Tau polarimetry with inclusive decays.

The spin asymmetry parameter Aτ characterizing the angular distribution of the total hadron momentum in the decay of a polarized tau can be calculated rigorously using perturbative QCD and the operator product expansion. Perturbative QCD corrections to the free quark result Aτ = 1/3 can be expressed as a power series in αs(Mτ ) and nonperturbative QCD corrections can be expanded systematically in powers of 1/M2 τ . The QCD prediction is Aτ = 0.41 ± 0.02. In the decay of a high energy tau into hadrons, the value of the hadronic energy distribution dRτ/dz evaluated at the maximum hadronic energy fraction z = 1 can also be calculated rigorously from QCD. The spin-dependence of processes involving elementary particles contains a wealth of information about their fundamental interactions. Unfortunately this information is not easily accessible to experiment. It requires either the use of polarized beams and targets, or the measurement of the polarization of final state particles. The tau lepton is one of the few elementary particles whose spin can be effectively analyzed by its decays. It is well known that several of the exclusive decay modes of the tau can be used to analyze its spin [1, 2]. In this Letter, I point out that inclusive decays into hadrons can also be used for this purpose. The polarization of a sample of taus that decay into hadrons can be determined from the angular distribution of the total momentum of the hadrons. The asymmetry parameter that characterizes the angular distribution can be computed systematically using perturbative QCD and the operator product expansion. In a sample of high energy taus that decay into hadrons, the endpoint value of the hadronic energy distribution can also be computed rigorously from QCD, and can be used to measure the average helicity of the taus. Measurements of these spin-dependent observables could provide dramatic confirmation of the applicability of perturbative QCD to the inclusive hadronic decays of the tau. It is convenient to normalize the inclusive decay rate of the tau lepton into a neutrino plus hadrons to the electronic decay rate by defining the ratio Rτ = Γ(τ → ντ + hadrons) Γ(τ− → ντeν̄e) . (1) For a sample of taus with polarization P , the angle θ between the total momentum of the hadrons in the tau rest frame and the spin quantization axis has a distribution proportional to 1 + AτP cos θ, where Aτ is an asymmetry parameter. This angular distribution can be used to separate Rτ into “forward” and “backward” components RF and RB: dRτ d cos θ = RF 1 + P cos θ 2 + RB 1− P cos θ 2 . (2) The asymmetry parameter Aτ is then Aτ = RF − RB RF +RB . (3) A naive estimate of the asymmetry parameter can be obtained by considering the decay of the tau into hadrons at the quark level, where it proceeds through the processes 1 τ → ντdū and τ − → ντsū. The momentum of the dū and sū pairs can be identified with the total momentum of the hadrons. Ignoring the QCD interactions that bind the quarks into color singlet hadrons, the angular distribution of the total hadron momentum is dRτ d cos θ ≈ 3 2 ( |Vud| 2 + |Vus| 2 ) (