Search for the Decay τ − → 3 π − 2 π + 2 π 0 ν τ

A search for the decay of the τ lepton to ﬁve charged and two neutral pions is performed using data collected by the B A B AR detector at the PEP-II asymmetric-energy e + e − collider. The analysis uses 232 fb − 1 of data at center-of-mass energies on or near the Υ (4 S ) resonance. We observe 10 events with an expected background of 6 . 5 +2 . 0 − 1 . 4 events. In the absence of a signal, we set the limit on the branching ratio B ( τ − → 3 π − 2 π + 2 π 0 ν τ ) < 3 . 4 × 10 − 6 at the 90 % conﬁdence level. This is a signiﬁcant improvement over the previously established limit. In addition, we search for the decay mode τ − → 2 ωπ − ν τ . We observe 1 event with an expected background of 0.4 +1 . 0 − 0 . 4 events and calculate the upper limit B ( τ − → 2 ωπ − ν τ ) < 5 . 4 × 10 − 7 at the 90 % conﬁdence level. This is the ﬁrst upper limit for this mode.

A search for the decay of the τ lepton to five charged and two neutral pions is performed using data collected by the BABAR detector at the PEP-II asymmetric-energy e + e − collider. The analysis uses 232 fb −1 of data at center-of-mass energies on or near the Υ (4S) resonance. We observe 10 events with an expected background of 6.5 +2.0 −1.4 events. In the absence of a signal, we set the limit on the branching ratio B(τ − → 3π − 2π + 2π 0 ντ ) < 3.4 × 10 −6 at the 90 % confidence level. This is a significant improvement over the previously established limit. In addition, we search for the decay mode τ − → 2ωπ − ντ . We observe 1 event with an expected background of 0.4 +1.0 −0.4 events and calculate the upper limit B(τ − → 2ωπ − ντ ) < 5.4 × 10 −7 at the 90 % confidence level. This is the first upper limit for this mode. Hadronic decays of τ leptons provide an excellent laboratory for the study of the strong interaction. Decays of the τ with one or three charged particles in the final state have been well studied in the past [1]. Higher multiplicity decays, however, have considerably lower branching ratios [1], and high luminosity experiments are needed to study their dynamics and search for new modes. The BABAR experiment has recorded a large sample of e + e − → τ + τ − events suitable for detailed searches for high multiplicity τ decays.
The τ − → 3π − 2π + 2π 0 ν τ mode [2] is of particular interest. It has not been observed yet, and only an upper limit B(τ − → 3π − 2π + 2π 0 ν τ ) < 1.1 × 10 −4 at the 90 % confidence level (CL) has been set by the CLEO collaboration [3]. The reason for the suppression of seven-pion τ decays is the limited phase space of this decay [4,5]. For the same reason, if this decay is observed with sufficient statistics, it may lead to a more stringent limit on the τ neutrino mass.
This analysis is based on data recorded with the BABAR detector at the PEP-II asymmetric-energy e + e − storage ring operated at the Stanford Linear Accelerator Center. The data sample consists of 232 fb −1 recorded at centerof-mass (CM) energies of 10.58 GeV and 10.54 GeV. With an expected cross section for τ pairs of σ τ τ = (0.89 ± 0.02) nb [8], the number of produced τ -pair events is N τ τ = (206.5 ± 4.7) × 10 6 .
The BABAR detector is described in detail in Ref. [9], and only a brief description is given here. Chargedparticle momenta are measured with a 5-layer doublesided silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) inside a solenoidal magnet with a 1.5 T magnetic field. A calorimeter (EMC) consisting of 6580 CsI(Tl) crystals is used to measure the energy of electrons, positrons, and photons. A ring-imaging Cherenkov detector is used to identify charged hadrons, in combina-tion with ionization energy loss measurements in the SVT and the DCH. Muons are identified by an instrumented magnetic-flux return (IFR).
Monte Carlo (MC) simulations are used to estimate the τ − → 3π − 2π + 2π 0 ν τ signal efficiency and background contamination from other τ decay modes. The production of τ pairs is simulated with the KK generator [10], and non-signal τ lepton decays are modeled with TAUOLA [11] according to measured rates [1]. The background processes e + e − → qq (q = u, d, s, c, b) are simulated using the JetSet package [12]. Signal events are generated using phase space with a V − A interaction. We find no significant variation in efficiency within the phase space. The simulation of the BABAR detector is based on GEANT 4 [13].
The event selection criteria were developed to suppress the background while maintaining high signal efficiency. Events with six charged particle tracks and a net charge of zero are first selected. To ensure well-reconstructed tracks, each track is required to have a minimum transverse momentum of 100 MeV/c, a distance of closest approach to the interaction point in the plane transverse to the beam axis (DOCA XY ) less than 1.5 cm, and a distance of closest approach along the beam direction less than 10 cm. Four or more tracks are required to have hits in at least 12 DCH layers. Photons are reconstructed from clusters in the EMC and are required to have a minimum energy of 50 MeV, energy deposited in at least three crystals, and a lateral energy profile consistent with that of a photon. In addition, to suppress background from backscattering in the EMC, the angle between the position of a cluster and the impact point of the nearest charged track at the EMC surface, as seen from the interaction point, is required to be more than 0.08 radians.
The π 0 mesons are reconstructed from two photon candidates passing the photon selection criteria described above. We first search for π 0 candidates with energy E π 0 > 450 MeV and mass 113 < M γγ < 155 MeV/c 2 . If two or more π 0 candidates share a photon, only the one with the smallest |M γγ − M PDG value is taken from [1], is retained. Next, we repeat the procedure for π 0 candidates with energy 300 < E π 0 < 450 MeV and mass 120 < M γγ < 148 MeV/c 2 .
The τ pair is produced approximately back-to-back in the e + e − CM frame. This allows the event to be divided into two hemispheres by a plane perpendicular to the thrust axis, where the thrust is calculated from all charged particles and photons in the event [12]. The event thrust magnitude is required to be larger than 0.9. This requirement rejects more than 90 % of the qq background and the e + e − → BB background is suppressed to a negligible level. Events are required to have one track in one hemisphere (the tag side) and five tracks in the other hemisphere (the signal side). To further suppress the background from e + e − → qq events, we demand a well-identified electron or muon on the tag side with at most one additional photon with energy E γ < 500 MeV. The combined mass of all charged particles and photons in each hemisphere is required to be less than 3 GeV/c 2 . Finally, only events with exactly two π 0 candidates on the signal side are kept for further study. The efficiency of the two π 0 selection in the signal MC is 13.0 %.
The visible energy, defined as the sum of the CM energy of the charged tracks and the reconstructed π 0 mesons, is required to be less than the CM beam energy E beam = 5.29 GeV in each hemisphere of the event. The residual energy E res , defined as the neutral energy on the signal side not associated with the reconstructed τ decay products, is required to be less than 300 MeV, reducing the background from e + e − → qq and τ − → 2π − π + 3π 0 ν τ events.
To reconstruct the signal event, an approximation of the τ invariant mass is used: where the τ neutrino is assumed to be massless and travel along the direction of the combined momentum vector P 7h of the seven hadrons and its energy is taken to be the difference between E beam and the combined energy E 7h of the hadrons in the CM system. The variable M * is called the τ pseudo mass [14], and its distributions for signal and background MC events are shown in Figure 1.
The advantage of M * over the invariant mass M 7h is a considerably better separation of the signal from the hadronic qq background. We apply particle identification on the signal side, demanding four out of five tracks to be identified as pions with high probability, and apply looser identification criteria to the fifth track. This requirement significantly reduces the background from τ events with photon conversions and e + e − → qq events containing kaons.
We further suppress photon conversions by requiring the invariant mass of each pair of oppositely charged tracks to be larger than 5 MeV/c 2 . In addition, we apply cuts on the sums of the two lowest transverse momenta and two largest DOCA XY of the tracks on the signal side: The final event count is performed in the signal region 1.3 < M * < 1.8 GeV/c 2 . According to MC studies, the signal efficiency after all cuts is (0.66±0.05) %. The error is a combination of systematic and statistical uncertainties. The systematic uncertainty on the signal efficiency includes contributions from the reconstruction of charged tracks and photons (4.3 %), the reconstruction of two π 0 mesons (6.6 %), and the uncertainty associated with the particle identification on the signal and tag sides (1.7 %). A statistical uncertainty (1.8 %) due to limited MC samples is added in quadrature to the systematic uncertainty.
The simulation of τ -pair events yields a reliable estimate of their expected background contribution, verified by modifying the event selection criteria to suppress the qq background and allow for more τ events. The largest background is predicted to come from τ − → 3π − 2π + π 0 ν τ decays. For a detailed study, we use an MC sample of τ − → 3π − 2π + π 0 ν τ events corresponding to 1900 fb −1 of data. The pseudo-mass spectrum of the events passing the selection criteria is fitted with a "Crystal Ball" probability density function (PDF) [15]. In order to determine the shape parameters of this PDF, we first fit a larger sample selected without tagging of the one-prong side. Using this fixed shape, we then estimate the number of τ − → 3π − 2π + π 0 ν τ events within our signal region (1.3 < M * < 1.8 GeV/c 2 ) from the MC sam-ple with the one-prong tag applied. We obtain 3.6±0.6 events, scaled to the luminosity of 232 fb −1 , where the uncertainty is statistical only (see Figure 2, left). Simply counting the number of events in the signal region yields 3.2 (scaled) MC events.
The uncertainty of the τ − → 3π − 2π + π 0 ν τ background estimate is based on the uncertainties of the fitted PDF shape parameters, namely, the central value and the width, and the correlation between them. The values of the PDF shape parameters are randomly generated according to their uncertainties expressed in the covariance matrix, and the resulting PDF is then used to estimate the number of background events in the signal region. The total uncertainty from the fitting (0.6 events, 16.7 %) is added in quadrature with systematic uncertainties in the reconstruction of the tracks and neutrals, particle identification, luminosity and τ -pair cross section (8.4 %) and the uncertainty in the branching ratio of the τ − → 3π − 2π + π 0 ν τ decay mode (14.9 %).
An additional background contribution is expected from the τ − → 2π − π + 2π 0 ν τ mode. Using an MC sample corresponding to 675 fb −1 of data we estimate 0.7±0.5 background events in the signal region from this source. The uncertainty is dominated by the MC statistics. Contributions from other generic τ decays are negligible. Combining both sources of the τ background, we expect a total of 4.3 ± 1.0 background events in the data.
For this analysis, a comparison of MC simulation and data has shown that the e + e − → qq background contributions cannot reliably be extracted from simulation due to difficulties in modeling the fragmentation processes. The shape of the simulated pseudo-mass distribution appears to agree with the shape in the data, but the overall normalization does not. Therefore, the qq background is estimated directly from the data, by fitting the data pseudo-mass spectrum with the sum of two Gaussians. This PDF is motivated by MC studies, which show that the e + e − → (uū, dd, ss) and e + e − → cc backgrounds have Gaussian pseudo-mass shapes with different parameters. The double-Gaussian fit to the MC pseudo-mass distribution of qq background is shown in Figure 2 (right).
To extract the qq background in the signal region, we subtract the expected τ background contribution from the data pseudo-mass distribution, and fit the resulting histogram in the range 1.8 < M * < 3.3 GeV/c 2 with a double-Gaussian PDF whose means and sigmas are allowed to float. To avoid experimenter bias, this fit is performed "blind", with the data in the signal region hidden. The fit function is then extrapolated below 1.8 GeV/c 2 and its integral between 1.3 and 1.8 GeV/c 2 yields the qq background estimate in the data, 2.2 events.
To calculate the statistical uncertainty of the qq background estimate we vary the number of events in each bin of the data qq pseudo-mass spectrum above 1.8 GeV/c 2 according to its Poisson error and refit the resulting his- −0.0 events. The total uncertainty is calculated by adding the statistical and systematic uncertainties in quadrature. Thus, the qq background estimate is 2.2 +1.7 −1.0 events. To validate the e + e − → qq background estimate method, we apply it to a τ -event-free data sample, obtained by requiring at least 3 photons with energies greater than 300 MeV on the tag side not associated with a π 0 . This requirement effectively suppresses τ events to a negligible level and provides a clean qq sample in the data. Comparison between the expected and observed qq background levels for this sample shows good agreement, 11.8 predicted background events vs. 12 observed.
Another cross-check we perform is the branching ratio measurement of the τ − → 3π − 2π + π 0 ν τ decay mode using the same selection criteria (except for demanding only one π 0 on the signal side instead of two) as described above. The measured branching ratio is consistent with the Particle Data Group's value [1].
Combining the background estimates from τ and qq events, we calculate a total of 6.5 +2.0 −1.4 background events. Figure 3 illustrates the final pseudo-mass spectrum of the data, along with the expected background PDF. We observe 10 events in the signal region and conclude that there is no evidence for the τ − → 3π − 2π + 2π 0 ν τ decay.
The upper limit for the τ − → 3π − 2π + 2π 0 ν τ decay branching ratio is calculated from where λ N signal is the upper limit on the number of signal events at the 90 % CL. This number is obtained using a limit calculator program [16] that follows the Cousins and Highland approach [17] of incorporating systematic uncertainties into the upper limit, using the numbers of expected background and observed events, as well as the uncertainties on the background, signal efficiency and the number of τ pairs. We find λ N signal = 9.2 events and B(τ − → 3π − 2π + 2π 0 ν τ ) < 3.4 × 10 −6 at the 90 % CL. Table I summarizes the results of this analysis.
In addition to this inclusive result, we also search for the resonant decay mode τ − → 2ωπ − ν τ with the subsequent decay ω → π − π + π 0 , which is predicted to be the main channel for the τ − → 3π − 2π + 2π 0 ν τ decay [7]. The τ − → 2ωπ − ν τ mode has a much narrower allowed pseudo-mass range (1.7 < M * < 1.8 GeV/c 2 ) due to its kinematics. For the same reason, the background level is expected to be much smaller. The event selection is re-optimized for this analysis. Photons are required to have a minimum energy of 50 MeV, energy deposited in at least two crystals and a lateral energy profile consistent with that of a photon. Reconstructed π 0 candidates must have energies above 200 MeV. The ω resonance is reconstructed as a π + π − π 0 combination with an invariant mass of 0.76 < M π + π − π 0 < 0.80 GeV/c 2 .
Reconstruction of both ω mesons suppresses the background and therefore further selection cuts can be sub-stantially loosened to increase the signal efficiency. The conversion veto and the E res cuts are not used. In addition, we allow one charged particle of any type on the tag side, and only loose pion identification is required on the signal side. As a result, the τ − → 2ωπ − ν τ efficiency for this selection is (1.53±0.13) %. The uncertainty is a combination of systematic and statistical uncertainties, as described above for the inclusive τ − → 3π − 2π + 2π 0 ν τ analysis.
The background is estimated from MC simulation (see Figure 4). As in the inclusive analysis, while there is a discrepancy between the data and MC qq yields, the shape of the MC qq pseudo-mass spectrum agrees with the data. As a result of the study we expect negligible qq contribution in the signal region. The uncertainty on the qq background estimate is calculated using the same technique described for the inclusive τ − → 3π − 2π + 2π 0 ν τ analysis. The total expected qq background is 0.0 +0.1 −0.0 events. An additional contribution comes from the τ − → ω2π − π + ν τ mode. Out of 530 fb −1 of MC simulated τ − → ω2π − π + ν τ events, only 1 event is found in the signal region. Thus, we expect 0.4 +1.0 −0.4 events in 232 fb −1 of data. The uncertainty in the τ background estimate is calculated as a Poisson error of 1 event at 68 % CL. MC (shaded histograms) events passing the τ − → 2ωπ − ντ selection criteria. The dark shaded histogram corresponds to the τ background, whose level is determined from the simulation. The light histogram shows the total background, with the level of the qq contribution scaled to agree with the data. The data signal region below 1.8 GeV/c 2 was blinded during the background estimation.
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), Institute of High Energy Physics (China), the Commissariatà 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 Science and Technology of the Russian Federation, and the Particle Physics and As-tronomy Research Council (United Kingdom). Individuals have received support from CONACyT (Mexico), the Marie-Curie Intra European Fellowship program (European Union), the A. P. Sloan Foundation, the Research Corporation, and the Alexander von Humboldt Foundation.