Non-factorisable electroweak virtual corrections to single-resonant processes

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Abstract
A bstract: We consider electroweak (EW) virtual corrections to 2 → 2 fermion scattering processes mediated by a vector boson V ( V = W ± , Z ) in the pole approximation. As is well known, the computation can be organised into factorisable and non-factorisable contributions. The factorisable corrections can be computed by evaluating the (polarised) EW form factor of the vector boson at the relevant perturbative order. The non-factorisable corrections are instead driven by soft-photon exchanges between the initial- and final-state fermions and/or the resonance. We perform an explicit two-loop computation to show that, once the heavy degrees of freedom are properly decoupled, such non-factorisable corrections can be expressed as an iteration of the one-loop result, plus a new contribution due to (light) fermion loops. The final two-loop result, which can be expected on general grounds from soft-photon factorisation, is shown to hold exactly in dimensional regularisation and is peculiar to the exchange of a single resonance. We discuss its extension to all perturbative orders.
Funding Information
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (200020$_$219367)
  • Deutsche Forschungsgemeinschaft (EXC-2094-390783311)
  • European Commission (101044599)

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