Evidence for the Rare Decay B+ -->Ds+ pi0

We have searched for the rare decay B+ -->Ds+ pi0. The analysis is based on a sample of 232 million Upsilon(4S) -->B anti-B decays collected with the BABAR detector at the PEP-II e+ e- storage ring. We find 19.6 signal events, corresponding to a significance of 4.7 sigma. The extracted signal yield including statistical and systematic uncertainties is 20.1+6.8+0.4 -6.0-1.5, and we measure B(B+ -->Ds+ pi0) =(1.5 +0.5 -0.4 +- 0.1 +- 0.2) 10^-5, where the first uncertainty is statistical, the second is systematic, and the last is due to the uncertainty on the Ds+ decay and its daughter decay branching fractions.

We have searched for the rare decay B + → D + s π 0 . The analysis is based on a sample of 232 million Υ (4S) → BB decays collected with the BABAR detector at the PEP-II e + e − storage ring. We find 19.6 signal events, corresponding to a significance of 4.7 σ. The extracted signal yield including statistical and systematic uncertainties is 20.1 +6.8+0.4 −6.0−1.5 , and we measure B(B + → D + s π 0 ) = (1.5 +0. 5 −0.4 ± 0.1 ± 0.2) × 10 −5 , where the first uncertainty is statistical, the second is systematic, and the last is due to the uncertainty on the D + s decay and its daughter decay branching fractions.
PACS numbers: 12.15.Hh,11.30.Er,13.25.Hw Significant CP violation in the standard model (SM) of particle physics is induced by the 3 × 3 unitary Cabibbo- Kobayashi-Maskawa (CKM) quark flavor mixing matrix V [1] but is considered too small to produce the observed matter-antimatter asymmetry in the universe. Hence, New Physics contributions are searched for by testing unitarity conditions for V in a variety of processes. In these tests the parameter γ = arctan(η/ρ), where ρ + i · η ≡ −V ud V * ub /V cd V * cb , plays a crucial role as it is extracted from processes dominated by SM tree-amplitudes and can be compared with γ obtained from constraints dominated by loop amplitudes which are mutually sensitive to New Physics. Constraints on sin(2β + γ) (β = arctan(η/(1 − ρ))) can be obtained from the measurement of time-dependent decay rates in B 0 , B 0 →D − π + or D * − π + [2], where CKM-favored (∝ V * cb V ud ) and CKMsuppressed (∝ V * ub V cd ) processes interfere [3]. First measurements have been recently published [4].
The ratio r = |A(B 0 →D + π − )/A(B 0 →D − π + )| of decay amplitudes is required in order to constrain sin(2β + γ) from B 0 →D ∓ π ± . The amplitude A(B 0 →D − π + ) is well known from the precisely measured branching fraction B(B 0 →D − π + ) [5]. With the currently available data samples the measurement of the CKM-suppressed decay B 0 →D + π − is not feasible due to the presence of a very large background from the CKM-favored decay B 0 →D + π − . This problem could be avoided with the measurement of the isospin related decay B + → D + π 0 which is currently out of reach due to its small branching fraction (< 10 −6 ). However, r can be related to B(B 0 → D + s π − ) [3] as well as to B(B + → D + s π 0 ) with the use of SU(3) flavor symmetry. Tree and W -exchange amplitudes contribute to B 0 → D + π − , whereas only a tree amplitude contributes to B 0(+) → D + s π −(0) . The exchange amplitude is expected to be small and has been estimated at 10−15% of the total decay amplitude [6]. This estimate uses B(B 0 → D − s K + ) [7] and neglects finalstate rescattering interactions. Non-factorizable SU(3)breaking effects are hard to quantify and often assumed to not exceed the 30% level [4] consistent with the spread of theoretical estimates of r [8].
The branching fraction B(B 0 → D + s π − ) has been measured by the Belle and BABAR collaborations [7]. The decay B + → D + s π 0 provides an independent estimate of r, though not as precise as the one from B 0 → D + s π − due to the smaller branching fraction and reconstruction efficiency. It also represents a significant background source for analyses of other decays related to the extraction of sin(2β +γ), such as B + → D + π 0 , D * + s π 0 or B 0 → D + s ρ − . For B(B + → D + s π 0 ) only an upper limit of 2 × 10 −4 at 90% confidence level [9] has been established so far. Here, we present evidence for the decay B + → D + s π 0 and a measurement of its branching fraction.
The analysis uses a sample of 232 million Υ (4S) decays into BB pairs collected with the BABAR detector at the PEP-II asymmetric-energy B-factory. The BABAR detector is described in detail elsewhere [10]. We use the GEANT4 [11] Monte Carlo (MC) software to simulate interactions of particles traversing the BABAR detector.
We select events with a minimum of three reconstructed tracks. To reject e + e − → qq (q = u, d, s, c) continuum events, the ratio of the second and zeroth order Fox-Wolfram moments [12], determined from all clusters in the electromagnetic calorimeter with an energy above 30 MeV and all tracks, must be less than 0.5.
We reconstruct D + s -meson candidates in the decay modes D + s → φπ + , K 0 S K + , and K * 0 K + , with φ→K + K − , K 0 S →π + π − , and K * 0 →K − π + . Charged kaon (pion) candidates are required to fulfill kaon (pion) selection criteria with high efficiency (80−95%) and small misidentification probability (1 − 10%) depending on the selector used [10,13]. K 0 S candidates, reconstructed from two oppositely-charged tracks, are required to have a measured flight distance from the primary interaction point that is at least three times the measurement error and an invariant π + π − mass of ±15 MeV/c 2 around the PDG mass [5]. φ (K * 0 ) candidates are required to have an invariant K + K − (K − π + ) mass of ±30 (±75) MeV/c 2 around the PDG mass [5]. D + s candidates are required to have invariant masses m D + s within 60 MeV/c 2 around m PDG [5]. We further define a sig- where σ has been determined from the MC simulation and found to be 4.7 (5.0) MeV/c 2 for D + s → φπ + (K * 0 K + ) and To suppress background from B + → D * + s π 0 events we restrict the D + s momentum in the Υ (4S) system to lie within [2.073, 2.550] GeV/c. Decay daughters from K * 0 , K 0 S , D + s , and B + candidates are constrained to a geometric vertex.
Neutral pions are reconstructed in π 0 → γγ requiring a π 0 laboratory energy above 200 MeV and an invariant mass m γγ ∈ [115, 150] MeV/c 2 . To improve the momentum resolution a kinematic fit is applied to the daughter photons constraining m γγ to the PDG π 0 mass [5].
Charged B-meson candidates are obtained by combining D + s and π 0 candidates and are identified by two kinematic variables. The first is the beam-energy-substituted where E 0 and p 0 are the energy, respectively, the momentum of the e + e − system, p B the B + candidates momentum, and √ s the For signal events the m ES distribution is centered at the B-meson mass with a resolution of about 2.5 MeV/c 2 , and the ∆E distribution has a maximum close to zero with a resolution of about 50 MeV. The m ES and ∆E signal distributions are both asymmetric with a tail towards smaller values due to energy leakage in the electromagnetic calorimeter when reconstructing π 0 → γγ. The signal region is defined by m ES ∈ [5.2, 5.3] GeV/c 2 and |∆E| < 0.2 GeV. In a small fraction of events (< 5%) multiple signal candidates are found. In this case, the candidate with the smallest deviation of m γγ from the PDG π 0 mass [5] is retained. If multiple candidates still remain, the final candidate is selected randomly.
A neural network (N N ) [14] built from event topology and invariant mass variables is used to suppress continuum background, mainly coming from e + e − → cc. The N N variables are: (1) thrust [15] and (2) sphericity [16], both calculated from all tracks and neutral candidates in the event; (3) the cosine of the angle between the thrust axis of the B + candidate and the thrust axis calculated from all tracks and neutral candidates not belonging to the B + candidate; (4) the energy flow moments L 0 and L 2 [17]; (5) the cosine of the angle between the thrust axis of the B + candidate in the Υ (4S) system and the beam axis; (6) the cosine of the angle between the B + momentum vector in the Υ (4S) system and the beam axis; (7) the invariant mass of the corresponding φ, K 0 S and K * 0 candidate, and (8) the cosine of the helicity angle between the φ (K * 0 ) momentum in the D + s rest frame and the momentum vector of the φ (K * 0 ) decay daughter in the φ (K * 0 ) rest system. The N N has been trained on simulated B + → D + s π 0 and simulated continuum events. With an optimized N N cut, signal events are retained with an efficiency of order 60%, while about 96% (70%) of continuum events (non-signal B decays) are rejected.
We extract the signal yield with a two-dimensional extended unbinned maximum likelihood fit in the variables m ES and ∆E where we combine the three D + s modes. The extended log-likelihood function used is given by where the sum is over i = 1, ..., N = 154 selected events inside the signal region and the n j represent the three yields after the aforementioned selection: (1) signal (SIG), (2) combinatorial background (CBG) that comes from random combinations of tracks and π 0 candidates, mainly from continuum events, and (3) B background peaking at m ES values close to the nominal B-meson mass and at negative ∆E values (PBG) mostly due to B + → D * + s π 0 . P j (x i ) is the product of probability density functions (PDF's) of candidate i in the variables To take into account correlations observed in the simulation we allow in some cases for a functional dependence of the PDF parameters of P j,1 (m ES ) on ∆E, or of P j,2 (∆E) on m ES .
The signal PDF has been determined from the MC simulation. The m ES PDF is described by an asymmetric Gaussian G(m ES , µ, σ) with σ = σ L (σ R ) for x−µ < 0(≥ 0). The parameters µ, σ L and σ R are given by second order polynomials in ∆E in order to take into account a non-linear correlation between ∆E and m ES observed in the MC simulation. The ∆E signal PDF is described by a Crystal Ball function [18].
The CBG PDF in m ES is parameterized by where m max ES is the kinematic limit √ s/2 fixed at 5.2895 GeV/c 2 . The CBG PDF in ∆E is described by a second order polynomial Pol(∆E) = 1 + p 1 · ∆E + p 2 (m ES ) · ∆E 2 . To take into account a possible correlation between ∆E and m ES of order 5%, the parameter p 2 depends linearly on m ES . The parameters ξ, p 1 , and p 2 are determined from the likelihood fit on data.
The PBG component is modeled by simulated B + → D * + s π 0 MC events. The ∆E PDF is described by a Gaussian. As in the case for the signal, the m ES PDF is described by an asymmetric Gaussian, and its parameters µ, σ L and σ R are given by second order polynomials in ∆E. Additional backgrounds that peak at negative ∆E values are due to B-meson decays such as B 0 → D ( * )− ρ + with a similiar decay topology and kinematics as the signal decay. This kind of background is found to be well described by the B + → D * + s π 0 PDF. Another sizeable background source from the decay B 0 → D + s ρ − is not well described by the B + → D * + s π 0 PDF. However, the expected number of B 0 → D + s ρ − events estimated from Ref. [20] is small compared to the other peaking background sources. As a consequence, we do not introduce an additional PDF and estimate the fit bias introduced in this way from a dedicated MC simulation study.
The fit has been validated on samples using signal and peaking background events from the full MC simulation. From the likelihood fit we find the yield estimatorsn SIG = 19.6 +6.8 −6.0 ,n CBG = 116.7 ± 12.5 and n PBG = 17.7 ± 6.9, the latter being consistent with the expectation from the MC simulation. The signal significance is determined from a MC simulation containing no signal events, where we use the background yields and the CBG parameters as measured by the fit on data. We include the statistical uncertainties on the CBG PDF parameters and the uncertainties on the background yields and find a probability to observe at leastn SIG events of 1.5 × 10 −6 corresponding to a 4.7 σ significance. Fit projections for ∆E and m ES are shown in Fig. 1 where background contributions are suppressed by a cut on the signal-to-background likelihood ratio where the cut values are determined from MC by maximizing the ratiô n SIG / √n SIG +n CBG +n PBG . We assume B(Υ (4S) → B + B − ) = B(Υ (4S) → B 0 B 0 ) and calculate the branching fraction from B(B + → D + s π 0 ) =n SIG /(N BB k ε k B k ), where N BB is the number of charged and neutral B-meson pairs, ε k is the signal efficiency, and B k is the branching fraction of D + s decay mode k (k = φπ + , K 0 S K + , K * 0 K + ) including their daughter decay modes taken from Ref. [5] and scaled to the recent result [21] for D + s → φπ + (B φπ + = 2.3%, B K 0 S K + = 1.7%, B K * 0 K + = 2.9%). Signal efficiencies (ε φπ + = 9.7%, ε K 0 S K + = 9.1%, ε K * 0 K + = 7.1%) are estimated from the MC simulation and are corrected for differences between data and simulation using high statis-tics control samples of high purity. The result is where the first uncertainty is statistical, the second systematic (Table I) and the third due to the branching fraction uncertainties of the D + s [21] and its daughter decays (Table I and Ref. [5]). We also quote the product B(B + → D + s π 0 )B(D + s → φπ + )=(7.0 +2.4+0.5 −2.1−0.7 ±0.4)×10 −7 . Several systematic uncertainties on the signal yield have been considered. Background from B decays into charmless final states (CPBG, e.g. B + → φρ + ) peaking in the same region in m ES and ∆E as B + → D + s π 0 has been estimated from a fit in the D + s mass sidebands. Scaled to the D + s mass signal region we find n scaled CPBG = −1.4 ± 1.4 and assign the statistical error as a one-sided systematic error. The background peaking at negative ∆E values found in this fit is consistent with the MC expectation. MC studies with many samples of the same size as the data sample indicate a small negative fit bias. We correct for this bias (+0.5 events) and assign the statistical uncertainty as a systematic error (±0.3 events). The PDF parameters for signal and peaking background have been varied within their errors as found in the fit on MC resulting in a variation of ±0.20 events in the signal yield. The change in the signal yield when m max ES is free to vary is +0.16 events and is assigned as a systematic error. The possible bias inn SIG due to the presence of B 0 → D + s ρ − events is estimated to be −0.18 events where the upper limit at 90% confidence level [20], B(B 0 → D + s ρ − ) < 1.9 × 10 −5 , has been assumed, and is assigned as a systematic uncertainty. We obtain a total systematic uncertainty on the signal yield of +0.4 −1.5 events.
Other systematic uncertainties on the branching fraction are due to the uncertainty on N BB , the statistical uncertainty on the MC samples used, and possible differences in detection and reconstruction efficiencies between data and MC simulation for: N N and m D + s selection requirements estimated with a high-purity control sample of B + → D + sD 0 (D 0 → K + π − , K + π − π + π − ) events; charged particle tracking; K 0 S and π 0 reconstruction; and charged particle identification (PID).
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), I: Contributions to the relative systematic uncertainty (in %) on the branching fraction B(B + → D + s π 0 ) coming from the signal efficiency subdivided in the reconstructed D + s modes, the signal yield, and the number of BB pairs. Also shown is the total relative systematic uncertainty and the uncertainty due to the individual B k (both in %).