One-loop gauge invariant amplitudes with a space-like gluon

A new subtraction scheme at NLO exploiting the privilege of kT-factorization

“…It was argued in [29] that the cancellation should happen exactly the same way for the case with a space-like JHEP06(2024)167 initial-state as for the completely on-shell case. More precisely, the divergences in the one-loop amplitudes that do not fit in the universal formula (as given for example in [32]) where identified in [29], and confirmed in [28], and found to be universal themselves, so they can be treated within a renormalization prescription. In the following, we show that the divergences from the real radiation we found here indeed match the one-loop formula as in [32].…”

“…One can extract the necessary extra Feynman rules to construct the desired space-like amplitudes directly as is done in KaTie, or one can use a complete expression of an embedding onshell amplitude to extract the desired space-like amplitude. The latter method was applied in [27,28], to calculates space-like one-loop amplitudes for selected processes.…”

Hybrid kT-factorization at NLO

“…In [5] one-loop amplitudes were calculated for some processes by applying the auxiliary parton method to existing expressions for on-shell one-loop amplitudes. It was found that for all of the considered processes, the amplitudes could be decomposed into two parts, referred to as familiar and unfamiliar.…”