Experimental review of τ lepton studies at the B factories

Recent results of a high-statistics τ lepton studies at B factories are reported. Reviewed are the measurements of Michel parameters in lepto nic and radiative leptonic τ decays at Belle, as well as the measurement of the branching f ractions of the radiative leptonicτ decays atBABAR. Searches for CP symmetry violation in hadronic decays with K0 S are also briefly discussed.


Introduction
The world largest data set of τ leptons collected at e + e − B factories [1] opens new era in the precision tests of the Standard Model (SM). An essential progress has been made in the study of the main τ properties at Belle and BABAR, namely, lifetime [2,3], mass [4,5], EDM [6] have been measured with the best or competitive to the world best accuracies.
In the SM, τ decays due to the charged weak interaction described by the exchange of W ± with a pure vector coupling to only left-handed chirality fermions. There are two main classes of tau decays: leptonic decays 1 (τ − → ℓ −ν ℓ ν τ , τ − → ℓ −ν ℓ ν τ γ, τ − → ℓ − ℓ ′+ ℓ ′−ν ℓ ν τ ; ℓ, ℓ ′ = e, µ), and hadronic decays. Leptonic decays are the only ones in which the electroweak couplings can be probed without disturbance from the strong interactions. This makes them an ideal system to study the Lorentz structure of the charged weak current. Recently, leptonic and radiative leptonic τ decays have been studied at B factories. While Belle focused on the measurement of Michel parameters in these decays [7,8], BABAR performed precision tests of the lepton universality [9] and measurement of the branching fractions [10].
Hadronic decays of τ offer unique tools for the precision studies of low energy QCD [11]. Of particular interest are strangeness changing Cabibbo-suppressed hadronic τ decays, in which large CP symmetry violation (CPV) could appear from a charged scalar boson exchange [12].
left-and right-handedness of the charged leptons, index N denotes the properties of the currents under Lorentz transformation (scalar(S ), vector(V), tensor(T )). In the SM, the only non-zero coupling constant is g V LL = 1, this property is also known as (V-A)⊗(V-A) Lorentz structure of the matrix element. In the case where neutrinos are not detected and the spin of the outgoing charged lepton is not determined, only four Michel parameters (MP) ρ, η, ξ and δ are experimentally accessible, they are bilinear combinations of the g N i j coupling constants [13,14]. In the SM, the (V-A) charged weak current is characterized by ρ = 3/4, η = 0, ξ = 1 and δ = 3/4.

Radiative leptonic τ decays
Emission of the photon in the final state of the radiative leptonic τ decay results in three additional Michel parameters:η, η ′′ and ξκ [19]. Measurement of these parameters provides a further constraint on the Lorentz structure of the charged weak current. The ξκ, like ξ and δ, appears in the τ spin-dependent part of the differential decay width, so, spin-spin correlations between the τ + and τ − allow one to measure ξκ. The total differential decay width of the radiative leptonic decay depends on seven Michel parameters: ρ, η, ξ, δ,η, η ′′ and κ. In this analysis, ρ, η, ξ, δ and ξ ρ parameters are fixed to their SM values. Also, feasibility study showed that the sensitivity to the η ′′ is very poor in comparison with theη and κ, so, η ′′ was also fixed to its SM expectation η ′′ = 0. In the signal events one tau decays to radiative leptonic mode, τ − → ℓ −ν ℓ ν τ γ, while the other tau decays via τ + → π + π 0ν τ . The p.d.f. function for the vector of the measured parameters z = {p ℓ , cos θ ℓ , φ ℓ , p γ , cos θ γ , φ γ , p ρ , cos θ ρ , φ ρ , m ππ , cosθ π ,φ π } is constructed from the total differential cross section of the reaction , which is linear function ofη and ξκ. Michel parameters are extracted in the unbinned maximum likelihood fit of the (ℓ − γ; ρ + ) events in the full twelve-dimensional phase space. The dominant background processes are ordinary leptonic decay with the photon from the external bremsstrahlung and radiative leptonic decay with the external bremsstrahlung for the (e − γ; ρ + ) events; ordinary leptonic decay plus beam background or initial/final state radiation photon for the (µ − γ; ρ + ) events. The dominant background contributions are included in the p.d.f. analytically. The remaining background with the fraction λ 0 is described by the P MC bg ( z) p.d.f., evaluated from the MC sample. The total p.d.f. reads: where S ( z | Θ) is analytical cross section for the signal, B i ( z) is analytical cross section of the ith background (i = 1, 2 for the (e − γ; ρ + ), and i = 1 ÷ 5 for the (µ − γ; ρ + ) events), λ i is the fraction of the ith background and ε( z) is the detection efficiency in the full phase space.
The statistics of about 703 fb −1 collected at Belle, which contains 646 × 10 6 τ + τ − pairs was used for the analysis [8]. Summary of the selected data sample is shown in Table 2. Figures 1(a) and 1(b) show the distribution of the photon energy and the spatial angle between lepton and photon for the (µ − γ; ρ + ) sample. Theη was measured to beη = −1.3 ± 1.5 ± 0.8 only in the (µ − γ; ρ + ) sample, because of the poor sensitivity to this parameter in the (e − γ; ρ + ) sample. The first error is statistical and the second one is systematic. The ξκ was measured to be ξκ = 0.5 ± 0.4 ± 0.2 in both samples.  ] (57.4%)

Study of radiative leptonic τ decays at BABAR
The analysis is based on a 431 fb −1 data sample collected at BABAR, which corresponds to 400 × 10 6 τ-pairs [10]. Basically, events with track and photon from the signal tau and 1-prong decay of the second tau were selected.
Each of two oppositely charged tracks is required to have the transverse momentum p T > 0.3 GeV/c, and the cosine of the polar angle −0.75 < cos θ track < 0.95 to ensure good particle identification. The electron and muon identification efficiencies are 91% and 62%, respectively. The total missing transverse momentum of the event is required to be p T,miss > 0.5 GeV/c. The photon energy threshold is 50 MeV. Each event is divided into two hemispheres (signal and tag hemispheres) in the center-of-mass (CM) frame by a plane perpendicular to the thrust axis. The magnitude of the thrust is required to be between 0.9 and 0.995. The signal hemisphere must contain one track and one photon. The tag hemisphere must contain one track, and possibly one additional photon or one or two π 0 candidates. Each π 0 candidate is reconstructed from a pair of photons with γγ invariant mass to be 100 ≤ M γγ ≤ 160 MeV/c 2 . The total energy deposition in the calorimeter is less than 9 GeV. In the signal hemisphere, the distance between the track and photon cluster, measured on the inner wall of the calorimeter, must be d lγ < 100 cm. To suppress radiative µ + µ − and Bhabha background, events with two leptons of the same flavors in the signal and tag hemispheres were rejected.
After these selections, both samples are dominated by background events. For the τ → eννγ sample, the dominant background comes from the ordinary τ leptonic decay with the external bremsstrahlung in the material of the detector. For the τ → µννγ sample, the main background comes from the initial-state radiation, τ → ππ 0 ν decays, e + e − → µ + µ − (γ) process, and τ → πν decays.
The decay-rate asymmetry A CP = S (≥π 0 )ν τ ) was studied at BABAR with a 476 fb −1 data sample. The obtained result A CP = (−0.36 ± 0.23 ± 0.11)% is about 2.8 standard deviations from the SM expectation A K 0 CP = (+0.36 ± 0.01)%. At Belle, CPV search was performed as a blinded analysis based on a 699 fb −1 data sample. Specially constructed asymmetry, which is a difference between the mean values of cos β cos ψ for τ − and τ + events, was measured in bins of K 0 S π − mass squared (Q 2 = M 2 (K 0 S π)): ≃ cos β cos ψ τ − − cos β cos ψ τ + , where β, θ and ψ are the angles, evaluated from the measured parameters of the final hadrons, dω = dQ 2 dcos θdcos β. In contrary to the decay-rate asymmetry, the introduced A CP i (Q 2 i ) is already sensitive to the CPV effects from the charged scalar boson exchange [12,25]. No CP violation was observed and the upper limit on the CPV parameter η S was extracted |Im(η S )| < 0.026 at 90% CL. Using this limit parameters of the Multi-Higgs-Doublet models [26,27] can be constrained as |Im(XZ * )| < 0.15 M 2 H ± /(1 GeV 2 /c 4 ), where M H ± is the mass of the lightest charged Higgs boson, the complex constants Z and X describe the coupling of the Higgs boson to leptons and quarks, respectively.