A search for B+ -->tau+ nu with Hadronic B tags

We present a search for the decay B^+ -->tau^+ nu using $383 \times 10^{6}}$ BBbar pairs collected at the Upsilon(4S) resonance with the BABAR detector at the SLAC PEP-II B Factory. We select a sample of events with one completely reconstructed tag B in a hadronic decay mode ($B^- \to D^{(*)0} X^-$), and examine the rest of the event to search for a B^+ -->tau^+ nu decay. We identify the tau lepton in the following modes: tau^+ -->e^+ nu nu,tau^+ -->mu^+ nu nu, tau^+ -->pi^+ nu and tau^+ -->pi^+ pi^0 nu. We find a 2.2 sigma excess in data and measure a branching fraction of B(B+ -->tau^+ nu) = (1.8^{+0.9}_{-0.8}(stat.) \pm 0.4(bkg. syst.) \pm 0.2 (other syst.)) \times 10^{4}. We calculate the product of the B meson decay constant f_{B} and |V_{ub}| to be f_{B} |V_{ub}| = (10.1^{+2.3}_{-2.5}(stat.)^{+1.2}_{-1.5}(syst.))\times10^{-4} GeV

The process B + → τ + ν is also sensitive to extensions of the SM. For instance, in two-Higgs doublet models [6] and in the MSSM [7,8] it could be mediated by charged Higgs bosons. The branching fraction measurement can therefore also be used to constrain the parameter space of extensions to the SM.
The B + → µ + ν and B + → e + ν decays are significantly helicity suppressed with respect to the B + → τ + ν channel. However, a search for B + → τ + ν is experimentally more challenging, due to the presence of multiple neutrinos in the final state, which makes the experimental signature less distinctive. In a previously published analysis using a sample of 383 × 10 6 Υ (4S) → BB decays, based on the reconstruction of a semileptonic B decay on the tag side, the BABAR collaboration set an upper limit B(B + → τ + ν) < 1.7 × 10 −4 at the 90% confidence level (CL) [9]. The Belle Collaboration has reported evidence from a search for this decay and the branching fraction was measured to be B(B + → τ + ν) = (1.79 +0.56 −0.49 (stat.) +0.46 −0.51 (syst.)) × 10 −4 [10].
The data used in this analysis were collected with the BABAR detector at the PEP-II storage ring. The sample corresponds to an integrated luminosity of 346 fb −1 at the Υ (4S) resonance (on-resonance) and 36.3 fb −1 taken at 40 MeV below the Υ (4S) resonance (off-resonance). The on-resonance sample contains 383 × 10 6 BB decays. The detector is described in detail elsewhere [11]. Chargedparticle trajectories are measured in the tracking sys- * Deceased † Now at Tel Aviv University, Tel Aviv, 69978, Israel ‡ Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy § Also with Università della Basilicata, Potenza, Italy ¶ Also with Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain tem composed of a five-layer silicon vertex detector and a 40-layer drift chamber (DCH), operating in a 1.5 T solenoidal magnetic field. A Cherenkov detector is used for π-K discrimination, a CsI calorimeter for photon detection and electron identification, and the flux return of the solenoid, which consists of layers of steel interspersed with resistive plate chambers or limited streamer tubes, for muon and neutral hadron identification. In order to estimate signal selection efficiencies and to study physics backgrounds, we use a BABAR Monte Carlo (MC) simulation based on GEANT4 [12]. In MC simulated signal events one B + meson decays to τ + ν and the other into any final state. The BB and continuum MC samples are, respectively, equivalent to approximatively three times and 1.5 times the accumulated data sample. Beam-related background and detector noise are taken from data and overlaid on the simulated events.
We reconstruct an exclusive decay of one of the B mesons in the event (tag B) and examine the remaining particle(s) for the experimental signature of B + → τ + ν. In order to avoid experimenter bias, the signal region in data is blinded until the final yield extraction is performed.
The tag B candidate is reconstructed in the set of hadronic B decay modes B − → D ( * )0 X − [1], where X − denotes a system of charged and neutral hadrons with total charge −1 composed of n 1 π ± , n 2 K ± , n 3 K 0 S , n 4 π 0 , where n 1 + n 2 ≤ 5, n 3 ≤ 2, and n 4 ≤ 2. We reconstruct D * 0 → D 0 π 0 , D 0 γ; D 0 → K − π + , K − π + π 0 , K − π + π − π + , K 0 S π + π − and K 0 S → π + π − . The kinematic consistency of tag B candidates is checked with the beam energy-substituted mass m ES = s/4 − p 2 B and the en- Here √ s is the total energy in the Υ (4S) center-of-mass (CM) frame, and p B and E B denote, respectively, the momentum and energy of the tag B candidate in the CM frame. The resolution on ∆E is measured to be σ ∆E = 10 − 35 MeV, depending on the decay mode; we require |∆E| < 3σ ∆E . The purity P of each reconstructed B decay mode is estimated, using on-resonance data, as the ratio of the number of peaking events with m ES > 5.27 GeV/c 2 to the total number of events in the same range. If multiple tag B candidates are reconstructed, the one with the highest purity P is selected. If more than one candidate with the same purity is reconstructed, the one with the lowest value of |∆E| is selected. From the dataset obtained as described above, we consider only those events in which the tag B is reconstructed in the decay modes of highest purity P. The set of decay modes used is defined by the requirement that the purity of the resulting sample is not less than 30%.
The background consists of e + e − → qq (q = u, d, s, c) events and other Υ (4S) → B 0 B 0 or B + B − decays in which the tag B candidate is mis-reconstructed using particles coming from both B mesons in the event. To reduce the e + e − → qq background, we require | cos θ * T B | < 0.9, where θ * T B is the angle in the CM frame between the thrust axis [13] of the tag B candidate and the thrust axis of the remaining reconstructed charged and neutral candidates.
In order to determine the number of correctly reconstructed B + decays, we classify the background events in four categories: e + e − → cc; e + e − → uu, dd, ss; Υ (4S) The m ES shapes of these background distributions are taken from MC simulation. The normalization of the e + e − → cc and e + e − → uu, dd, ss backgrounds is taken from off-resonance data, scaled by the luminosity and corrected for the different selection efficiencies evaluated with the MC. The normalization of the B 0 B 0 , B + B − components are obtained by means of a χ 2 fit to the m ES distribution in the data sideband region (5.22 GeV/c 2 < m ES < 5.26 GeV/c 2 ). The number of background events in the signal region (m ES > 5.27 GeV/c 2 ) is extrapolated from the fit and subtracted from the data. We estimate the total number of tagged B's in the data to be N B = (5.92±0.11(stat))×10 5 .  After the reconstruction of the tag B meson, a set of selection criteria is applied to the rest of the event (recoil) in order to enhance the sensitivity to B + → τ + ν decays. We require the presence of only one well-reconstructed charged track (signal track) with charge opposite to that of the tag B. The signal track is required to have at least 12 hits in the DCH, momentum transverse to the beam axis, p T , greater than 0.1 GeV/c, and the point of closest approach to the interaction point less than 10 cm along the beam axis and less than 1.5 cm transverse to it.
The τ lepton is identified in four decay modes constituting approximately 71% of the total τ decay width: τ + → e + νν, τ + → µ + νν, τ + → π + ν, and τ + → π + π 0 ν. Particle identification criteria on the signal track are used to separate the four categories. The τ + → π + π 0 ν sample is obtained by associating the signal track, identified as pion, with a π 0 reconstructed from a pair of neutral clusters with invariant mass between 0.115 and 0.155 GeV/c 2 and total energy greater than 250 MeV. In case of multiple π + π 0 candidates, the one with largest center-of-mass momentum p * π + π 0 is chosen. We place a mode-dependent cut on | cos θ * T B | to reduce the background due to continuum events and incorrectly reconstructed tag B candidates (combinatorial). The remaining sources of background consists of B + B − events in which the tag B meson was correctly reconstructed and the recoil contains one track and additional particles that are not reconstructed by the tracking detectors and calorimeter. MC simulation shows that most of this background is from semileptonic B decays.
We define the discriminating variable E extra as the sum of the energies of the neutral clusters not associated with the tag B or with the signal π 0 from the τ + → π + π 0 ν mode, and passing a minimum energy requirement. The required energy depends on the selected signal mode and on the calorimeter region involved and varies from 50 to 70 MeV. Signal events tend to peak at low E extra values, whereas background events, which contain additional sources of neutral clusters, are distributed toward higher E extra values.
Other variables used to discriminate between signal and background are the CM momentum of the signal candidates, the multiplicities of low p T charged tracks and of π 0 candidates in the recoil, and the direction of the missing momentum four-vector in the CM frame. For the τ + → π + π 0 ν mode, we exploit the presence of the π 0 in the final state and the dominance of the decay through the ρ + resonance by means of the combined quantity x ρ = [(m π + π 0 −m ρ )/(Γ ρ )] 2 +[(m γγ −m π 0 )/(σ π 0 )] 2 , where m π + π 0 is the reconstructed invariant mass of the π + π 0 candidate, m γγ is the reconstructed invariant mass of the π 0 candidate, m ρ and Γ ρ are the nominal values [4] for the ρ mass and width, m π 0 is the nominal π 0 mass and σ π 0 = 8 MeV/c 2 is the experimental resolution on the π 0 mass determined from data.
We optimize the selection by maximizing s/ √ s + b using the B + B − MC and signal MC, where b is the expected background from B + B − events and s is the expected number of signal events in the hypothesis of a branching fraction of 1 × 10 −4 . The optimization is performed separately for each τ decay mode and with all the cuts applied simultaneously in order to take into account any correlations among the discriminating variables. The optimized signal selection cuts are reported in Table I.
We compute the signal selection efficiency as the ratio of the number of signal MC events passing the selection criteria to the number of signal events that have a correctly reconstructed tag B candidate in the signal region m ES > 5.27 GeV/c 2 . We evaluate the efficiencies on a signal MC sample which is distinct from the sample used in the optimization procedure. A small cross-feed in some modes is estimated from MC and is taken into account in the computation of the total efficiency. Variable e + µ + π + π + π 0 Eextra ( GeV) < 0.160 < 0.100 < 0.230 < 0.290 π 0 multiplicity 0 0 ≤ 2 -Track multiplicity The total efficiency for each selection is given by: where ε j i is the efficiency of the selection i for the τ decay mode j, n dec = 7 is the number of τ decay modes that can contribute to the reconstructed modes and f j are the fractions of the τ decay mode as estimated from the signal MC sample with a reconstructed tag B. Table II shows the estimated efficiencies. II: Efficiency (in percent) of the most relevant τ decay modes (rows) to be selected in one of the four modes considered in this analysis (column). The All decay row shows the selection efficiency of each reconstruction mode, adding the contribution from the previous rows, weighted by the decay abundance at the tag selection level fj . The last row shows the total signal selection efficiency. The uncertainties are statistical only.
Mode To determine the expected number of background events in the data, we use the final selected data samples with E extra between 0 and 2.4 GeV. We first perform an extended unbinned maximum likelihood fit to the m ES distribution in the E extra sideband region 0.4 GeV < E extra < 2.4 GeV of the final sample. For the peaking component of the background we use a probability density function (PDF) which is a Gaussian function joined to an exponential tail (Crystal Ball function) [14]. As a PDF for the non-peaking component, we use a phase space motivated threshold function (ARGUS function) [15]. From this fit, we determine a peaking yield N side,data pk and signal shape parameters, to be used in later fits. We apply the same procedure to B + B − MC events which pass the final selection and determine the peaking yield N side,MC After finalizing the signal selection criteria, we measure the yield of events in each decay mode in on-resonance data. Table III reports the number of observed events together with the expected number of background events, for each τ decay mode. Figure 2 shows the E extra distribution for data and expected background at the end of the selection. The signal MC, normalized to a branching fraction of 3 × 10 −3 for illustrative purposes, is overlaid for comparison. The E extra distribution is also plotted separately for each τ decay mode.
We combine the results on the observed number of events n i and on the expected background b i from each of the four signal decay modes (n ch ) using the estimator Q = L(s + b)/L(b), where L(s + b) and L(b) are the likelihood functions for signal plus background and background-only hypotheses, respectively:  2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2  Eextra distribution after all selection criteria have been applied. The upper plot shows the distribution of all the modes combined while lower plots show the (a) τ + → e + νν, (b) τ + → µ + νν, (c) τ + → π + ν, and (d) τ + → π + π 0 ν modes separately. The on-resonance data (black dots) distribution is compared with the total background prediction (continuous histogram). The hatched histrogram represents the combinatorial background component. B + → τ + ν signal MC (dashed histogram), normalized to a branching fraction of 3 × 10 −3 for illustrative purposes, is shown for comparison. fraction by: where N tag B + is the number of tag B + mesons correctly reconstructed, ε tag B and ε tag sig are the tag B efficiencies in generic BB and signal events respectively, and ε i are the signal efficiencies defined in equation 2. We fix the ratio ε tag sig /ε tag B = 0.939 ± 0.007(stat.) to the value obtained from MC simulation.
We estimate the branching fraction (including statistical uncertainty and uncertainty from the background) by scanning over signal branching fraction hypotheses and computing the value of L(s + b)/L(b) for each hypothesis. The branching fraction is the hypothesis which minimizes the likelihood ratio −2 ln Q = −2 ln(L(s+b)/L(b)), and we determine the statistical uncertainty by finding the points on the likelihood scan that occur at one unit above the minimum.
The dominant uncertainty on the background predic-tions b i is due to the finite B + B − MC statistics. We also check possible systematic effects in the estimation of combinatorial background by means of a sample of events with looser selection requirements; we find it to be negligible with respect to the statistical uncertainty. The background uncertainty is incorporated in the likelihood definition used to extract the branching fraction, by convolving it with a Gaussian function with standard deviation equal to the error on b i [16]. The other sources of systematic uncertainty in the determination of the B + → τ + ν branching fraction come from the estimation of the tag yield and efficiency and the reconstruction efficiency of the signal modes. We estimate the systematic uncertainty on the tag B yield and reconstruction efficiency by varying the MC B + B − nonpeaking component of the m ES shape, assigning a systematic uncertainty of 3% on the branching fraction. The systematic uncertainties due to mismodeling of charged particle tracking efficiency, E extra shape, particle identification efficiency, π 0 reconstruction and signal MC statistics depend on the τ decay mode. The uncertainty on the branching fraction is evaluated for each mode separately. We obtain the total contributions due to tracking and E extra systematics by adding linearly the contributions of each decay channel. The total contributions due to MC statistics and particle identification are obtained by adding systematics uncertainties of each reconstruction mode in quadrature.
We check the low p T charged track multiplicity distribution agreement between data and MC with a sample enriched in background by loosening the selection criteria. The disagreement, which is mode dependent, is quantified by comparing the MC PDF with the data PDF. We correct the MC to reproduce the distribution in data and apply the correction to the signal MC distribution. We take 100% of the correction as a systematic uncertainty, resulting in a total systematic uncertainty of 5.8% on the branching fraction.
The systematic uncertainty due to the E extra mismodeling is determined by means of a data sample containing events with two non-overlapping tag B candidates. The sample is selected by reconstructing a second B meson in a hadronic decay mode B − → D ( * )0 X − on the recoil of the tag B. In addition to the requirements on the tag B described above, we consider only second B candidates satisfying |∆E| < 50 MeV and m ES > 5.27 GeV/c 2 having opposite charge to that of the tag B. If multiple candidates are reconstructed, the one with the highest purity P is selected. We compare the distribution of the total energy of the unassigned neutral clusters E extra in data and in MC. We compute the ratio of the number of events in the signal region of each τ mode to the total number of events in the sample. For each τ mode, we evaluate the systematic uncertainty, comparing the ratio estimated from MC to the ratio estimated from data. This procedure results in a 8.8% systematic uncertainty on the branching fraction. Table IV shows the contributions in percent to the systematic uncertainties on the branching fraction. In summary, we measure the branching fraction where the first error is statistical, the second is due to the background uncertainty, and the third is due to other systematic sources. Taking into account the uncertainty on the expected background, as described above, we obtain a significance of 2.2 σ. Using Eq. 1, we calculate the product of the B meson decay constant f B and |V ub | to be f B · |V ub | = (10.1 +2.3 −2.5 (stat.) +1.2 −1.5 (syst.)) × 10 −4 GeV. We also measure the 90% C.L. upper limit using the CL s method [17] to be B(B + → τ + ν) < 3.4 × 10 −4 .
(7) The significance of the combined result is 2.6 σ including the uncertainty on the expected background (3.2 σ if this uncertainty is not included).
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