A General Treatment of Tau Semi-Leptonic Decays

Abstract

The most general Lorentz invariant spin-correlation functions for $τ^{-}\rightarrow ρ^{-}ν,a_1^{-}ν,K^{*-}ν, π^{-}ν,K^{-}ν$ are expressed in terms of eight semi-leptonic parameters. They are physically defined in terms of tau-decay partial-width-intensities for polarized-final-states. The parameters are also expressed in terms of a ``$(V-A)\ +\ $additional chiral coupling'' structure in the ${J^{Charged}}_{Lepton}$ current, so as to bound the scales $Λ$\ for ``new physics'' such as arising from leptonic CP violation, tau weak magnetism, weak electricity, and/or second-class currents. The two tests for leptonic CP violation in $τ\rightarrow ρν\ $ decay are generalized to $τ\rightarrow a_1ν\ $ decay and to two additional tests if there are $ν_R\ $ and $\bar ν_L\ $ couplings.