Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

Abstract

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.

On higher-order flavour-singlet splitting and coefficient functions at large x

“…The coefficient functions C φ,i have been determined recently in Refs. [23] and [24] to the second and third order in α s , respectively.…”

Real-virtual corrections for gluon scattering at NNLO

“…This can be accomplished using the techniques described in [91] and analytic expressions for all of the integrated three-parton one-loop antennae are available in Refs. [21,72,74]. It is the purpose of this subsection to present a new term denoted by dσ V S,b N N LO which removes the explicit ǫ-poles present in dσ V S,a N N LO .…”

“…These contain explicit poles from the loop integration. The integrated forms for the final-final, initial-final and initial-initial cases are available in [21], [72] and [74] respectively.…”

“…Some care needs to be taken in the continuation, since the final-final antenna function is renormalised at µ 2 = q 2 = s 123 , while the initial-final antenna function is renormalised at µ 2 = −q 2 = −s 123 [72]. With this in mind, and defining again the y ij = s ij /s 123 , Eq.…”

“…The formalism has been fully worked out for initial state hadrons at NLO [71] and further developed at NNLO [72][73][74]. Within this method, the subtraction terms are constructed from so-called antenna functions which describe all unresolved partonic radiation (soft and collinear) between a hard pair of radiator partons.…”