Search for Lepton Flavor Violating tau- Decays Including with a K0s Meson

We have searched for the lepton flavor violating decays $\tau^-\to \ell^-\ks$ ($\ell = e {or} \mu$), using a data sample of 281 fb$^{-1}$ collected with the Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. No evidence for a signal was found in either of the decay modes, and we set the following upper limits for the branching fractions: ${\cal{B}}(\tau^-\to e^-\ks)<5.6\times 10^{-8}$ and ${\cal{B}}(\tau^-\to \mu^-\ks)<4.9\times 10^{-8}$ at the 90% confidence level. These results improve the previously published limits set by the CLEO collaboration by factors of 16 and 19, respectively.


INTRODUCTION
Lepton flavor violation (LFV) is allowed in many extensions of the Standard Model (SM), such as Supersymmetry (SUSY) and leptoquark models. In particular, lepton flavor violating decays with K 0 S mesons are discussed in models with heavy singlet Dirac neutrinos [1], R−parity violation in SUSY [2,3], dimension-six effective fermionic operators that induce τ − µ mixing [4]. Experiments at the B-factories allow searches for lepton flavor violating decays with a very high sensitivity. The best upper limits of B(τ − → e − K 0 S ) < 9.1×10 −7 and B(τ − → µ − K 0 S ) < 9.5 × 10 −7 at the 90% confidence level were set by the CLEO experiment using 13.9 fb −1 of data [5].
In this paper, we report a search for the lepton flavor violating decays τ − → ℓ − K 0 S (ℓ = e or µ)[ †] using 281 fb −1 of data collected at the Υ(4S) resonance and 60 MeV below it with the Belle detector at the KEKB e + e − asymmetric-energy collider [6]. 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 thresholď Cerenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL), all located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron fluxreturn located outside of the coil is instrumented to detect K 0 L mesons and to identify muons (KLM). The detector is described in detail elsewhere [7].
Particle identification is very important in this measurement. We use particle identification likelihood variables based on the ratio of the energy deposited in the ECL to the momentum measured in the SVD and CDC, the shower shape in the ECL, the particle range in the KLM, the hit information from the ACC, the measured dE/dX in the CDC and the particle's time-of-flight from the TOF. For lepton identification, we form a likelihood ratio based on the electron probability P(e) [8] and the muon probability P(µ) [9] determined by the responses of the appropriate subdetectors.
For Monte Carlo (MC) simulation studies, the following programs have been used to generate background events: KORALB/TAUOLA [10] for τ + τ − , QQ [11] for BB and continuum, BHLUMI [12] for Bhabha events, KKMC [13] for e + e − → µ + µ − and AAFH [14] for two-photon processes. Since the QQ generator does not include some rare processes that potentially contribute to final states with a K 0 S meson, we generated special samples of e + e − → D * + D ( * )− , a process that was recently observed by the Belle collaboration [15]. Signal MC is generated by KORALB/TAUOLA. Signal τ decays are two-body and assumed to have a uniform angular distribution in the τ lepton's rest frame. The Belle detector response is simulated by a GEANT 3 [16] based program. All kinematic variables are calculated in the laboratory frame unless otherwise specified. In particular, variables calculated in the e + e − center-of-mass (CM) frame are indicated by the superscript "CM".

DATA ANALYSIS
We search for τ + τ − events in which one τ (signal side) decays into ℓK 0 S (K 0 S → π + π − ), while the other τ (tag side) decays into one charged track (with a sign opposite to that of the signal-side lepton) and any number of additional photons and neutrinos. Thus, the [ †] Unless otherwise stated, charge conjugate decays are included throughout this paper. experimental signature is: All charged tracks and photons are required to be reconstructed within a fiducial volume, defined by −0.866 < cos θ < 0.956, where θ is the polar angle with respect to the direction opposite to the e + beam. We select charged tracks with momenta transverse to the e + beam p t > 0.1 GeV/c and photons with energies E γ > 0.1 GeV. Candidate τ -pair events are required to have four charged tracks with a zero net charge. Events are separated into two hemispheres corresponding to the signal (three-prong) and tag (one-prong) sides by the plane perpendicular to the thrust axis [17]. The magnitude of the thrust is required to be larger than 0.9 to suppress the qq continuum background. The K 0 S is reconstructed from two oppositely-charged tracks in the signal side that have an invariant mass 0.482 GeV/c 2 < M π + π − < 0.514 GeV/c 2 , assuming a pion mass for both tracks. The π + π − vertex is required to be displaced from the interaction point (IP) in the direction of the pion pair momentum [18]. In order to avoid fake K 0 S candidates from photon conversions (i.e. γ → e + e − ), the invariant mass reconstructed by assigning the electron mass to the tracks, is required to be greater than 0.2 GeV/c 2 . The signal side track not used in the K 0 S reconstruction is required to satisfy the lepton identification selection. The electron and muon identification criteria are P(e) > 0.9 with p > 0.3 GeV/c and P(µ) > 0.9 with p > 0.6 GeV/c, respectively. After the event selection described above, most of the remaining background comes from generic τ + τ − and continuum events that contain a real K 0 S meson. To ensure that the missing particles are neutrinos rather than photons or charged particles that fall outside the detector acceptance, we impose additional requirements on the missing momentum vector, p miss , calculated by subtracting the vector sum of the momenta of all tracks and photons from the sum of the e + and e − beam momenta. We require that the magnitude of p miss be greater than 0.4 GeV/c and that its direction point into the fiducial volume of the detector, as shown for the τ − → µ − K 0 S mode in Fig. 1 (a) and (b). The total visible energy in the CM frame, E CM vis , is defined as the sum of the energies of the K 0 S candidate, the lepton, the tag-side track (with a pion mass hypothesis) and all photon candidates. We require E CM vis to satisfy the condition: 5.29 GeV < E CM vis < 10.0 GeV (see Fig. 1 (c)). Since neutrinos are emitted only on the tag side, the direction of p miss should lie within the tag side of the event. The cosine of the opening angle between p miss and the tag-side track in the CM system, cos θ CM tag−miss , is therefore required to be greater than 0 (see Fig. 1 (d)). For all kinematic distributions shown in Fig. 1, reasonable agreement between the data and background MC is observed. In order to suppress background from qq (q = u, d, s, c) continuum events, the following requirements on the number of the photon candidates on the signal and tag side are imposed: n SIG ≤ 1 and n TAG ≤ 2, respectively.
Finally, the correlation between the reconstructed momentum of the ℓK 0 S system, p ℓK S , and the cosine of the opening angle between the lepton and K 0 S , cos θ ℓK S is employed to further suppress background from generic τ + τ − and continuum events via the requirements: cos θ ℓK S < 0.14 × log(p ℓK S − 2.7) + 0.7, where p ℓK S is in GeV/c (see Fig. 2). While this condition retains 99% of the signal, 99% of the generic τ + τ − and 84% of the uds continuum background are removed. Following all the selection criteria, the signal detection efficiencies for the τ − → e − K 0 S and τ − → µ − K 0 S modes are 15.0% and 16.2%, respectively. decays. The remaining continuum backgrounds in the τ − → µ − K 0 S mode are combinations of a true K 0 S meson and a fake lepton. To optimize our search sensitivity, we select an elliptically shaped signal region of minimum area with the same signal acceptance as that of a rectangular box corresponding to ±5σ in the MC resolution for the M ℓK 0 S − ∆E plane. The signal efficiencies after all requirements are 11.8% for the τ − → e − K 0 S and 13.5% for the τ − → µ − K 0 S , respectively. As there are few remaining MC background events in the signal ellipse, we estimate the background contribution using the M ℓK 0 S sideband regions defined by rectangular areas beside the signal ellipse shown in Fig. 3 (a) and (b). Extrapolation to the signal region assumes that the background distribution is flat in M ℓK 0 S . We find the expected background in the ellipse to be 0.2 ± 0.2 events for both modes. Finally, we uncover the blinded region and find no data events in the signal region of the τ − → e − K 0 S and τ − → µ − K 0 S modes (see Fig. 3 (a) and (b)). Since no statistically significant excess of data over the expected background in the signal region is observed, we apply a frequentist approach to calculate upper limits on the signal yields [19]. The resulting limits for the signal yields at 90% confidence level, s 90 , are 2.23 events in both modes. The upper limits on the branching fraction before the inclusion of systematic uncertainties are then calculated as where B(K 0 S → π + π − ) = 0.6895 ± 0.0014 [20] and N τ τ = 251 × 10 6 is the number of τ −pairs produced in 281 fb −1 of data. We obtain N τ τ using σ τ τ = 0.892±0.002 nb, the e + e − → τ + τ − cross section at the Υ(4S) resonance calculated by KKMC [13]. The resulting values are The dominant systematic uncertainties on the detection sensitivity: 2εN τ τ B(K 0 S → π + π − ) come from K 0 S reconstruction and tracking efficiencies. These are 4.5% and 4.0%, respectively, for both modes. Other sources of the systematic uncertainties are: the trigger efficiency (0.5%), lepton identification (2.0%), MC statistics (0.3%), branching fraction of K 0 S → π + π − (0.2%) and luminosity (1.4%). Assuming no correlation between them, all these uncertainties are combined in quadrature to give a total of 6.5%.
While the angular distribution of τ − → ℓ − K 0 S decay is initially assumed to be uniform in this analysis, it is sensitive to the lepton flavor violating interaction structure [21]. The spin correlation between the τ lepton in the signal and that in the tag side must be considered. A possible nonuniformity was taken into account by comparing the uniform case with those assuming V − A and V + A interactions, which result in the maximum possible variations. No statistically significant difference in the M ℓK 0 S -∆E distribution or the efficiencies is found compared to the case of the uniform distribution. Therefore, systematic uncertainties due to these effects are neglected in the upper limit evaluation.
Upper limits on the branching fractions at the 90% confidence level including these systematic uncertainties are calculated with the POLE program without conditioning [22]. The resulting upper limits on the branching fractions at the 90% confidence level are

DISCUSSION
In the R−parity violating SUSY scenario, there are three kinds of terms (λ, λ ′ and λ ′′ ) with a total of 45 couplings. In this model, τ − could decay into ℓ − K 0 S via tree-level scalar neutrino exchange by the λλ ′ couplings. Using our results, the limits on the products λλ ′ as a function of the scalar neutrino mass (Mν) are given as [2], where i is the generation number. These bounds are more stringent than the previous bounds obtained in R−parity violating models from τ − decay including a pseudoscalar meson [2,3]. The improved sensitivity to rare τ lepton decays achieved in this work can be used to constrain the new physics scale for the dimension-six fermionic effective operators involving τ − µ flavor violation, motivated by neutrino oscillations [4]. From our upper limit for the branching fraction of the τ − → µ − K 0 S decay, lower bounds of 36.2 TeV and 37.2 TeV can be obtained for the axial-vector and pseudoscalar operators, respectively.

CONCLUSION
In conclusion, we have searched for the lepton flavor violating decays τ − → ℓ − K 0 S (ℓ = e or µ) using data collected with the Belle detector at the KEKB e + e − asymmetric-energy collider. We found no signal in either mode. The following upper limits on the branching fractions at the 90% confidence level are obtained: B(τ − → e − K 0 S ) < 5.6 × 10 −8 and B(τ − → µ − K 0 S ) < 4.9 × 10 −8 . These results improve the search sensitivity by factors of 16 and 19, respectively, compared to the previous limits obtained by the CLEO experiment.