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

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.