A Gauge-Independent Approach to Resonant Transition Amplitudes

Abstract

We present a new gauge-independent approach to resonant transition amplitudes with nonconserved external currents, based on the pinch technique method. In the context of $2\to 2$ and $2\to 3$ scattering processes, we show explicitly that the analytic results derived respect $U(1)_{em}$ gauge symmetry and do not depend on the choice of the $SU(2)_L$ gauge fixing. Our analytic approach treats, on equal footing, fermionic as well as bosonic contributions to the resummed gauge boson propagators, does not contain any residual space-like threshold terms, shows the correct high-energy unitarity behaviour, admits renormalization, and satisfies a number of other required properties, including the optical theorem. Even though our analysis has mainly focused on the Standard Model gauge bosons, our method can easily be extended to the top quark, and be directly applied to the study of unstable particles present in renormalizable models of new physics.