Abstract

Abstract The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required in unintegrated and integrated forms. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the full set of initial-initial double real radiation antenna functions in integrated form.

Highlights

  • To determine the contribution to NNLO jet observables from these configurations, one has to find subtraction terms which coincide with the full matrix element in the unresolved limits and are still sufficiently simple to be integrated analytically in order to cancel their infrared pole structure with the virtual contributions

  • Other approaches to perform NNLO calculations of exclusive observables with initial state partons are the use of sector decomposition and a subtraction method based on the transverse momentum structure of the final state

  • With the results presented in this paper, combined with the finalfinal [46], initial-final [82] and virtual one-loop initial-initial antennae [83], all antenna functions required for the calculation of jet cross sections at hadron colliders are available in unintegrated and integrated form

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Summary

Initial-initial antenna subtraction at NNLO

The partonic double real contribution to an NNLO m-jet cross section reads dσNRRN LO. The real radiation contribution (2.1) contains infrared divergencies, which arise when one or two of the final state partons become unresolved. A subtraction term dσNS NLO is defined on the same phase space as dσNRRNLO, and it approaches its integrand in all unresolved limits. The double real radiation contribution dσNRRNLO can become singular if either one or two final state partons are unresolved (soft or collinear). When constructing the corresponding subtraction term dσNS NLO in the antenna subtraction method, we must distinguish the following configurations according to the colour connection of the unresolved partons:. The corresponding subtraction term for both radiators in the initial state reads: dσNS,Nb,(LiiO). Its single unresolved limits are subtracted by products of three-particle antenna functions, ensuring that dσNS,Nb,(LiiO) is only active in the double unresolved region.

Antenna functions for double real radiation
Phase space factorisation and mappings
Integration over the double real radiation phase space
Results
Quark-antiquark antenna functions
Quark-gluon antenna functions
Conclusions
A Master integrals
Dk2Dj12
Hard region
Soft region

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