BB backgrounds and detector response [9] are used to establish the event selection criteria. The MC signal events are simulated as B 0 decays to a 1 (1260)π with a 1 → ρπ. For the a 1 (1260) meson parameters we take the mass m 0 = 1230 MeV/c 2 and Γ 0 = 400 MeV/c 2 [6,10] .
We reconstruct the decay a ± 1 (1260) → π ∓ π ± π ± with the following requirement on the invariant mass: 0.83 < m a 1 (1260) < 1.8 GeV/c 2 . The intermediate dipion state is reconstructed with an invariant mass between 0.51 and 1.1 GeV/c 2 . We impose several PID requirements to ensure the identity of the signal pions. For the bachelor charged track we require an associated DIRC Cherenkov angle between −2 σ and +5 σ from the expected value for a pion. With this requirement all but 1.4% of any background from a 1 (1260)K is removed.
A B meson candidate is characterized kinematically by the energy-substituted mass where the subscripts 0 and B refer to the initial Υ(4S) and to the B candidate in the lab-frame, respectively, and the asterisk denotes the Υ(4S) frame. The resolutions in m ES and in ∆E are about 3.0 MeV/c 2 and 20 MeV respectively. We require |∆E| ≤ 0.2 GeV and 5.25 ≤ m ES ≤ 5.29 GeV/c 2 . To reduce fake B meson candidates we require a B vertex χ 2 probability > 0.01. The cosine of the angle between the direction of the π meson from a 1 (1260) → ρπ with respect to the flight direction of the B in the a 1 (1260) meson rest frame is required to be between −0.85 and 0.85 to suppress combinatorial background. The distribution of this variable is flat for signal and peaks near ±1 for this background.
To reject continuum background, we use the angle θ T between the thrust axis of the B candidate and that of the rest of the tracks and neutral clusters in the event, calculated in the center-of-mass frame. The distribution of cos θ T is sharply peaked near ±1 for combinations drawn from jet-like qq pairs and is nearly uniform for the isotropic B meson decays; we require | cos θ T | < 0.65. The remaining continuum background is modeled from off-resonance data. We use MC simulations of B 0 B 0 and B + B − decays to look for BB backgrounds, which can come from both charmless and charm decays. We find that the decay mode B 0 → D − π + , with D − → K + π − π − or D − → K 0 S π − , are the dominant BB backgrounds to ultimate final states different than the signal. The decay modes B 0 → a ± 2 (1320) π ∓ and B 0 → π ± (1300) π ∓ have the same final daughters as the signal. We suppress these with the angular variable A, defined as the cosine of the angle between the normal to the plane of the 3π resonance and the flight direction of the bachelor pion evaluated in the 3π resonance rest frame. Since the a 1 (1260), a 2 (1320) and π(1300) have spins of 1, 2 and 0 respectively, the distributions of the variable A for these three resonances differ. We require |A| < 0.62.
We use an unbinned, multivariate maximumlikelihood fit to extract the yields of B 0 → a ± 1 (1260) π ∓ , B 0 → a ± 2 (1320) π ∓ and B 0 → π ± (1300) π ∓ . The likelihood function incorporates five variables. As mentioned above, we describe the B decay kinematics with two variables: ∆E and m ES . We also include the invariant mass of the 3π system, a Fisher discriminant F , and the variable A (though the later provides little discrimination after the requirement mentioned above). The Fisher discriminant combines four variables: the angles with respect to the beam axis, in the Υ(4S) frame, of the B momentum and B thrust axis, and the zeroth and second angular moments L 0,2 of the energy flow around the B thrust axis. The moments are defined by where θ i is the angle with respect to the B thrust axis of track or neutral cluster i, p i is its momentum, and the sum excludes tracks and clusters used to build the B candidate.
We have on average 1.4 candidates per event and we select the B candidate with the smallest χ 2 formed from the ρ mass. The efficiency of the best candidate algorithm is 94 %.
Since the correlation between the observables in the selected data and in MC signal events is small, we take the probability density function (PDF) for each event to be a product of the PDFs for the separate observables. The product PDF for event i and hypothesis j, where j can be signal a ± 1 (1260) π ∓ , a ± 2 (1320) π ∓ and π ± (1300) π ∓ backgrounds, continuum background or BB background (2 types), is given by: The probability that inside the signal event the primary pion from the B candidate is confused with a pion from the a 1 (1260) is negligible because of the high momentum of the primary pion in Υ(4S) frame. There is the possibility that a track from a a ± 1 (1260) π ∓ , a ± 2 (1320) π ∓ and π ± (1300) π ∓ event is exchanged with a track from the rest of the event. These so-called self cross feed (SCF) events are considered as background events. The likeli-hood function for the event i is defined as where n k and n SCF k (k = 1, 3) are the signal and SCF yields for a ± 1 (1260) π ∓ , a ± 2 (1320) π ∓ , and π ± (1300) π ∓ , respectively, n qq is the number of continuum background events, n BB1 is the number of BB background events D − π + with D − → K + π − π − and n BB2 is the number of BB background events D − π + with D − → K 0 S π − . P k is the PDF for correctly reconstructed MC signal events;P SCF k is the PDF for SCF events, P qq is the PDF for continuum background events, and P BB1 and P BB2 are the PDFs for the two types of BB backgrounds, all evaluated with the observables of the ith event.
We write the extended likelihood function for all events as : where n j is the number of events of hypothesis j found by the fitter, and N is the number of events in the sample. The first factor takes into account the Poisson fluctuations in the total number of events. We determine the PDFs for signal and BB backgrounds from MC distributions in each observable. For the continuum background we establish the functional forms and initial parameter values of the PDFs with offresonance data.
The PDF of the invariant mass of the a 1 (1260) meson in signal events is parameterized as a relativistic Breit-Wigner line-shape with a mass dependent width which takes into account the effect of the mass-dependent ρ width [11]. The PDFs of the invariant masses of the a 2 (1320) and π(1300) mesons are parameterized by triple Gaussian functions. The m ES and ∆E distributions for signal are parameterized as double Gaussian functions. The ∆E distribution for continuum background is parameterized by a linear function. The combinatorial background in m ES is described by a phase-spacemotivated empirical function [12]. We model the Fisher distribution F using a Gaussian function with different widths above and below the mean. The A distributions are modeled using polynomials.
In the fit there are fourteen free parameters: six yields, the signal a 1 (1260) mass and width, and six parameters affecting the shape of the combinatorial background. Table I lists the results of the final fits. Fitted values of a 1 (1260) mass and width have statistical errors only.
Equal production rates to B 0 B 0 and B + B − pairs are assumed.
We find no evidence of the decay B 0 → π ± (1300) π ∓ , and therefore we have not included this component in the final fit. The yield of the decay B 0 → a ± 2 (1320) π ∓ is 8.3 ± 23.6 events. 16.6 ± 1.9 ± 1.5 m(a1(1260)) 1229 ± 21 MeV/c 2 Γ(a1 (1260) We find a signal yield bias of +3.8 % by generating and fitting MC simulated samples containing signal and background populations expected for data. We find that − ln L max from the on-resonance data lies well within the distribution of − ln L max from these simulated samples. The signal reconstruction efficiency is obtained from the fraction of signal MC events passing the selection criteria, adjusted for the bias in the likelihood fit. The statistical significance is taken as the square root of the difference between the value of −2 ln L for zero signal and the value at its minimum.
In Fig. 1 we show the ∆E, m ES , m a1 , and F projections made by selecting events with a signal likelihood (computed without the variable shown in the figure) exceeding a threshold that optimizes the expected sensitivity. The enhancement at 1.7 GeV/c 2 in Fig. 1(c) comes from D − π + background.
In Fig. 2 we show the distribution of the ratio of the likelihood for signal events L(Sg) and the sum of likelihoods for signal and all types of background [L(Sg) + L(Bg)] for on-resonance data and for Monte Carlo events generated from PDFs. We see good agreement between the model and the data. By construction the background is concentrated near zero, while the signal appears as an excess of events near one. Most of the systematic errors on the signal yield that arise from uncertainties in the values of the PDF parameters have already been incorporated into the overall statistical error, since they are floated in the fit. We determine the sensitivity to the other parameters of the signal and background PDF components by varying these within their uncertainties.
The uncertainty in our knowledge of the efficiency is found to be 3.2%. The systematic error on the fit yield is 6.2 %, which is obtained by varing the PDF parameters within their uncertainties. We estimate the uncertainty in the number of BB pairs to be 1.1 %. The uncertainty in the fit bias correction is 1.9 %, taken as half of the fit bias correction. Published world averages [6] provide the B daughter branching fraction uncertainties. The systematic errors on a 1 (1260)K cross-feed background and on SCF are both estimated to be 1.4 %. The potential background contribution from B 0 decays to ρ 0 ρ 0 , ρ 0 π + π − and 4π is estimated assuming the branching fractions of 1, 2, and 2 in 10 −6 respectively [13]. The associated systematic uncertainty is 3.9 %. The systematic effect due to differences between data and MC for the cos θ T selection is 1.8%. A systematic uncertainty of 2.5 % is estimated for the difference in reconstruction efficiency in the decay modes through the dominant Pwave (ππ) ρ and the S-wave (ππ) σ . The contribution of interference between a 2 (1320) and a 1 (1260) is negligible. In fact, varying the a 2 (1320)π background with different selection criteria on the angular variable A gives no significant change to the efficiency-corrected signal yield of a 1 (1260)π. We find also that the systematic effect due to different form factors in MC signal simulation is negligible. The total systematic error is 9.1 %.