Search for lepton and baryon number violating ${\tau }^{-}$ decays into $\overline{\Lambda }{\pi }^{-}$ and $\Lambda {\pi }^{-}$

Abstract

We have searched for τ lepton decays, ${\tau }^{-}\to \overline{\Lambda }{\pi }^{-}$ and ${\tau }^{-}\to \Lambda {\pi }^{-}$, that simultaneously violate the conservation of the lepton (L) and baryon (B) number using a data sample of $154{\text{fb}}^{\mathrm{-1}}$ 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: $\mathcal{B}({\tau }^{-}\to \overline{\Lambda }{\pi }^{-})<1.4\times {10}^{\mathrm{-7}}$ and $\mathcal{B}({\tau }^{-}\to \Lambda {\pi }^{-})<0.72\times {10}^{\mathrm{-7}}$ at the 90% confidence level. This is the first search ever performed for these modes.

Introduction

While the Standard Model (SM) assumes both the baryon (B) and lepton number (L) conservation, in some extensions of the SM, such as supersymmetric [1] and superstring [2] models, B and L violation is expected while their difference $B-L$ should be conserved. Existing searches for baryon number violation are restricted to experiments with nucleons [3]. Limits from searches for proton decay imply that the τ lepton decays with baryon number violation can be expected to have a probability well below the current experimental sensitivity [4]. However, high luminosity B-factories provide an opportunity to look for decays of the τ lepton, D and B mesons that violate B and L with unprecedented sensitivity. Until now, searches for τ lepton decays with a baryon final state involved a proton only [5]. Upper limits for the branching fraction of these decays are in the range of 10⁻⁵–10⁻⁶. In a recent extension of the SM [6], decays of τ lepton as well as D and B mesons that violate B and L were considered using right-handed four-fermion couplings that conserve $B-L$ and it was suggested that ${\tau }^{-}\to \overline{\Lambda }{\pi }^{-}$ decay involving the second and third generation transition might be interesting.

We report here our search for ${\tau }^{-}\to \overline{\Lambda }{\pi }^{-}$ and ${\tau }^{-}\to \Lambda {\pi }^{-}$ decays with a data sample of $154{\text{fb}}^{\mathrm{-1}}$ collected at the $\Upsilon (4S)$ resonance and 60 MeV below it with the Belle detector at the KEKB $e^{+}{e}^{-}$ asymmetric-energy collider [7]. These τ lepton decay modes have never been studied before.¹

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 Čerenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to detect $K_L^0$ mesons and to identify muons (KLM). The detector is described in detail elsewhere [8].

Particle identification is very important in this measurement. It is 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, $dE/dX$ in the CDC and time-of-flight from the TOF. To distinguish hadron species, we use likelihood ratios, for instance, $\mathcal{P}(p/\pi )={\mathcal{L}}_p/({\mathcal{L}}_p+{\mathcal{L}}_{\pi })$, where ${\mathcal{L}}_i$ is the likelihood for the detector response to the track with flavor hypothesis i. For lepton identification, we use likelihood ratios as electron probability $\mathcal{P}(e)$ [9] and muon probability $\mathcal{P}(\mu )$ [10] determined by the responses of the appropriate subdetectors.

For the Monte Carlo (MC) studies, the following programs are used to generate background events: KORALB/TAUOLA [11] for ${\tau }^{+}{\tau }^{-}$, QQ [12] for $B\overline{B}$ and continuum, BHLUMI [13] for Bhabha, KKMC [14] for ${\mu }^{+}{\mu }^{-}$ and AAFH [15] for two-photon processes. Signal MC is generated by KORALB/TAUOLA. To take a range of possible ${\tau }^{-}\to \overline{\Lambda }{\pi }^{-}$ and ${\tau }^{-}\to \Lambda {\pi }^{-}$ decay mechanisms into account, we generate events under three different assumptions: uniform angular distribution in the τ rest frame, $V-A$ and $V+A$ interactions. We initially assume all τ decays to have a uniform angular distribution and take the other hypotheses into account later. The Belle detector response is simulated by a GEANT 3 [16] based program. Unless stated otherwise, all kinematic variables are calculated in the laboratory frame, while the ones calculated in the $e^{+}{e}^{-}$ center-of-mass (CM) frame are indicated by the superscript “CM”.