Belle Collaboration

We present the first observation of τ lepton decays to hadronic final states with a φ-meson. This analysis is based on 401 fb −1 of data accumulated at the Belle experiment. The branching fraction obtained is B(τ − → φK − ν τ) = (4.05 ± 0.25 ± 0.26) × 10 −5 .

After the first observation of the charmless baryonic B meson decay, B + → ppK + [1,2], many three-body baryonic decays were found [3,4,5,6].The dominant contributions for these decays are presumably via the b → s penguin diagram, shown in Fig. 1 (a); however B + → ppπ + is believed to proceed via the b → u tree diagram as shown in Fig. 1 (b).One interesting feature of these decays is that the dibaryon mass spectra show enhancements near threshold as conjectured in Ref. [7].Many theoretical explanations [8] have been proposed to describe these enhancements in the dibaryon system, which seem to be a universal feature of all charmless baryonic B decays.Study of the proton polar angular distribution for the dibaryon system in the ppK + mode [9] indicates a violation of the b → s short distance picture [10].Explicit predictions for the dibaryon mass spectra [11] and the angular distributions [12,13] for B + → ppK + /π + became available after the experimental findings were reported.
In this paper, we study the three-body charmless baryonic B meson decays B + → ppK + and B + → ppπ + .The differential branching fractions as a function of the dibaryon mass and the polar angle distributions of the proton in the dibaryon system are presented.We also search for intermediate two-body decays in ppπ + three-body final states.This is motivated by the observations of two-body decays of charmed baryons [14].Many predictions based on QCD sum rules [15], pole models [16] and a topological approach [17] indicate that B + → p∆ ++ and B + → p ∆0 should be observable in the large data samples accumulated at the B-factories.
We use a 414 fb −1 data sample, corresponding to 449 ×10 6 B B pairs, collected with the Belle detector at the KEKB asymmetric-energy e + e − (3.5 on 8 GeV) collider [18].The Belle detector is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter composed of CsI(Tl) crystals located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field.An iron flux-return located outside of the coil is instrumented to detect K 0 L mesons and to identify muons.The detector is described in detail elsewhere [19].Two inner detector configurations were used.A 2.0 cm beampipe and a 3-layer silicon vertex detector were used for the first sample of 152 ×10 6 B B pairs, while a 1.5 cm beampipe, a 4-layer silicon detector and a small-cell inner drift chamber were used to record the remaining 297 ×10 6 B B pairs [20].
The event selection criteria are based on information obtained from the tracking system (SVD and CDC) and the hadron identification system (CDC, ACC, and TOF).All primary charged tracks are required to satisfy track quality cri- teria based on the track impact parameters relative to the interaction point (IP).The deviations from the IP position are required to be within ±0.3 cm in the transverse (x-y) plane, and within ±3 cm in the z direction, where the z axis is opposite the positron beam direction.For each track, the likelihood values L p , L K , and L π that it is a proton, kaon, or pion, respectively, are determined from the information provided by the hadron identification system.The track is identified as a proton if L p /(L p + L K ) > 0.6 and L p /(L p + L π ) > 0.6, or as a kaon if L K /(L K + L π ) > 0.6, or as a pion if L π /(L K + L π ) > 0.6.For particles with momenta at 2 GeV/c, the proton selection efficiency is about 84% (88% for p and 80% for p) and the fake rate is about 10% for kaons and 3% for pions; the kaon selection efficiency is about 85% and the pion to kaon fake rate is about 2%; the pion selection efficiency is about 88% and the kaon to pion fake rate is about 11%.
Candidate B mesons are reconstructed in the B + → ppK + and B + → ppπ + modes.We use two kinematic variables in the center of mass (CM) frame to identify the reconstructed B meson candidates: the beam energy constrained mass M bc = E 2 beam − p 2 B , and the energy difference ∆E = E B −E beam , where E beam is the beam energy, and p B and E B are the momentum and energy, respectively, of the reconstructed B meson.The candidate region is defined as 5.20 GeV/c 2 < M bc < 5.29 GeV/c 2 and −0.1 GeV < ∆E < 0.3 GeV.The lower bound in ∆E for candidate events is chosen to exclude possible crossfeed background from the decays with additional pions to the search modes, e.g.B + → ppK * + .From a GEANT [21] based Monte Carlo (MC) simulation, the signal peaks in a signal box defined by 5.27 GeV/c 2 < M bc < 5.29 GeV/c 2 and |∆E| < 0.05 GeV, and there is no peaking background except cross-feed events between the ppK + and ppπ + modes.
The background in the fit region arises dominantly from the continuum e + e − → q q (q = u, d, s, c) process.We suppress the jet-like continuum background events relative to the more spherical B B signal events using a Fisher discriminant [22] that combines seven event shape variables, as described in Ref. [23].Probability density functions (PDFs) for the Fisher discriminant and the cosine of the angle between the B flight direction and the beam direction in the Υ(4S) rest frame are combined to form the signal (background) likelihood L s (L b ).The signal PDFs are determined using signal MC simulation; the background PDFs are obtained from the sideband data with M bc < 5.26 GeV/c 2 .We require the likelihood ratio R = L s /(L s + L b ) to be greater than 0.75 and 0.85 for the ppK + and ppπ + modes, respectively.These selection criteria are determined by optimization of n s / √ n s + n b , where n s and n b denote the expected numbers of signal and background events in the signal box, respectively.We use the branching fractions from our previous measurements [9,4] in the calculation of n s and use the number of sideband events to estimate n b .
If there are multiple B candidates in a single event, we select the one with the best χ 2 value from the vertex fit.The fractions of multiple B events are about 8% and 10% for the ppK + and ppπ + modes, respectively.
We perform an unbinned extended likelihood fit that maximizes the likelihood function, to estimate the signal yield in the candidate region; here P s (P b ) denotes the signal (background) PDF, N is the number of events in the fit, and N s and N b are fit parameters representing the number of signal and background events, respectively.
For the signal PDF, we use a Gaussian function to represent the signal M bc and a double Gaussian for ∆E with parameters determined by MC simulation.We then modify these parameters to account for the discrepancies between data and MC using the ppK + signal events ( M pp < 2.85 GeV/c 2 ).
With this correction, we can gain about 5% more signal yield.The continuum background PDF is taken as the product of shapes in M bc and ∆E, which are assumed to be uncorrelated.We use the parameterization first used by the ARGUS collaboration [24], to model the M bc background, with x given by M bc /E beam and ξ as a fit parameter.The ∆E background shape is modeled by a normalized second order polynomial whose coefficients are fit parameters.Because the ppπ + mode can contain non-negligible cross-feed events from the ppK + mode, we include the ppK + MC cross-feed shape in the fit for the determination of the ppπ + yield.The cross-feed from ppπ + to ppK + is negligible.Figure 2 illustrates the fits of the B yields in a proton-antiproton mass region below 2.85 GeV/c 2 , which we refer to as the threshold-mass-enhanced region.The fitted B yields are 632  Since there are two different detector configurations and the detection efficiency is dependent on M pp , we separate the data sample into two sets and determine the B yields in bins of M pp , where the signal PDF is assumed to be the same for all M pp bins.We generate corresponding MC samples in order to estimate the efficiencies properly.The partial branching fractions are obtained by correcting the fitted B yields for the mass dependent efficiencies for each data set; they agree well with each other for the two data sets and these results are then combined to obtain the final results.
The differential branching fractions as a function of the proton-antiproton mass for both ppK + and ppπ + modes are shown in Fig. 3, and the measured branching fractions for different M pp bins are listed in Table 1 and Table 2.Note that we have defined the charm veto: the regions 2.850 GeV/c 2 < M pp < 3.128 GeV/c 2 and 3.315 GeV/c 2 < M pp < 3.735 GeV/c 2 are excluded to remove background from B decay modes containing an η c , J/ψ, ψ ′ , χ c0 , or χ c1 meson.These results supersede our previous measurements [4,9] with better accuracy.The width of the ppπ + mode is narrower than that of the ppK + mode and agrees better with the theoretical expectation [11].The error bars show the statistical uncertainties only.The listed yield is the sum from the fits for two different periods; the listed efficiency is an effective one obtained by combining the two different detector configurations.Fig. 3. Differential branching fractions for (a) ppK + and (b) ppπ + modes as a function of proton-antiproton pair mass.The solid curves are theoretical predictions [11] that are scaled to the observed charmless branching fractions.The two shaded mass bins, 2.85 < M pp < 3.128 GeV/c 2 and 3.315 < M pp < 3.735 GeV/c 2 , are not counted in the charmless signal yields since they contain contributions from the intermediate resonances η c , J/ψ and ψ ′ , χ c0 , χ c1 mesons, respectively.
Systematic uncertainties are determined using high-statistics control data samples.For proton identification, we use a Λ → pπ − sample, while for K/π identification we use a D * + → D 0 π + , D 0 → K − π + sample.The average efficiency difference for hadron identification between data and MC has been corrected to obtain the final branching fraction measurements.The corrections are about 9% and 14% for the ppK + and ppπ + modes, respectively.The uncertainties associated with the hadron identification corrections are estimated to be 4.2% for two protons and 1% for one kaon/pion.Tracking uncertainty is determined with fully and partially reconstructed D * samples.It is about 1% per charged track.The R continuum suppression uncertainty is estimated from control samples with similar final states, B + → J/ψK + with J/ψ → µ + µ − .The uncertainties for R selection are 2.5% and 4% for the ppK + and ppπ + modes, respectively.A systematic uncertainty of 2% in the fit yield is determined by varying the parameters of the signal and background PDFs.The MC statistical uncertainty is less than 2%.The error on the number of B B pairs is 1.3%, where we assume that the branching fractions of Υ(4S) to neutral and charged B B pairs are equal.The systematic uncertainties for each decay channel are summarized in Table 3.We first sum the correlated errors linearly and then combine them with the uncorrelated ones in quadrature.The total systematic uncertainties are 6.5% and 7.4% for the ppK + and ppπ + modes, respectively.We study the baryon angular distribution in the proton-antiproton helicity frame at M pp < 2.85 GeV/c 2 .The angle θ p is defined as the angle between the baryon direction and the oppositely charged meson direction in the protonantiproton pair rest frame, i.e. this angle is determined by p and K − /π − , or by p and K + /π + .We use the same likelihood method to estimate the B yield in each θ p bin.Again, the signal PDF is fixed and the background shape is allowed to vary.The cos θ p distributions, shown in Fig. 4, for the ppK + and ppπ + modes have opposite trends.This distribution for the ppπ + mode does not match the theoretical prediction [12], which is based on an extrapolation of the ppK + data using the perturbative QCD framework.However, it does agree with the naive short distance picture for a b → u weak decay.Particles directly associated with b decay are more energetic and the particle containing the spectator quark is generally less energetic.After boosting to the protonantiproton rest frame, the fast moving anti-protons and π + 's are back-to-back most of the time.However, the b → s gluon process for the ppK + case seems to completely disagree with this short distance picture.The baryon with the spectator quark moves faster in the B rest frame.The same phenomenon has been observed in B 0 → p Λπ − [25] decays.Another theoretical prediction proposes a long distance effect, namely pp rescattering through a hypothetical baryonium bound state [13], in order to explain the violation of the short distance picture for the ppK + mode.Since this long distance effect should also occur for the ppπ + case, it seems that further theoretical investigations are needed to simultaneously explain the behavior of both the ppK + and ppπ + modes.
Because we have enough B + → ppK + signal events in the threshold enhancement region, we separate this region into five sub-regions.Fig. 5(a)-(e) shows the efficiency corrected B yield as a function of cos θ p for these five sub-regions.We define the angular asymmetry as A θp = N + −N − N + +N − , where N + and N − stand for the efficiency corrected B yield with cos θ p > 0 and cos θ p < 0, respectively.The measured angular asymmetry as a function of M pp is shown in Fig. 5(f).It is interesting to see that there is a clear trend, which indicates that the relative contributions from two (or more) competing decay amplitudes are changing in this mass range.The measured average A θp value of the threshold enhancement is given in Table 4.The systematic error, ∼ 0.03, is determined by checking the B + → J/ψK + (J/ψ → µ + µ − ) sample and the continuum background in B + → ppK + where no asymmetry is expected.The observed A θp 's are 0.02 ± 0.01 for B + → J/ψK + and 0.00 ± 0.02 for the continuum background.
We also search for the intermediate two-body decays, B + → p∆ ++ (∆ ++ → pπ + ) and B + → p ∆0 ( ∆0 → pπ + ), from the ppπ + three-body final state.Events with M pπ < 1.4 GeV/c 2 are selected.No significant signals are found from the likelihood fit in those decay chains.We observe 59 and 86 events in the signal box; the expected numbers of background events from the fits are 73.0 ± 1.6 and 81.4 ± 1.6 for B + → p∆ ++ and B + → p ∆0 , respectively.We set upper limits on the branching fractions at the 90% confidence level using  the methods described in Refs.[26,27] where the 7.4% systematic uncertainty for B + → ppπ + is taken into account.The results are B(B + → p∆ ++ ) < 0.14 × 10 −6 and B(B + → p ∆0 ) < 1.38 × 10 −6 .These numbers are smaller than the theoretical expectations but agree with other experimental findings [28].
Since there is a prediction [29] that direct CP violation in B + → J/ψK + is at the 1% level, it is quite possible that this effect could be magnified due to the interference [30] between the resonance and the threshold enhancement.We define the charge asymmetry A CP as (N b − Nb)/(N b + Nb) for the ppK + and ppπ + modes, where N b (Nb) stands for the efficiency corrected B − (B + ) yield.
The selection criteria for J/ψ (η c ) and related consistency checks have been reported in Ref. [31].We adopt the same criteria and assume the signal PDFs are the same for both B − and B + samples.The results from the likelihood fits are listed in Table 4 for various mass/resonance regions.No significant charge asymmetries are found.The systematic uncertainty is assigned using the measured charge asymmetry for sideband data and is found to be −0.01 ± 0.01.
In summary, using 449 ×10 6 B B events, we measure the mass and the angular distributions of the proton-antiproton pair system near threshold for the ppK + and ppπ + baryonic B decay modes.These results supersede our previous measurements [4,9] with better accuracy.The width of the threshold enhancement in the ppπ + mode is narrower than that of the ppK + mode and agrees better with the theoretical expectation [11].The proton polar angular distributions of the ppK + and ppπ + modes have opposite trends.This shows that the b → s and b → u processes are kinematically different at short distance.

2 Fig. 2 .
Fig.2.Distributions of ∆E (with M bc > 5.27 GeV/c 2 ) and M bc (with |∆E| < 0.05 GeV), respectively, for (a) ppK + and (b) ppπ + modes with proton-antiproton pair mass less than 2.85 GeV/c 2 .The solid curves, solid peaks, and dashed curves represent the combined fit result, fitted signal and fitted background, respectively.The dot-dashed curve indicates the ppK + cross-feed background in the fit to the ppπ + mode.

Table 1 The
B yields from ∆E − M bc fits for the B + → ppK + data sample, detection efficiencies and branching fractions (B) in different M pp regions.

Table 2 The
B yields from ∆E − M bc fits for the B + → ppπ + data sample, detection efficiencies and branching fractions (B) in different M pp regions.

Table 3
Systematic uncertainties(%) in the branching fraction for each decay channel.