Evidence of B-->tau nu decays with hadronic B tags

We present a search for the decay B+ -->tau+ nu using 467.8 x 10^6 B B pairs collected at the Y(4S) resonance with the BaBar detector at the SLAC PEP-II B-Factory. We select a sample of events with one completely reconstructed B- in the hadronic decay modes (B- -->D(*)0 X- and B- -->J/\psi X-). We 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+ -->rho+ nu. We find an excess of events with respect to the expected background, which excludes the null signal hypothesis at the level of 3.8 sigma (including systematic uncertainties) and corresponds to a branching fraction central value of B(B+ -->tau+ nu)=(1.83^{+0.53}_{-0.49}(stat.) +/- 0.24 (syst.)) x 10^-4.

The study of the purely leptonic decay B + → τ + ν [1] is of particular interest to test the predictions of the Standard Model (SM) and to probe of new physics effects.It is sensitive to the product of the B meson decay constant f B , and the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element |V ub | [2].In the SM the branching fraction is given by: where G F is the Fermi constant, m B and m τ are, the B + meson and τ lepton masses, respectively, and τ B + is the B + lifetime.Using the Lattice QCD calculation of f B = (189 ± 4) MeV [3], and the BABAR measurement of |V ub | from charmless semileptonic B exclusive decays [4], the predicted SM value of the brancing fraction is B SM (B + → τ + ν) = (0.62 ± 0.12) × 10 −4 .If we use the BABAR measurement of |V ub | from inclusive charmless semileptonic B decays [5], the SM prediction is B SM (B + → τ + ν) = (1.18± 0.16) × 10 −4 .
The process is sensitive to possible extensions of the SM.For instance, in two-Higgs doublet models (2HDM) [6] and in minimal supersymmetric extensions [7] it can be mediated by a charged Higgs boson.A branching fraction measurement can, therefore, also be used to constrain the parameter space of new physics models.
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 426 fb −1 at the Υ (4S) resonance.The sample contains (467.8±5.1)×10BB decays (N BB ).The detector is described in detail elsewhere [12].Charged particle trajectories are measured in the tracking system composed of a five-layer double-sided silicon vertex tracker and a 40-layer drift chamber, operating in a 1.5 T solenoidal magnetic field.A Cherenkov detector is used for charged π-K discrimination, a CsI calorimeter for photon and electron identification, and the flux return of the solenoid, which consists of layers of iron interspersed with resistive plate chambers or limited streamer tubes, for muon and neutral hadron identification.
We use a Monte Carlo (MC) simulation based on GEANT4 [13] to estimate signal selection efficiencies and to study backgrounds.In MC simulated signal events, one B + meson decays as B + → τ + ν and the other decays in any final state.The BB and continuum MC samples are equivalent to approximately 3 times and 1.5 times the data sample, respectively.Beam-related background and detector noise are sampled from data and overlaid on the simulated events.
We reconstruct an exclusive decay of one of the B mesons in the event (which we refer to as the tag-B) and examine the rest of the event for the experimental signature of B + → τ + ν.The tag-B reconstruction can be performed by looking at both hadronic B decays and semileptonic B decays.Published results from both BABAR and Belle are summarized in Table I.
We reconstruct the tag-B candidate in the set of hadronic decays B − → M 0 X − , where M 0 denotes a D ( * )0 or a J/ψ , and X − denotes a system of hadrons with total charge −1 composed of We reconstruct the D * 0 meson as D * 0 → D 0 π 0 , D 0 γ, and the J/ψ meson via their decays J/ψ → e + e − , µ + µ − .Two kinematic variables are used to discriminate between correctly reconstructed tag-B candidates and misreconstructed events: the beam energy-substituted mass m ES ≡ s/4 − p 2 B , and the energy difference ∆E ≡ E B − √ s/2, where √ s is the total energy in the Υ (4S) center-of-mass system (CM) and p B and E B respectively denote the momentum and the energy of the tag-B candidate in the CM.The resolution on ∆E is measured to be σ ∆E = 10 − 35 MeV, depending on the decay mode; we require |∆E| < 3σ ∆E .Events with a tag-B candidate arise from two possible classes with different m ES distributions.One class includes signal events with a correctly reconstructed tag-B, and background events from Υ (4S) → B + B − with a correctly reconstructed tag-B.All these events are characterized by an m ES distribution peaked at the nominal B mass(signal and peaking background).The other classes of events consist of continuum background, e + e − → qq (q = u, , .s, ) ¸and e + e − → τ + τ − , and combinatorial background, Υ (4S) → B 0 B 0 or B + B − in which the tag-B is misreconstructed.These events are characterized by a smooth m ES distribution.
If multiple tag-B candidates are reconstructed in the event, we select the one with the lowest value of |∆E|.After the reconstruction of the tag-B, we require the presence of only one well-reconstructed track (signal track), with charge opposite to that of the tag-B.The purity P of each reconstructed tag-B decay mode is estimated as the ratio of the number of peaking events with m ES > 5.27 GeV to the total number of events in the same range.The yield in data is determined by means of an extended unbinned maximum likelihood fit to the m ES distribution, as shown in Fig. 1.We use a phenomenologically motivated threshold function (ARGUS function [14]) as probability density function (PDF) to describe the continuum and combinatorial background components in the fit, while for the correctly reconstructed tag-B component we use a Gaussian distribution plus an exponential tail for the PDF (Crystal Ball function) [15].We use only events with the tag-B reconstructed in decay modes with P > 0.  The signal-side τ lepton is reconstructed in four decay modes: τ + → e + ν ν, τ + → µ + ν ν, τ + → π + ν, and τ + → ρ + ν, totaling approximately 70% of all τ decays.We separate the event sample into four categories using particle identification criteria applied to the signal track (e + , µ + , and π + ).The τ + → ρ + ν sample is obtained by associating the signal track π + with a π 0 reconstructed from a pair of neutral clusters with an invariant mass between 115 MeV/c 2 and 155 MeV/c 2 .
In order to remove the e + e − → τ + τ − background, we impose τ mode dependent requirements on the ratio between the 2 nd and the 0 th Fox-Wolfram moments R2 [16] calculated using all the tracks and neutral clusters of the event.This preserves 90% of the B + → τ + ν signal.
To reject continuum background, we use the absolute value of cos θ T B , the cosine of the angle in the CM frame between the thrust axis [17] of the tag-B and the thrust axis of the remaining charged and neutral candidates in the event.For correctly reconstructed tag-B candidates the |cos θ T B | distribution is expected to be uniform, while for jet-like e + e − → qq continuum events it peaks strongly at 1.In order to reject background from events with a correctly reconstructed tag-B, we study the distribution of several discriminating variables exploiting the different kinematics between the signal and background of the remaining reconstructed candidates.We use the missing momentum polar angle in the laboratory frame p miss = p CM − p tagB − p trk − neut p i , where p CM is the total momentum of the beams, p tagB is the reconstructed momentum of the tag-B, and p trk is the reconstructed track momentum, and the sum is extended on all the neutral candidates reconstructed in the calorimeter not assigned to the tag-B.For the τ + → π + ν mode, we combine p * trk (where the star denotes the CM frame) and the cosine of the angle between p miss and the beam axis (cos θ miss ) in a likelihood ratio where the signal (S) and background (B) likelihoods have been obtained from the product of the PDFs of the two discriminating variables: Similarly, for the τ + → ρ + ν mode we combine four discriminating variables in the likelihood ratio L P : cos θ miss , the invariant mass of the π 0 candidate, the ρ + candidate momentum, and the invariant mass of the π + π 0 pair used to make the ρ + candidate.The PDFs used in the likelihood ratio for the signal and background are determined from signal and B + B − MC samples, respectively.
The most powerful discriminating variable is E extra , defined 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 + → ρ + ν mode, and passing a minimum energy requirement (60 MeV).Signal events tend to peak at low E extra .Background events, which contain addi-tional sources of neutral clusters, tend to be distributed at higher values.The signal region in data is kept blind until the end of the analysis chain when we extract the signal yield, meaning that we do not use events in data with E extra < 400 MeV during the selection optimization procedure and for the evaluation of background shapes.
We optimize the selection requirements, including those on the purity P of the tag-B and the minimum energy of the neutral clusters, minimizing the expected uncertainty in the branching fraction fit.In order to estimate the uncertainty, which includes the statistical and the dominant systematic sources, we run 1000 MC simulated pseudo experiments extracted from the background and signal expected E extra distributions for a set of possible selection requirements, assuming a signal branching fraction of 1.8 × 10 −4 [8].
Table II summarizes the signal selection requirements and Fig. 2 shows the E extra distribution with all the selection requirements applied.The background events populating the low E extra region are mostly semileptonic B decays for the leptonic modes.For the τ + → π + ν mode the background is composed mostly of charmless hadronic B decays and semileptonic B decays with a muon in the final state.For the τ + → ρ + ν mode the backgrounds are charmed hadronic B decays, semileptonic B decays with a muon in the final state and a small fraction with a τ .We use an extended unbinned maximum likelihood fit to the measured E extra distribution to extract the B + → τ + ν branching fraction.The likelihood function for the N k candidates reconstructed in one of the four τ decay modes k is where n s,k is the signal yield, n b,k is the background yield, E i,k is the E extra value of the i th event, P s k is the PDF of signal events, and P b k is the PDF of background events.The background yields in each decay mode are permitted to float independently of each other in the fit, while the signal yields are constrained to a single branching ratio via the relation: where ǫ k is the reconstruction efficiency of a particular τ decay mode, and B is the while B is allowed to vary.The reconstruction efficiencies ǫ k , which include the τ branching fractions, are obtained from MC-simulated signal events (see Table III).Since the tag-B reconstruction efficiency is included in ǫ k and is estimated from the signal MC, we apply a correction factor of R data/MC = 0.926 ± 0.010 to take into account data/MC differences.This is derived from the ratio of the peaking component of the m ES distribution for the hadronic tag-B in data and in MC simulated events.The signal PDF is obtained from a high statistics signal sample of MC simulated data.We use a sample of fully reconstructed events to correct the signal PDF for data/MC disagreement In addition to the reconstructed tag-B, a second B is reconstructed in the hadronic or the semileptonic decay mode using tracks and neutral clusters not assigned to the tag-B.In order to estimate the correction to the signal PDF, we compare the distribution of E extra in this double tagged event sample from experimental data and MC simulations.The MC distributions are normalized to the experimental data and the comparison is shown in Fig. 3.We extract the correction function by taking the ratio of the two distributions and fitting it with a second order polynomial.We determine the PDF of the combinatorial background from the m ES sideband.The normalization of this component in the signal region is obtained by fitting the m ES distribution after the selection has been applied.The shape of the peaking background is taken from B + B − MC.The two background components are added together into a single background PDF.We estimate the branching fraction by minimizing − ln L, where L = Π 4 k=1 L k , and L k is given in Eq. 3. The projections of the fit results are shown in Fig. 2.
We observe an excess of events with respect to the expected background level and measure a branching fraction of B(B + → τ + ν) = (1.83+0.53 −0.49 ) × 10 −4 , where the uncertainty is statistical.Table III summarizes the results from the fit.We evaluate the significance of the observed signal, including only statistical uncertainty, as S = 2 ln(L s+b /L b ), where L s+b and L b denote the obtained maximum likelihood values in the signal and background, and the background only hypotheses, respectively.We find S = 4.2σ.
Additive systematic uncertainties are due to the uncertainties in the signal and background E extra PDF TABLE III: Reconstruction efficiency ǫ, measured branching fractions, and statistical uncertainty obtained from the fit with all the modes separately and constrained to the same branching fraction.The τ decay mode branching fractions are included in the efficiencies.
Decay Mode ǫ k (×10 −4 ) Signal yield B(×10 −4 ) τ + → e + ν ν 2.47 ± 0.14 4.1 ± 9.1 0.35 +0.84 −0.73 τ + → µ + ν ν 2.45 ± 0.14 12.9 ± 9.7 1.12 +0.90 −0.78 τ + → π + ν 0.98 ± 0.14 17.1 ± 6.  shapes used in the fit.To estimate the systematic uncertainty in the background PDF shape we repeat the fit of the branching fraction with 1000 variations of the background PDFs, varying each bin content within its statistical uncertainty.We use the range of fitted branching fractions covering 68% of the distribution as systematic uncertainty yielding an overall contribution of 10%.We correct the systematic effects of disagreements between data and MC E extra distributions for signal events using a sample of completely reconstructed events in data and MC, as already described.To estimate the related systematic uncertainties, we vary the parameters of the second-order polynomial defining the correction within their uncertainty and repeat the fit to the B + → τ + ν branching fraction.We observe a 2.6% variation that we take as the systematic uncertainty on the signal shape.
Including the effects of additive systematic uncertainties, the significance of the result is evaluated as 3.8σ.Multiplicative systematic uncertainties on the efficiency stem from the uncertainty in the tag-B efficiency correction (5.0%), electron identification (2.6%), muon identification (4.7%), charged kaon veto (0.4%), and the finite signal MC statistics (0.8%).Table IV summarizes the systematic uncertainties.The total systematic uncertainty is obtained by combining all sources in quadrature.
In summary, we have measured the branching fraction of the decay B + → τ + ν using a tagging algorithm based on the reconstruction of hadronic B decays using a data sample of 467.8 × 10 6 BB pairs collected with the BABAR detector at the PEP-II B-Factory.We measure the branching fraction to be B(B + → τ + ν) = (1.83+0.53 −0.49(stat.)± 0.24(syst.))× 10 −4 , excluding the null hypothesis by 3.8σ.(including systematic uncertainty).This result supersedes our previous result using the same technique [8].Combining this result with the other BABAR measurement of B(B + → τ + ν) derived from a statistically independent sample [9], we obtain B(B + → τ + ν) = (1.79 ± 0.48) × 10 −4 , where both statistical and systematic uncertainties are combined in quadrature.Our measurement of the branching fraction B(B + → τ + ν) exceeds the prediction of the SM determined using the values of |V ub | extracted from exclusive semileptonic events and from inclusive semileptonic events by 2.4σ and 1.6σ, respectively.We also determine, separately for the exclusive and inclusive |V ub | BABAR measurements, 90% C.L. exclusion regions in the parameter space of the 2HDM -type II (m H + , tan β), where m H + is the charged Higgs mass and tan β is the ratio of the vacuum expectation values of the two Higgs doublets.We find that, taking |V ub | from the exclusive measurement, most of the parameters space is excluded at 90% C.L. Using the higher value of |V ub | from the inclusive measurement, the constraints are less stringent but already set a lower limits at the TeV scale for high tan β.The same implications on 2HDM are supported by a recent BABAR study of the B(B → D ( * ) τ ν) decays [18].Fig. 4 shows a comparison between the measured B(B + → τ + ν) branching fraction with the prediction of the 2HDM as a function of tan β/m H + and the exclusion plots in the (m H + , tan β) plane for the exclusive and inclusive measurements of |V ub | .
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible.The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR.The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them.This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l'Energie Atomique and Institut National de Physique Nucléaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovación (Spain), and the Science and Technology Facilities Council (United Kingdom).Individuals have received support from the Marie-Curie IEF program (European Union), the A. P. Sloan Foundation (USA) and the Binational Science Foundation (USA-Israel).
1. Combinatorial and continuum background distributions in any discriminating variable are estimated from a sideband in m ES (5.209 GeV < m ES < 5.260 GeV) and are extrapolated into the signal region (m ES > 5.270 GeV) using the results of a fit to an ARGUS function.The peaking B + B − background shape is determined from B + B − MC, after subtraction of the combinatorial component to avoid double counting.

FIG. 1 :
FIG. 1: Fit to the mES distribution in data.Dots are data, the upper curve is the global fit result and the lower curve represents the fitted combinatorial and continuum background.

FIG. 3 :
FIG.3: Eextra distribution for double tagged events.The "signal" B is reconstructed in hadronic decays (left plot) or semileptonic decays (right plot).Points are data and boxes are MC simulation.

3 FIG. 4 :
FIG. 4: Top plot: Comparison between the measured B(B + → τ + ν) branching fraction (horizontal band) with the prediction of the 2HDM as a function of tan β/m H + , using exclusive (red/light gray) or inclusive (blue/dark gray) |V ub | measurement.Bottom plots: 90% and 99% C.L. exclusion regions in the (m H + , tan β) plane using the exclusive (left) and inclusive (right) measurements of |V ub |.

TABLE I :
Published results for B + → τ + ν from BABAR and Belle collaborations.

TABLE II :
Optimized signal selection criteria for each τ mode.

TABLE IV :
Contributions to systematic uncertainty on the branching fraction.