Gauge invariance and finite width effects in radiative two-pion tau lepton decay

TL;DR

This paper investigates the rho meson's magnetic dipole moment through tau decay, ensuring gauge invariance with finite width effects, and finds the decay distributions are sensitive to the rho's magnetic properties.

Contribution

It introduces a gauge-invariant method to incorporate finite width effects of the rho meson in tau decay calculations, highlighting the universality of certain one-loop corrections.

Findings

Photon distributions are sensitive to the rho magnetic dipole moment.

Finite width effects can be incorporated without breaking gauge invariance.

Absorptive parts of loop corrections are universal for spin-one particles.

Abstract

The contribution of the rho^{\pm} vector meson to the tau -> pi pi nu gamma decay is considered as a potential source for the determination of the magnetic dipole moment of this light vector meson. In order to keep gauge-invariance of the whole decay amplitude, a procedure similar to the fermion loop-scheme for charged gauge bosons is implemented to incorporate the finite width effects of the rho^{\pm} vector meson. The absorptive pieces of the one-loop corrections to the propagators and electromagnetic vertices of the rho^{\pm} meson and W^{\pm} gauge boson have identical forms in the limit of massless particles in the loops, suggesting this to be a universal feature of spin-one unstable particles. Model-dependent contributions to the tau -> pi pi nu gamma decay are suppressed by fixing the two-pion invariant mass distribution at the rho meson mass value. The resulting photon energy and angular distribution is relatively sensitive to the effects of the rho magnetic dipole moment.