Electroweak radiative corrections to the three channels of the process f_1 bar-f_1 ZA --> 0

TL;DR

This paper calculates electroweak radiative corrections at the one-loop level for three related fermion-antifermion and gauge boson processes, providing analytical results and validation checks within the SANC computational system.

Contribution

It presents the first complete analytical calculation of electroweak radiative corrections for three specific channels involving fermions, Z bosons, and photons, implemented in the SANC system.

Findings

Analytical expressions for covariant and helicity amplitudes provided.

Validation through gauge invariance and Ward identity checks.

Numerical results agree with independent calculations.

Abstract

We have calculated the electroweak radiative corrections at the O(alpha) level to the three channels of the process f_1 bar-f_1 Z A --> 0 and implemented them into the SANC system. Here A stands for the photon and f_1 for a first generation fermion whose mass is neglected everywhere except in arguments of logarithmic functions. The symbol --> 0 means that 4-momenta of all the external particles flow inwards. We present the complete analytical results for the covariant and helicity amplitudes for three cross channels: f_1 + bar-f_1 --> Z + gamma, Z --> f_1 + bar-f_1 + gamma and f_1 + gamma --> f_1 + Z. The one-loop scalar form factors of these channels are simply related by an appropriate permutation of their arguments s,t,u. To check the correctness of our results we first of all observe the independence of the scalar form factors on the gauge parameters and the validity of the Ward identity, i.e. external photon transversality, and, secondly, compare our numerical results with the other independent calculations available to us.