Numerical integration of subtraction terms

Understand

Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections.

• These subtraction terms have to be added back.
• In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalisation constants and -- in the case of initial-state partons -- the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically.
• This is useful for an extension towards NNLO.