Abstract
The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiatior partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction terms, classify all relevant antenna functions and describe their integration over the relevant antenna phase space. For the initial-initial antenna functions with two quark flavours, we derive the phase space master integrals and obtain the integrated antennae.
Highlights
Beyond the leading order, each partonic channel contains both ultraviolet and infrared divergences
We focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at nextto-next-to-leading order (NNLO)
For the task of next-to-leading order (NLO) calculations, the infrared divergences present in real radiation contributions can be systematically extracted by process-independent procedures, called subtraction methods
Summary
In the antenna formalism, in any of the three configurations (final-final, initial-final or initial-initial) the subtraction terms are constructed from products of antenna functions with reduced matrix elements (with fewer final state partons than the original matrix element). The initial-final tree-level three- and four-parton antennae denoted by Xi0,jk and Xi0,jkl are in principle obtained by crossing one-parton to the initial state starting from the corresponding final-final antennae This crossing might be ambiguous as was first noticed in [61] for the quark-gluon type antenna. The initial-initial tree-level three- and four-parton antennae denoted by Xi0k,l and Xi0l,jk are obtained by crossing two partons to the initial state, starting from the final-final antennae. This crossing procedure, unlike in the initial-final case, is free of ambiguity as the pair of hard partons the initial-initial antenna collapses to is always uniquely defined.
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