Search for Lepton-Flavor Violation in the Decay τ − → ℓ ∓ h ± h − The BABAR Collaboration

A search for the lepton-flavor-violating decay of the tau into three charged leptons has been performed using 91.5 fb - 1 of data collected at an e + e - center-of-mass energy around 10.58 GeV with the BABAR detector at the SLAC storage ring PEP-II. In all six decay modes considered, the numbers of events found in data are compatible with the background expectations. Upper limits on the branching fractions are set in the range (1-3) × 10 - 7 at 90% confidence level.

A search for the nonconservation of lepton flavor number in the decay τ ± → µ ± γ has been performed using 2.07×10 8 e + e − → τ + τ − events produced at a center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage ring. We find no evidence for a signal and set an upper limit on the branching ratio of B(τ ± → µ ± γ) < 6.8 × 10 −8 at 90% confidence level.
PACS numbers: 13.35.Dx,14.60.Fg,11.30.Hv Decays violating lepton flavor number, if observed, would be among the most theoretically clean signatures of new physics and the decay τ ± → µ ± γ is one such process. It is expected with rates as high as several parts per million in some supersymmetric models [1,2], despite the stringent experimental limit on the related µ ± → e ± γ decay [3]. In a modest extension to the Standard Model (SM) incorporating finite ν masses [4], the branching ratio is many orders of magnitude below experimental accessibility [5], and so an observation of this mode would unambigously indicate new physics. Currently the most stringent limit is B(τ ± → µ ± γ) < 3.1 × 10 −7 at 90% confidence level (c.l.) from the BELLE experiment [6].
The search for τ ± → µ ± γ decays reported here uses data recorded by the BABAR detector at the SLAC PEP-II asymmetric-energy e + e − storage ring. The data sample consists of an integrated luminosity of L= 210.6 fb −1 recorded at a center-of-mass energy ( √ s) of √ s = 10.58 GeV, and 21.6 fb −1 recorded at √ s = 10.54 GeV. The luminosity-weighted average cross section for e + e − → τ + τ − is σ τ τ = (0.89 ± 0.02) nb [7], corresponding to a data sample of 2.07 × 10 8 τ -pair events.
The BABAR detector is described in detail in Ref. [8]. Charged particles are reconstructed as tracks with a 5layer silicon vertex tracker and a 40-layer drift chamber (DCH) inside a 1.5-T solenoidal magnet. An electromagnetic calorimeter (EMC) consisting of 6580 CsI(Tl) crystals is used to identify electrons and photons. The flux return of the solenoid, instrumented with resistive plate chambers (IFR), is used to identify muons.
The signature of the signal process is the presence of an isolated µ and γ having an invariant mass consistent with that of the τ (1.777 GeV/c 2 [9]) and a total energy (E µγ ) equal to √ s/2 in the event center-of-mass (c.m.) frame, and properties of the other particles in the event which are consistent with a SM τ decay. Such events are simulated with higher-order radiative corrections using the KK2f Monte Carlo (MC) generator [7] where one τ decays into µγ according to phase space [10], while the other τ decays according to measured rates [11] simulated with Tauola [12,13]. The detector response is simulated with GEANT4 [14]. The simulated events for signal as well as SM background processes [7,12,13,15,16] are then reconstructed in the same manner as data. The MC backgrounds are used for selection optimization and efficiency systematic studies, but not for the final background estimation, which relies solely on data.
Events with two or four well reconstructed tracks and zero net charge are selected. The magnitude of the thrust vector calculated with all observed charged and neutral particles, characterising the direction of maximum energy flow in the event [17], is required to lie between 0.900 and 0.975 to suppress e + e − → qq backgrounds with low thrust and e + e − → µ + µ − and Bhabha backgrounds with thrust close to unity. Other non-τ backgrounds are suppressed by requiring the polar angle (θ miss ) of the missing momentum associated with the neutrinos in the event to lie within the detector acceptance (−0.76 < cos θ miss < 0.92), and the scaled missing c.m. transverse momentum relative to the beam axis (p T miss / √ s) to be greater than 0.068 (0.009) for events with two (four) tracks.
The signal-side hemisphere, defined with respect to the thrust axis, is required to contain one track with c.m. momentum less than 4.5 GeV/c and at least one γ with a c.m. energy greater than 200 MeV. The track must be identified as a µ using DCH, EMC and IFR information and the γ candidate is the one which gives the mass of the µγ system closest to the τ mass. This provides the correct pairing for 99.9% of selected signal events. The resolution of the µγ mass is improved by assigning the point of closest approach of the µ track to the e + e − collision axis as the origin of the γ candidate and by using a kinematic fit with E µγ constrained to √ s/2. This energy-constrained mass (m EC ) and ∆E = E µγ − √ s/2 are independent variables apart from small correlations arising from initial and final state radiation. The mean and standard deviation of the m EC and ∆E distributions for reconstructed MC signal events are: m EC = 1777 MeV/c 2 , σ(m EC ) = 9 MeV/c 2 , ∆E = −9 MeV, σ(∆E) = 45 MeV, where the shift in ∆E comes from photon energy reconstruction effects. We blind the data events within a 3σ ellipse centered on m EC and ∆E until completing all optimization and systematic studies of the selection criteria.
The dominant backgrounds are from e + e − → µ + µ − and e + e − → τ + τ − (with a τ ± → µ ± νν decay) events with an energetic γ from initial or final state radiation or in the τ decay. For these backgrounds, the γ is predominantly along the µ flight direction; thus we require | cos θ H | < 0.8, where θ H is the angle between the µ momentum in the reconstructed τ rest frame and the τ momentum in the laboratory frame. Backgrounds arising from τ ± → h ± (≥ 1)π 0 ν decays with the hadronic track (h) mis-identified as a µ, are reduced by requiring the total c.m. energy of non-signal γ candidates in the signal-side hemisphere to be less than 200 MeV. If the reconstructed neutral candidate identified as the signal γ, has at least 1% likelihood of arising from overlapping daughters in π 0 → γγ decays, then the event is rejected.
The tag-side hemisphere, which is expected to contain a SM τ decay, is required to have a total invariant mass less than 1.6 GeV/c 2 and a c.m. momentum for each track less than 4.0 GeV/c to reduce background from e + e − → qq and e + e − → µ + µ − processes, respectively. The qq background is further reduced by requiring the hemisphere to have no more than six γ candidates.
A tag-side hemisphere containing a single track is classified as e-tag, µ-tag or h-tag if the total photon c.m. energy in the hemisphere is no more than 200 MeV and the track is exclusively identified as an electron (e-tag), as a muon (µ-tag) or as neither (h-tag). If the total photon c.m. energy in the hemisphere is more than 200 MeV, then events are selected if the track is exclusively identified as an electron (eγ-tag) or as neither an electron nor as a muon (hγ-tag). These allow for the presence of radiation in τ ± → e ± νν decays and for photons from π 0 → γγ in τ ± → h ± (≥ 1)π 0 ν decays. If the tag-side contains three tracks, the event is classified as a 3h-tag. We explored other tag-side channels but the sensitivity of the search does not improve by including them.
Hadronic τ decays have only one missing ν, a feature used to purify the sample. Taking the tag-side τ direction to be opposite the fitted signal µγ candidate, we use all tracks and γ candidates on the tag-side to calculate the invariant mass squared of the missing ν (m 2 ν ), and require |m 2 ν | to be less than 0.4 GeV 2 /c 4 for h-tag and 3h-tag events and less than 0.8 GeV 2 /c 4 for hγ-tag events.
At this stage of the analysis, 15% of the MC signal events survive within a Grand Side Band (GSB) region defined as: m EC ∈ [1.5, 2.1] GeV/c 2 , ∆E ∈ [-1.0, 0.5] GeV. The non-blinded part of the GSB contains 4688 data events, which agrees with the MC background expectation of 4924 events to within 5%. Out of these MC events, 80% are from e + e − → τ + τ − , 82% of which are τ ± → µ ± νν decays on the signal-side.
To further suppress the backgrounds, separate neural net (NN) based discriminators are used for each of the six tags. Five observables serve as input to the NN: the missing mass of the event, the highest c.m. momentum of the tag-side track(s), cos θ H , p T miss and m 2 ν . Each NN is trained using data in the non-blinded part of the GSB to describe the background and µγ MC in the full GSB region to describe the signal. The NN output distributions of the data (Figure 1) are in good agreement with MC backgrounds both in shape and absolute rates, as are the input observables. The MC signal within a 2σ ellipse in the m EC -∆E plane centered on m EC and ∆E , and the MC background interpolated from m EC sidebands (|m EC − m EC | > 3σ within the GSB and |∆E − ∆E | < 3σ) are then used to optimize the cut value on the NN output based on the expected 90% c.l. upper limit. The optimized NN cut values are restricted to be > 0.5. Within the ±3σ band in ∆E, the MC predicts that 66% of the selected background comes from e + e − → µ + µ − , 27% from e + e − → τ + τ − and the rest from e + e − → qq processes.
With the data unblinded, we find four events in the 2σ signal ellipse where we expect 6.2 ± 0.5 events, obtained from a linear interpolation of the data in the m EC sidebands. Other polynomials up to at least fifth order predict the same level of background to within half a standard deviation. The agreement between observed data and background expectations across the different tagging modes are shown in Table I   efficiency, tracking and photon reconstruction efficiencies, and particle identification are estimated to be 1.2%, 1.3%, 1.8% and 1.2%, respectively. We obtain a measure of the systematic error of the efficiency due to simulation uncertainties of the NN input variables by fixing each input variable to its average value one at a time, without retraining or changing the architecture of the NN, and re-calculating the efficiency. This has the effect of removing each input variable completely from the NN selection and gives a 1.9% relative error on the signal efficiency. Adding these errors in quadrature gives 3.4%.
As we use 1.2 × 10 6 MC signal events, the contribution to the error arising from signal MC statistics is negligible. Alternatively, these (and other potential sources of systematic uncertainty not necessarily accounted for in the above procedure) can be collectively estimated from the detector modelling uncertainty obtained by comparing data to the MC backgrounds in the non-blinded part of the GSB, where the background and signal have similar properties apart from m EC and ∆E. Data and MC background statistics as well as signal efficiencies (ε) are shown in Table I inside the full GSB. The agreement in the GSB between data and the background MC for each tag-mode and their combination validates the ability of the MC to simulate these signal-like events. The statistical precision of this data-to-MC ratio is augmented by using the expanded range m EC ∈ [1.0, 2.5] GeV/c 2 to obtain a value of 1.052 ± 0.056(stat) ± 0.024(norm) in the non-blinded part of the GSB. To be conservative, we quote the total 6.1% uncertainty on this ratio, which includes a 2.3% normalization error on the product Lσ τ τ , as the relative systematic error on the ε in the GSB.
To obtain the branching ratio, we perform an extended unbinned maximum likelihood (EML) fit to the m EC data distribution ( Figure 2) after all requirements but that on m EC have been applied. Within this ±2σ band in ∆E the efficiencies for the different tag-modes are given in Table I for a total value of ε = (9.4±0.6)%, where the systematic error here includes an additional contribution from the ∆E requirement. A linear parameterization describes the background and a double Gaussian serves as the probability density function (PDF) of the signal. Uncertainities in the mean and resolution of m EC are incorporated into the fit by convoluting the signal PDF with another Gaussian with σ = 4 MeV/c 2 and by increasing the σ of the convoluted Gaussian by 1 MeV/c 2 . The quoted limit is insensitive to these variations, however.
In the EML fit, the number of signal events is given by 2 Lσ τ τ εB(τ ± → µ ± γ) and we fit for the branching ratio, the number of background events and slope of the background. The systematic uncertainty on ε is incorporated into the likelihood by adding ε as a fourth fit parameter under the constraint that it follows a Gaussian spread about its measured value within the estimated errors. This yields the same upper limit as the fit without the constraint on ε to within the quoted number of significant figures. The fit gives B(τ ± → µ ± γ) = (−5.6 +8.3 −6.3 ) × 10 −8 , which corresponds to −2.2 +3.2 −2.4 signal and 143 ± 12 background events. From the likelihood function of this fit, a Bayesian upper limit can be derived [18].
In keeping with established τ ± → µ ± γ studies [6,19], we derive a frequentist upper limit [20]. We generate MC samples with Poisson-distributed numbers of signal and background events. The expected number of background events is fixed to 143 and we scan over the expected number of signal events, s. The m EC values are distributed according to the signal and background PDFs, where the background slope is generated from a Gaussian distribution with mean and standard deviation given by the fit to the data. The number of signal events in each sample is extracted using the same EML fit procedure as that applied to the data. We vary s until we find a value for which 90% of the sample yields a fitted number of signal events greater than that observed in the data, i.e. −2.2. At 90% c.l. this procedure gives an upper limit of B(τ ± → µ ± γ) < 6.8 × 10 −8 [21].
As confirmation of this result, we also undertake an analysis without the NN, having the same sensitivity of 12 × 10 −8 for the expected 90% c.l. upper limit. Events with a tag-side muon are vetoed but single-track tag events are otherwise not classified. Cuts are applied on the signal µ momentum, signal γ energy, θ miss , p T miss , the tag-side invariant mass and ∆E, and m EC is required to be within 30 MeV of m τ . This selection retains 10.7% of the signal and has a background of 28.5±2.3 events as estimated from the sidebands.
To enhance the signal/background discrimination, a likelihood-ratio variable, R, is built from four discriminating variables: p T miss , ∆E, the difference between the signal µ and γ energy in the c.m., and the acoplanarity between the signal µγ system and the tag system. We observe no evidence of signal and we compare the twodimensional (m EC , R) distribution of the 27 events in data with the background and signal expectations, utilizing a classical frequentist CL S+B method [22]. The limit set is consistent with the above value and amounts to a 90% c.l. limit of 9.4 × 10 −8 .
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