Search for neutral B-meson decays to a0π, a0K, ηρ0, and ηf0

We present a search for B 0 decays to charmless ﬁnal states involving an (cid:1) meson, a charged pion, and a second charged pion or kaon. The data sample corresponds to 383 (cid:1) 10 6 B (cid:1) B pairs collected with the BABAR detector operating at the PEP-II asymmetric-energy B factory at SLAC. We ﬁnd no signiﬁcant signals and determine the following C.L.

We present a search for B 0 decays to charmless final states involving an meson, a charged pion, and a second charged pion or kaon. The data sample corresponds to 383 10 6 B B pairs collected with the BABAR detector operating at the PEP-II asymmetric-energy B factory at SLAC. We find no significant signals and determine the following 90% C.L. upper limits: BB 0 ! a ÿ 0 Ba ÿ 0 ! ÿ < 3:1 10 ÿ6 , BB 0 ! a ÿ 0 K Ba ÿ 0 ! ÿ < 1:9 10 ÿ6 , BB 0 ! a 0 1450 ÿ Ba 0 1450 ÿ ! ÿ < 2:3 10 ÿ6 , BB 0 ! a 0 1450 ÿ K Ba 0 1450 ÿ ! ÿ < 3:1 10 ÿ6 , BB 0 ! 0 < 1: 5 10 ÿ6 , and BB 0 ! f 0 980 Bf 0 980 ! ÿ < 0: 4  We investigate the decays of a B 0 meson to final states with an meson, a charged pion, and either a second charged pion or kaon. The Dalitz plots for the decays without an intermediate charmed meson are expected to have contributions from quasi-two-body decays such as . The last of these has been investigated recently [2] so in this paper we concentrate on the others, where a 0 is either a 0 980 or a 0 1450 and f 0 is f 0 980. Measurements of B decays involving a scalar meson are interesting since they provide information on such B decays and the nature of scalar mesons. Several B decays involving scalar mesons have been observed, either with an f 0 980 [3,4] or K 1430 [2, 3,5] in the final state.
Specific predictions can be made for the decays B ! a 0 if factorization is assumed and if the decay involves only tree or penguin (loop) processes. The dominant amplitude is shown in Fig. 1(a). The companion tree amplitude, shown in Fig. 1(b), is expected to be greatly suppressed, since, neglecting light-quark mass splittings, the virtual W cannot produce an a 0 meson [6]. This is a firm prediction of the standard model because the weak current has a G-parity even vector part and a G-parity odd axial-vector part. The latter can produce an axial-vector or pseudoscalar particle while the former produces a vector particle, but neither can produce a G-parity odd scalar meson (e.g. a 0 ). Thus the decay B ! a 0 is expected to be ''self-tagging''-the pion charge specifies the B flavor. Penguin processes such as shown in Fig. 1(c) are allowed, but are suppressed relative to the tree processes. The decays with a kaon in the final state should be dominated by the penguin processes [ Fig. 1(c)], though there is a cancellation between two terms in the penguin amplitudes for these decays [7].
The theoretical expectations for these decays with an a 0 980 meson [7][8][9][10] are larger than previous experimental limits [11]. The decays with a 0 meson are expected to have branching fractions & 1 10 ÿ7 [12] since they are dominated by color-suppressed tree amplitudes [ Fig. 1(d)]. There are no predictions for the decay B 0 ! f 0 , but it should have a small branching fraction for the same reason.
The nature of the a 0 meson is not well understood. It is thought to be a q q state with a possible admixture of a K K bound-state component due to the proximity to the K K threshold [13,14]. The a 0 mass is known to be about 985 MeV with a width of 71 7MeV [15] for the dominant a 0 ! decay mode [13]. The a 0 1450 has a measured width of 265 MeV [13]. Since the branching fraction for a 0 ! is not well known, we report the product branching fraction BB 0 ! a ÿ 0 X Ba 0 ! , where X indicates K or . The properties of the f 0 980 meson are well measured for the ÿ channel that is used in this analysis [16].
Only limits for the following decays have been reported previously: B 0 ! a 0 980 ÿ and B 0 ! a 0 980 ÿ K [11] and B 0 ! 0 [17][18][19]. There have been no previous searches for B 0 ! f 0 or the decays with an a 0 1450. The results presented here are based on data collected with the BABAR detector [20] at the PEP-II asymmetric-energy e e ÿ collider located at the Stanford Linear Accelerator Center. An integrated luminosity of approximately 347 fb ÿ1 , corresponding to 383 10 6 B B pairs, was recorded at the 4S resonance (center-of-mass energy s p 10:58 GeV).
The track parameters of charged particles are measured by a combination of a silicon vertex tracker, with five layers of double-sided silicon sensors, and a 40-layer central drift chamber, both operating in the 1.5 T magnetic field of a superconducting solenoid. We identify photons and electrons using a CsI(Tl) electromagnetic calorimeter (EMC). Further charged particle identification (PID) is provided by measurements of the average energy loss (dE=dx) in the tracking devices and by an internally reflecting, ring-imaging Cherenkov detector (DIRC) covering the central region.
We select a 0 candidates from the decay channel a 0 ! with the decays ! ( ) and ! ÿ 0 ( 3 ). All charged tracks are required to originate from a common vertex. For the decays B 0 ! 0 and B 0 ! f 0 , we use the same decay modes and 0 ! ÿ or f 0 ! ÿ . We apply the following requirements on the invariant masses (in MeV) relevant here: 500 < m < 585 for , 535 < m < 560 for 3 , 120 < m < 150 for 0 , and 510 < m < 1060 for 0 =f 0 . For the a 0 980 analysis we use a mass range 775 < m < 1175, while for a 0 1450 we require 775 < m < 1750; the latter upper limit removes background from D decays. These requirements, except for 0 and , are chosen to remove & 10% of real signal and retain sufficient sidebands to characterize the background for subsequent fitting.
The average number of candidates found per selected event is in the range 1.04 to 1.17, depending on the final state. We choose the candidate with mass closest to the nominal PDG value [13].
We make several PID requirements to ensure the identity of the pions and kaons. Secondary tracks from , 0 , or f 0 decays must have measured DIRC, dE=dx, and EMC outputs consistent with pions. For the B 0 ! a ÿ 0 (B 0 ! a ÿ 0 K ) decays, we require an associated DIRC Cherenkov angle between ÿ2 and 5 ( ÿ 5 and 2) standard deviations () from the expected value for a pion (kaon); the requirement is more restrictive on the side where there is kaon (pion) background. The distributions are corrected as a function of momenta and angles so that the distributions are normalized Gaussians. These requirements keep >90% of the wanted particle species with a misidentification background of <10%.
A B-meson candidate is characterized kinematically by the energy-substituted mass m ES 1 4 s ÿ p 2 B 1=2 and en- Backgrounds arise primarily from random combinations in continuum e e ÿ ! q q (q u, d, s, c) events. We reduce these by using the angle T between the thrust axis of the B 0 candidate in the 4S frame and that of the rest of the charged tracks and neutral clusters in the event. The distribution of j cos T j is sharply peaked near 1:0 for combinations drawn from jetlike q q pairs, and nearly uniform for B-meson decays. We require j cos T j < 0:70:8 for the ( 3 ) channels. We also use, in the fit described below, a Fisher discriminant F that combines the angles of the candidate direction with respect to the beam axis of the B momentum and B thrust axis [in the 4S frame], and moments describing the energy flow about the B thrust axis [21].
We use additional event-selection criteria to further reduce backgrounds from B decays. For the ! modes we remove backgrounds with one high-energy photon and a spurious low-energy photon such as B ! K by requiring j cos dec j 0:86, where dec is the angle of the photons in the rest frame with respect to the direction of the particle recoiling against the . Many backgrounds with low-energy ; K; or a 0 mesons are reduced with the requirement j cos a 0 dec j 0:8, where a 0 dec is defined similarly to dec . For B 0 ! 0 decays, we define H to be the magnitude of the cosine of the angle between the pion from the and the B 0 momentum in the rest frame, and require H < 0:75 to remove background from B 0 ! D ÿ that populates a narrow region near H 0:8. These additional requirements reduce the backgrounds by a factor of 2 -4, depending on the decay mode. We use Monte Carlo (MC) simulation [22] for an estimate of the residual B B background and to identify the few (mostly charmless) decays that survive the candidate selection and have characteristics similar to the signal (20 -270 events, depending on mode). We include a component in the fit to account for them.
We obtain yields and branching fractions from extended unbinned maximum-likelihood fits, with input observables E, m ES , m res for the a 0 1450 fits, these observables plus F for the a 0 980 fits, and these plus H for the 0 =f 0 fits. The observable m res denotes the mass for the a 0 analyses and the and ÿ masses for the 0 =f 0 fits. Early MC studies showed that a fit to the restricted lowmass range yields 20% better sensitivity for a 0 980, due to simplified PDF description and lower B B backgrounds. Thus we employ separate fits to determine the a 0 980 and a 0 1450 yields. The a 0 1450 fit has a component for a 0 980 with the yield fixed to the value found in the a 0 980 fit, corrected for the small efficiency difference. No a 0 1450 component is used for the a 0 980 fit since none of the subsamples have evidence of a 0 1450 signals.
For each event i and hypothesis j (signal, continuum background, B B background), we define a product of probability density functions (PDF) The bracketed variables F and H are not used in all fits. For all decays except for those involving a 0 1450, the absence of significant correlations among observables in the background is confirmed with the backgrounddominated data samples entering the fits. For the a 0 1450 decays, we find a substantial correlation in data between F and the invariant mass, due to the large mass range. We therefore require F < 0 for these modes, which keeps 90% of the signal, and exclude F from the fit. For the signal component, we correct for effects due to the neglect of small correlations (more details are provided in the systematics discussion below). The B B background yield is free in the 0 =f 0 fits and is found to be in agreement with expectations from MC simulations. For the decays involving a 0 mesons, we fix the B B yield to the value predicted by MC and include the uncertainty in the systematic errors (see below).
The likelihood function is where Y j is the yield of events of hypothesis j that we find by maximizing L, and N is the number of events in the sample. We determine the PDF parameters from simulation for the signal and B B background components. We parameterize each of the functions P sig m ES , P sig E, P j F , and P sig m res with either the sum of two Gaussian functions, a Breit-Wigner shape, or an asymmetric Gaussian function, as required to describe the distribution. P sig H for B 0 ! 0 is described by a second order polynomial. The shape of the real-meson component of P j m res in the combinatorial background is described with the same parameters as for signal. The distributions of m res , E, and H for B B and combinatorial background are represented by second order Chebyshev polynomials and/or the sum of two Gaussian functions. The q q combinatorial background in m ES is described by the function [23] fx x 1 ÿ x 2 p expÿ1 ÿ x 2 , with x 2m ES = s p and free parameter ; for peaking B B background, generally with the same or similar final state as signal, we add a Gaussian function to the quantity fx.
Large control samples of B ! D with a topology similar to the signal are used to verify the simulated resolutions in E and m ES . Where the control data samples reveal small differences from MC, we shift or scale the resolution used in the likelihood fits. Examples of many of these PDF shapes from a similar analysis are shown in Ref. [21]. Additionally, the signal parameters for the a 0 980 mass (983.5 MeV) and width (80 MeV) are determined from an inclusive data set that is much larger than the sample used for this analysis; they are consistent with expectations from the natural-width values of Ref. [15]. The values for a 0 1450 are taken from Ref. [13].
In Table I we show for each decay mode the measured product branching fraction, together with the quantities entering into its determination. In order to account for the uncertainties in the background PDF parameterization, we include as free parameters in the fit, in addition to the signal and background yields, the principal parameters describing the background PDFs. These include slopes for the polynomial shape for the E and m res distributions, the parameter used for m ES , and three parameters describing the asymmetric Gaussian function for F . For calculation of branching fractions, we assume that the decay rates of the 4S to B B ÿ and B 0 B 0 are equal [24]. We combine branching fraction results from the two  decay channels by adding the values of ÿ2 lnL, adjusted for a fit bias (see below), and taking proper account of the correlated and uncorrelated systematic errors. We quote 90% confidence level (C.L.) upper limits, taken to be the branching fraction below which lies 90% of the total of the likelihood integral in the positive branching fraction region.
In Fig. 2 we show projections onto m ES and mass of subsamples enriched by a mode-dependent threshold requirement on the ratio of signal to total likelihood (computed without the variable plotted). We show analogous projections of m ES and the ÿ invariant mass in Fig. 3.
The significance is taken as the square root of the difference between the value of ÿ2 lnL (with additive systematic uncertainties included) for zero signal and the value at the minimum, with other parameters free in both cases.
Most of the yield uncertainties arising from lack of knowledge of the PDFs have been included in the statistical error since most background parameters are free in the fit. Varying the signal PDF parameters within their estimated uncertainties, we determine the uncertainties in the signal yields to be 0 -9 events, depending on the final state. This uncertainty is substantial only for the modes with one of the a 0 resonances, where it is dominated by uncertainties in the parameterization of the a 0 signal shape. The neglect of correlations among observables in the fit can cause a systematic bias; the correction for this bias (between ÿ4 and 26 events) and assignment of the resulting systematic uncertainty (0.1-13 events) is determined from simulated samples with varying background populations. For the a 0 modes where the B B background yield is fixed, we estimate the uncertainty from modeling the B B backgrounds by varying the expected B B yield by 100% (0.1-12 events).
The above uncertainties are additive in nature and affect the significance of the results. The largest multiplicative uncertainties include our knowledge of the efficiency and other quantities entering the branching fraction calculation. Selection efficiency uncertainties are 1%-2% for cos T and 0.5%-0.8% due to the limited size of the MC samples. Uncertainties in the reconstruction efficiency found from auxiliary studies on inclusive control samples For the a 0 1450 plots, the a 0 980 signal is included in the background curves. These plots are made with a minimum requirement on the likelihood that has an efficiency for signal of 60%-70%. [21], include 0:5% N t and 1:5% N , where N t and N are the number of signal tracks and photons, respectively. The uncertainty on the total number of B B events is 1.1%. Published data [13] provide the uncertainties in the B-daughter product branching fractions (1%-2%).
In conclusion, we do not find significant signals for the B-meson decays presented here. The measured branching fractions and 90% C.L. upper limits are given in Table I. The limits for the a 0 980 channels are smaller than expectations [7][8][9][10]. This has been cited as evidence that the a 0 980 meson is a four-quark state, not the lowest-lying member of the q q scalar multiplet [9]. The limits for the a 0 1450 channels and B 0 ! 0 are consistent with theoretical expectations [9,12]. There are no previous measure-ments or theoretical predictions for the B 0 ! f 0 decay.
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