Infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order

Abstract

We present universal factorization formulas describing the behavior of one-loop QCD amplitudes as external momenta become either soft or collinear. Our results are valid to all orders in the dimensional regularization parameter, ǫ. Terms through O(ǫ 2 ) can contribute in infrared divergent phase space integrals associated with next-to-next-to-leading order jet cross-sections.

A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission

“…In our work we use the formulae of ref. [20] for collinear parton splitting and those in ref. [21] for soft gluon emission.…”

“…[20]. In the case of gluon splitting those functions are symmetric under the exchange of z i and z r .…”

“…and taking the limit λ → 0, when the one-loop squared matrix element of an (m+1)-parton process has the following asymptotic form [20]:…”

“…To make this symmetry manifest, we have re-cast the original expression of ref. [20] for the gluon splitting into a qq pair into an equivalent form which exhibits the z i ↔ z r symmetry,…”

Real-virtual corrections for gluon scattering at NNLO

“…On the other hand, the requirement of building m-jets from (m + 1)-partons allows one of the final state partons to become unresolved, leading to implicit local infrared singularities which become explicit only after integration over the unresolved patch of the final state (m + 1)-parton phase space. The single unresolved infrared singularity structure of one-and two-loop amplitudes has been studied in [78][79][80][81][82][83][84][85][86][87][88][89][90].…”