Search for the decay B0 to a1 rho

We present a search for the rare B-meson decay B0 to a1+- rho-+ with a_1+- to pi+ pi- pi+-. We use (110 +/- 1.2) x 10^6 Upsilon(4S) to BBbar decays collected with the BaBar detector at the PEP-II asymmetric-energy B Factory at SLAC. We obtain an upper limit of 30 x 10-6 (90% C.L.) for the branching fraction product B(B0 to a_1+- rho-+)B(a_1+- to pi+ pi- pi+-), where we assume that the a_1+- decays exclusively to rho0 pi+-.

The data used in this analysis were collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC during the years 2003-2004. This represents a total integrated luminosity of 100 fb −1 taken at the Υ (4S) resonance (on-peak), corresponding to a sample of 110 ± 1.2 million BB pairs. An additional 21.6 fb −1 of data, collected at approximately 40 MeV below the Υ (4S) resonance (off-peak), were used to study background from e + e − → qq (q = u, d, s, c) continuum events.
The BABAR detector is described in detail elsewhere [11]. Surrounding the interaction point is a silicon vertex tracker (SVT) with 5 double-sided layers which measures the impact parameters of charged particle tracks in both the plane transverse to, and along the beam direction. A 40 layer drift chamber (DCH) surrounds the SVT and provides measurements of the transverse momenta for charged particles. Both the SVT and the DCH operate in the magnetic field of a 1.5 T solenoid. Charged hadron identification is achieved through measurements of particle energy-loss in the tracking system and the Cherenkov angle obtained from a detector of internally reflected Cherenkov light. A CsI(Tl) electromagnetic calorimeter (EMC) provides photon detection, electron identification, and π 0 reconstruction. Finally, the instrumented flux return of the magnet allows discrimination of muons from pions.
We form π 0 → γγ candidates from pairs of photon candidates that have been identified as localized energy deposits in the EMC that have the lateral energy distribution expected for a photon. Each photon is required to have an energy E γ > 50 MeV, and the π 0 is required to have an invariant mass of 0.10 < m γγ < 0.16 GeV/c 2 .
The ρ − mesons are formed from one track that is consistent with a π − and the aforementioned π 0 candidate. The candidate ρ − is required to have an invariant mass of 0.5 < m ρ − < 1.1 GeV/c 2 . We also constrain the cosine of the angle between the π 0 momentum and the direction opposite to the B 0 in the ρ − rest frame (cos θ ρ − ) to be between −0.9 and 0.98. This removes backgrounds which peak at the extremes of the distribution where the signal reconstruction efficiency also falls off.
We form the a + 1 candidate from combinations of three charged pions. We first form a ρ 0 → π + π − candidate from two oppositely charged tracks. This combination is required to have an invariant mass of 0.4 < m ρ 0 < 1.1 GeV/c 2 . The a + 1 candidate is then formed by adding another charged track to the ρ 0 , and requiring that the mass of the a + 1 satisfies 0.6 < m a + 1 < 1.5 GeV/c 2 . The vertex of the B-candidate is constrained to originate from the beam spot. In order to reduce background from continuum events we require that | cos(θ T )| < 0.7, where θ T is the angle between the B thrust axis and that of the rest of the event (ROE).
We use two kinematic variables, m ES and ∆E, in order to isolate any signal. We define the beam-energy substi- where √ s is the e + e − center-of-mass (CM) energy. The second kinematic variable, ∆E, is the difference between the B-candidate energy and the beam energy in the CM frame. We require m ES > 5.25 GeV/c 2 and −0.15 < ∆E < 0.1 GeV.
Additional separation between signal and continuum is obtained by combining several kinematic and topological variables into a Fisher discriminant (F ) [14]. The variables L 0 , L 2 , and | cos θ T R |, and the output of a multivariate tagging algorithm [15] are used as inputs to F . L 0 and L 2 are defined as where the sum is over the ROE, p * i is the particle momentum in the CM frame. θ i is the angle of the particle direction relative to the thrust axis of the B-candidate, and cos θ T R is the cosine of the angle between the B thrust axis and the beam axis. The multivariate tagging algorithm identifies the flavor of the other B in the event to be either a B 0 or B 0 . The output of this algorithm is ranked into categories of different signal purity.
We expect the polarization of the a + 1 ρ − final state to be predominantly longitudinal, as was found in the similar decay B → ρρ [4][5][6][7][8]. We have used both longitudinal and transverse polarized signal MC simulated data in this analysis. After applying the selection cuts above, we have 2.8 (2.3) longitudinal (transverse) polarized signal MC simulated data candidates per event.
We define as self-cross-feed (SCF) the set of candidates that were incorrectly reconstructed from particles in events that contain a true signal candidate. We select one B candidate per event in which the mass of the reconstructed ρ 0 is closest to that of the true ρ 0 mass [16]. Choosing the candidate using the ρ 0 mass reduces the SCF fraction by 18% relative to a random selection. To avoid potentially biasing our final result, we do not use information from the ρ 0 meson in the remainder of the analysis. After all selection cuts have been applied, the longitudinal and transverse signal SCF fractions are 0.58 and 0.42, respectively. The selection efficiency of longitudinal (transverse) signal is 9.44% (10.15%).
Besides the continuum background we also have background from B decays. We divide the B-background into the following four categories according to B-meson charge and the charm content of the final states: (i) B 0 → charm, (ii) B 0 → charmless, (iii) B ± → charm and (iv) B ± → charmless. From large samples of inclusive MC simulated data we expect 2394, 424, 3281 and 215 events of these background types, respectively. In addition, a number of exclusive B-background modes that have a similar final state to the signal were studied. This includes those that have an intermediate a 1 meson in the decay. None of these modes were seen to have a significant efficiency after the selection cuts had been applied.
We perform an extended unbinned maximum likelihood fit to the data. The likelihood model has the following types: (i)-(iv) the four aforementioned inclusive B-background categories, (v) true signal, (vi) SCF signal and the (vii) e + e − → qq (q = u, d, s, c) continuum background. The probability density function (PDF) for each event i has the form P i,c = P i,c (m ES , ∆E, F , m a + 1 , m ρ − , cos θ ρ − ). From these individual PDFs the total likelihood is constructed. The parameters n and n ′ are the numbers of selected on-peak events, and the sum of the yields N c , where c is one of the seven types in the likelihood model. Correlations between the m ρ − and cos θ ρ − variables are taken into account for the real (T) and fake combinatorial (F) ρ − candidates. All other correlations between fit variables are seen to be small. However, the effect of ignoring them results in a bias on the fitted signal yield which is discussed below. Each of the signal distributions has a signal yield and a polarization fraction that are denoted by N sig (N ′ sig ) and f L (f ′ L ), for the true (SCF) signal, such that the sum of the true and SCF signal is described by The continuum yield, N sig , N ′ sig , and the parameters of the continuum m ES and ∆E PDFs are allowed to vary in the fit. Under the assumption that no significant signal is observed, the value of f L is fixed to 1.0 in the fit. The value of f ′ L is also fixed to 1.0 in the fit since it is highly correlated with N sig , N ′ sig and f L . Only the fitted value of N sig is used to derive the final result. We also fix the B-background yields to the aforementioned values.
The PDFs used for each component are given in Table I. The signal and B-backgrounds are parameterized using MC. We use a non-parametric smoothing algorithm [17] when defining some of the background PDFs (as indicated by the abbreviation NP). We account for the difference between F and T ρ − → π − π 0 distributions in the background using the product of 1D PDFs, denoted in Table I as 'BG m-hel', such that where a T is the fraction of T events. The continuum shape for cos θ ρ − (m ρ − ) is derived from off-peak (onpeak) data. The true ρ − resonance Breit Wigner shape uses m ρ − = 0.77 GeV/c 2 , and Γ = 0.150 GeV [16]. The parameterizations used for this PDF are summarized in Table II. The results from the fit are N sig = 90±38(stat), N ′ sig = 42 ± 98 and a continuum yield of 25798 ± 182 events. The bias on the fitted signal yield is evaluated by performing ensembles of mock experiments using signal MC embedded into MC samples of background generated from   [18], ARGUS = ARGUS function , with x ≡ 2mES/ √ s and parameter ξ [19], which is allowed to vary in the fit, Pn = Polynomial of order n, BW = Breit-Wigner, helicity = cos 2 θ ρ − or sin 2 θ ρ − depending on partial wave which is modified by a quadratic acceptance function, BG m-hel = Background cos θ ρ − and m − ρ PDF of Eq. 4, off-peak = PDF taken from off-peak data, and 1D = smoothed 1D histogram.  Table I.
the PDF. The bias is found to be +22 events (24%), resulting in a corrected signal yield of 68 ± 38(stat). In Fig. 1 we compare the true signal and continuum PDF shapes (solid curves) to the data (points) using the eventweighting technique described in Ref. [20]. The distributions shown in Fig. 1 are not corrected for fit bias, and the uncertainty on each of the data points is statistical. No change in signal yield is seen when a + 2 (1320)ρ − and π + (1300)ρ − components are included in the fit. Table III summarises the systematic uncertainties on the signal yield. Each entry in the table indicates one systematic effect, and the contributions are added in quadrature to give the total presented. The uncertainty due to PDF parameterisation is evaluated by variation of both the signal and the background PDF parameters within their uncertainties about their nominal values. The uncertainty from the continuum m ES and ∆E PDFs which are allowed to vary in the fit, are only included in the quoted statistical uncertainty. We assign a systematic uncertainty due to fit bias, evaluated as half of the fit bias correction on the signal yield. To validate the expected B-background yields, and to assign a systematic uncertainty we perform a number of cross-checks in which we allow the background yields to vary in turn when fitting the data. We use a control sample of B → Dρ events to determine the systematic uncertainty in the fraction of SCF signal events. The effect of exclusive B meson decays to final states including a 1 -mesons were evaluated using ensembles of mock experiments. In particular, the systematic uncertainty on the signal yield from neglecting B → a 1 a 1 modes in the fit is 6 events. We assign a systematic uncertainty from using a relativistic Breit-Wigner with a Blatt-Weisskopf form factor with a range parameter of 3.0 GeV −1 for the a + 1 meson line shape. In the fit we assume that the a + 1 meson width, Γ a + 1 , is 400 MeV. We evaluate a systematic uncertainty due to this assumption by varying Γ a + 1 over the experimentally allowed range: 250 -600 MeV [16]. The difference in the distribution of F between data and MC is evaluated with a large sample of B → D ⋆ ρ decays. The systematic uncertainties that contribute to the branching fraction only through the efficiency come from charged particle identification (6.0%), π 0 meson reconstruction (3.0%), tracking efficiency (3.2%), and the number of B meson pairs (1.1%). The systematic error contribution from MC statistics is negligible. When the fit bias correction of −22 events is applied to the signal yield, and one accounts for systematic uncertainties, the significance of the result is using the weighting technique described in Ref. [20]. The points represent the weighted data, and solid curves represent the corresponding PDFs. 0.95 standard deviations. Figure 2 shows the distribution of −ln(L/L max ) for the fit, with and without these systematic errors. L max is the value of the likelihood corresponding to the nominal fit result. The branching fraction value for the fit-bias-corrected signal yield of 68 ± 38(stat) +45 −56 (syst) is B(B 0 → a + 1 ρ − )B(a + 1 → π + π − π + ) = (15.7 ± 8.7(stat) +10.3 −12.8 (syst))×10 −6 . This assumes that f L = 1.0 and that the branching fraction of a + 1 → π + π − π + = 0.5. As the signal yield obtained is not significant, we calculate the upper limit x UL , by integrating the likelihood function (including systematic uncertainties) from 0 to x UL , for different physically allowed values of f L , such that the C.L. of the upper limit is 90%. As the signal efficiency is a function of f L , we report the most conservative upper limit obtained, which corresponds to f L = 1.0. On doing this, an upper limit of 30×10 −6 (90% C.L.) is obtained. We have performed a search for the decay B 0 → a ± 1 ρ ∓ in a data sample of 100 fb −1 . After correcting for fit bias and accounting for systematic uncertainties, the signal yield is 68 ± 38(stat) +45 −56 (syst) events, with a significance of 0.95σ. As there is no significant evidence for a signal, we place an upper limit of 30×10 −6 (90% C.L.) on B(B 0 → a + 1 ρ − )B(a + 1 → π + π − π + ), where we assume that the a + 1 decays exclusively to ρ 0 π + . Assuming B(a + 1 → π + π − π + ) is equal to B(a + 1 → π + π 0 π 0 ), we obtain B(B 0 → a + 1 ρ − )B(a + 1 → (3π) + ) < 61×10 −6 (90% C.L.). This upper limit corresponds to a significant improvement over the previous bound and is compatible with theoretical expectations [10]. This result is a significant improvement in constraining an important B background contribution in B → ρρ decays.

ACKNOWLEDGMENTS
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