Eur. Phys. J. C (2008) 54: 187-197
https://doi.org/10.1140/epjc/s10052-007-0512-3

Regular Article - Theoretical Physics

Electroweak radiative corrections to the three channels of the process f₁f̄₁ZA→0

¹ Dzhelepov Laboratory for Nuclear Problems, JINR, 141980, Dubna, Russia
² Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Russia
³ IFJ, PAN, 31-342, Kraków, Poland
⁴ PNPI, RAN, 188300, Gatchina, Russia

^b bondarenko@jinr.ru

Received: 19 October 2007
Revised: 26 November 2007
Published online: 12 January 2008

Abstract

We have calculated the electroweak radiative corrections at the 𝒪(α) level to the three channels of the process f₁f̄₁ZA→0 and implemented them into the SANC system. Here A stands for the photon and f₁ for a first generation fermion whose mass is neglected everywhere except in the 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: f₁f̄₁→Zγ, Z→f₁f̄₁γ and f₁γ→f₁Z. 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.