Polarized observables in $τ\to VV ν_τ$ decays

Abstract

We study polarization observables in $τ^- \to V_1^- V_2^0 ν_τ$ decays for $(V_1^-, V_2^0)=(ρ^-, ρ^0), (ρ^-, ω), (K^{*-}, ρ^0), (K^{*-}, ω), (ρ^-, \bar{K}^{*0})$ using the helicity formalism within the generalized hidden local symmetry framework. The predicted branching fractions are comparable with those from the effective chiral model, but smaller than those from the angular momentum algebra model. Our results for the longitudinal polarization fractions $f_L$ indicate that nonnegligible corrections to the endpoint limit ($f_L = 1/3$), a consequence of Lorentz symmetry, are present at the scale of tau mass. Future measurements of $f_L$ at Belle II for $τ^- \to V_1^- V_2^0 ν_τ$ decays will provide crucial information on polarization patterns observed in nonleptonic charm decays.