Search for Lepton Flavor Violation in the Decay tau ->electron gamma

A search for the non-conservation of lepton flavor in the decay tau ->electron gamma has been performed with 2.07 x 10^8 e+e- ->tau+ tau- events collected by the BABAR detector at the PEP-II storage ring at a center-of-mass energy near 10.58 GeV. We find no evidence for a signal and set an upper limit on the branching ratio of BR(tau ->electron gamma)<1.1 x 10^-7 at 90% confidence level.

A search for the non-conservation of lepton flavor in the decay τ ± → e ± γ has been performed with 2.07 × 10 8 e + e − → τ + τ − events collected by the BABAR detector at the PEP-II storage ring at a center-of-mass energy near 10.58 GeV. We find no evidence for a signal and set an upper limit on the branching ratio of B(τ ± → e ± γ) < 1.1 × 10 −7 at 90% confidence level.
PACS numbers: 13.35.Dx, 11.30.Hv,14.60.Fg Lepton flavor conservation differs from other conservation laws in the Standard Model (SM) because it is not associated with an underlying conserved current symmetry. Consequently, new theories attempting to describe nature beyond the SM often include lepton flavor violating processes such as the neutrino-less decay of a µ or τ lepton, which have long been identified as unambiguous signatures of new physics. If no specific theoretical model is assumed, any or all of the µ → eγ, τ → µγ and τ → eγ decays can be expected to be observed, and therefore independent searches for each of these modes are required. Some theoretical models [1,2] respecting the current limits on B(µ + → e + γ) [3] and B(τ ± → µ ± γ) [4] in fact allow τ ± → e ± γ decays to occur up to the existing experimental bound [5].
A significant improvement on this τ ± → e ± γ limit is presented here using 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 (c.m.) energy ( √ s) of √ s = 10.58 GeV, and 21.6 fb −1 recorded at √ s = 10.54 GeV. With an average cross section of σ e + e − →τ + τ − = (0.89±0.02) nb [6] as determined using the KK2F Monte Carlo (MC) generator [7], this corresponds 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. A ringimaging Cherenkov detector (DIRC) is used to identify charged hadrons and provides additional electron identification information.
The signature of the signal process is the presence of an isolated eγ pair having an invariant mass consistent with that of the τ (1.777 GeV/c 2 [9]) and a total energy (E eγ ) equal to √ s/2 in the c.m. frame, along with other particles in the event with properties consistent with a SM τ decay. Such events are simulated with higher-order radiative corrections using the KK2F MC generator [7] where one τ decays into eγ according to phase space [10], while the other τ decays according to measured branching ratios [11] simulated with the TAUOLA MC generator [12,13]. The detector response is simulated with the GEANT4 package [14]. The simulated events for signal as well as SM background processes [7,12,13,15,16,17] are then reconstructed in the same manner as data. The MC backgrounds are used to optimize the selection criteria and study systematic errors in the efficiency estimates, but not for the estimation of the final background rate, which relies solely on data. For the background from Bhabha events, we do not rely upon MC predictions because the large Bhabha cross section makes generation of a sufficiently large MC sample impractical.
Events with zero total charge and with two or four well-reconstructed tracks inconsistent with coming from a photon conversion are selected. The event is divided into hemispheres by the plane perpendicular to the thrust axis. The thrust axis, which characterizes the direction of maximum energy flow in the c.m. frame of the event [18], is calculated using all observed charged and neutral particles.
The signal-side hemisphere is required to contain at least one γ with a c.m. energy greater than 500 MeV, and one track identified as an electron. The electron identification uses DCH, EMC and DIRC information, including a requirement that the E/p ratio (the energy deposited in the EMC by the charged particle divided by its momentum as measured in the DCH) lies between 0.89 and 1.2. The electron candidate is required to lie within the fiducial acceptance of the EMC and to have a momentum greater than 500 MeV/c. These criteria yield a π misidentification rate of less than 0.3%. The efficiency for correctly identifying reconstructed tracks in the fiducial volume as electrons in τ ± → e ± γ MC events is greater than 91%. For events with more than one signal-side γ candidate, we choose the γ which gives the mass of the eγ system closest to the τ mass. This provides the correct pairing for 99.9% of selected signal MC events.
The resolution of the eγ mass is improved by assigning the point of closest approach of the e track to the e + e − collision axis as the origin of the γ candidate and by using a kinematic fit with E eγ constrained to √ s/2. The resulting energy-constrained mass (m EC ) and ∆E = E eγ − √ 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 = −15 MeV, σ(∆E) = 51 MeV, where the shift in ∆E comes from photon energy reconstruction effects. To minimize possible biases, we perform a blind analysis by excluding all events in the data within a ±3σ rectangular box centered on m EC and ∆E until all optimization and systematic studies of the selection criteria have been completed. We optimize the selection to obtain the smallest expected upper limit in a background-only hypothesis for observing events inside a ±2σ rectangular box signal box defined by: |∆E − ∆E | < 2σ(∆E) and |m EC − m τ | < 2σ(m EC ), as shown in Figure 1.
The dominant backgrounds arise from Bhabha and e + e − → τ + τ − (with a τ → eνν decay) processes with an energetic γ from initial or final state radiation or from τ → eννγ decays. Backgrounds arising from radiation are reduced by requiring that the total c.m. energy of all non-signal γ candidates in the signal-side hemisphere be less than 200 MeV. To suppress non-τ backgrounds with significant radiation along the beam directions, the polar angle (θ miss ) of the missing momentum associated with the neutrino(s) in the event is required to lie within the detector acceptance (−0.76 < cos θ miss < 0.92).
The tag-side hemisphere, defined to be that opposite to the signal-side hemisphere, is expected to contain a SM τ decay characterized by the presence of one or three charged particles and missing momentum due to unobserved neutrino(s). Taking the direction of the tag-side τ to be opposite the signal eγ candidate, we use all tracks and γ candidates in the tag-side hemisphere to calculate the invariant mass squared of the tag-side missing momentum (m 2 ν ), which peaks around zero for the signal. To reduce backgrounds from radiative e + e − → τ + τ − processes, we require m 2 ν > −0.25 GeV 2 /c 4 . The component of the missing momentum of the event transverse to the collision axis scaled to the beam energy (2 × p T miss / √ s) is expected to be large for signal and e + e − → τ + τ − events, but small for Bhabha and 2-photon events. We exploit an observed correlation between m 2 ν and (2 × p T miss / √ s) in the non-τ backgrounds to significantly suppress them. We require the following: (m 2 ν /1.8 GeV 2 /c 4 ) − ln(2 × p T miss / √ s)/2.0 < 1, the highest c.m. momentum track on the tag-side hemisphere to be inconsistent with being an electron, including requirements that E/p be less than 0.5 and that the momentum be greater than 500 MeV/c, and the tag-side hemisphere to have a total c.m. momentum of all charged and neutral particles less than 4.75 GeV/c.
Backgrounds from e + e − → qq processes are further reduced by requiring the total invariant mass of particles in the tag-side hemisphere to be less than 1.8 GeV/c 2 .  Figure 1, along with a shaded region containing 50% of the selected signal MC events shown for illustrative purposes. The GSB excluding the ±3σ blind region contains 1110 data events, while the luminosity-normalized sum of the non-Bhabha MC backgrounds yield 1045 events. Of these MC events, 99.8% are e + e − → τ + τ − events, 99.9% of which have τ → eνν decays on the signal-side.
The (5.9±3.7)% difference between the number of data and τ -pair dominated MC events indicates that the Bhabha background level in the GSB is low. However, in the more restrictive |∆E − ∆E | < 2σ(∆E) region, the Bhabha background is expected to contribute a substantially higher background fraction because of the greater likelihood of a Bhabha than a τ -pair event to have a hemisphere containing the full beam energy. This residual Bhabha contamination is studied using data distributions of the deviation (∆E γ ) of the measured photon c.m. energy from the corresponding prediction assuming a fully contained e + e − → e + e − γ event. The predicted photon energy is obtained from the beam energy and kinematic information from all particles in the event except the measured photon energy. We observe that the excess of data over non-Bhabha MC events is clustered at low ∆E γ , where the Bhabha events are expected to appear. As we progressively loosen the electron veto on the tag-side track, the excess in the number of data events over the non-Bhabha MC background grows in the region with small ∆E γ , providing further confirmation that the Bhabha background is well understood. We cross check the Bhabha contamination in the |∆E − ∆E | < 2σ(∆E) region from a data sample without a tag-side electron veto, by removing the E/p requirement on the tag-side. To estimate the Bhabha contamination surviving our final event selection, which includes a cut of tag-side E/p < 0.5, we use the data in the adjacent Bhabha-dominated E/p region, 0.5 < E/p < 1.2. We extrapolate the rate from the 0.5 < E/p < 1.2 region to the E/p < 0.5 region, using a high statistics and high purity Bhabha control sample obtained by reversing the requirement on (m 2 ν /1.8 GeV 2 /c 4 ) − ln(2 × p T miss / √ s)/2.0 given above. We estimate the residual Bhabha contamination in our final selection by multiplying the number of events in the 0.5 < E/p < 1.2 region of the no tag-side electron veto sample by the ratio of the number of events in the Bhabha control sample in the E/p < 0.5 region to that in the 0.5 < E/p < 1.2 region. This method gives an estimate of 10.3±1.1 Bhabha events inside the ±2σ(∆E) band once the tag-side electron veto is applied.
In this band, we expect 12.9±2.5 events from the non-Bhabha MC backgrounds, thus obtaining a total background estimate of 23.2±2.7 events. This compares well with the 25 events observed inside the ±2σ(∆E) band in the data. We also find good agreement between the observed and expected number of events separately for the sub-samples with one and three tracks on the tag-side.
For the final background estimate we use the m EC distribution of data events inside the ±2σ(∆E) band, as shown in Figure 2 along with the signal shape included for illustrative purposes. The backgrounds from data inside the ±2σ(∆E) band with |m EC − m τ | > 3σ(m EC ) are fitted to different orders of polynomials in m EC using a maximum likelihood approach. A fit with a constant probability density function (PDF) yields a total χ 2 of 4.7 for the 10 bins shown in Figure 2, and predicts 1.9±0.4 events inside the final ±2σ(m EC ) signal region. Equally acceptable goodness of fit is obtained with higher-order polynomials. However, the coefficients of the higher order terms are statistically compatible with zero. The background predictions from these PDFs agree with the prediction from the constant PDF to within ±0.3 events. As these deviations are smaller than the statistical error on the prediction from the constant PDF, we conclude that the data m EC distribution is consistent with being uniform.
A cross check using non-Bhabha MC background contributions combined with residual Bhabha contamination estimates obtained from the data is also found to be reasonably uniform in m EC (Figure 2) and predicts 1.7±0.2 events inside the ±2σ(m EC ) signal box.
The (5.9±3.7)% difference between data and τ -pair MC predictions also provides a measure of our ability to model the signal-like events in the GSB, since these data events have very similar characteristics to the signal, both in terms of the trigger response of the experiment as well as for the distributions of all the selection variables apart from m EC and ∆E. The systematic error due to a particular cut is taken as the product of the marginal efficiency of the cut and the relative discrepancy between data and MC in the GSB after all other cuts have been applied. The contributions from all the different cuts added in quadrature yield a 2.3% relative systematic error, the only appreciable effect being associated with the requirements on m 2 ν and p T miss . This approach yields a more conservative estimate of the systematic uncertainty on the signal efficiency than the more traditional approach derived from considering the difference between the data and MC prediction for each selection variable, which gives a total estimate of 2.0% relative contribution from all the cuts.
The relative systematic uncertainties on the trigger efficiency, tracking and photon reconstruction efficiencies, and particle identification are estimated to be 1.4%, 1.3%, 1.8% and 1.3%, respectively. The requirement that the events fall within the ±2σ signal box in m EC and ∆E contributes a 4.4% systematic error associated with the scale and resolution uncertainties of these variables and a small contribution from the beam energy uncertainty. As we use 1.3 million MC signal events, the contribution to the uncertainty arising from signal MC statistics is negligible. Adding the contributions of the individual terms in quadrature with an additional 2.3% normalization error on the product Lσ τ τ gives a 6.2% total relative systematic uncertainty on Lσ τ τ ε in the signal box, where the efficiency is ε = (4.7±0.3)%. We note that our final limit on the branching ratio is insensitive to the systematic uncertainty as long as this uncertainty is below 10%.
We find one event in the signal box for an expected background of 1.9±0.4 events. Because of the low background levels, we do not fit for a signal in the m EC distribution as is done in our recent search for τ ± → µ ± γ [4]. Rather, we set an upper limit employing the same technique used in our search for τ ± → ℓ ± ℓ + ℓ − [19] where the background levels were also small. A 90% C.L. upper limit on the branching ratio is calculated according to B 90 UL = N 90 UL /(2ε Lσ τ τ ), where N 90 UL is the 90% C.L. upper limit with one event observed when 1.9±0.4 events are expected. The limit is calculated including all uncertainties using the technique of Cousins and Highland [20] following the implementation of Barlow [21]. At 90% C.L. this procedure gives an upper limit of B(τ ± → e ± γ) < 1.1 × 10 −7 [22]. This represents a more than three-fold reduction in the upper limit as reported in [5].
As an example of how this result constrains theories beyond the SM, we set bounds on the ratio of the first and the third generation element to the first generation diagonal element (M 2 L13 /M 2 L11 ) of the left-handed slepton mass matrix based on predictions from a minimal supergravity model [23,24]. Figure 3 shows the upper limits on M 2 L13 /M 2 L11 as a function of the ratio of the Higgs vacuum expectation values (tan β) and the universal scalar mass (m 0 ), which, for simplicity, is set equal to the universal gaugino mass.
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