Abstract
We use the antenna subtraction method to isolate the mixed real-virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In a previous paper, we derived the subtraction term that rendered the double real radiation tree-level process finite in the single and double unresolved regions of phase space. Here, we show how to construct the real-virtual subtraction term using antenna functions with both initial- and final-state partons which removes the explicit infrared poles present in the one-loop amplitude, as well as the implicit singularities that occur in the soft and collinear limits. As an explicit example, we write down the subtraction term that describes the single unresolved contributions from the five-gluon one-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space prior to integration, leaving a finite remainder that can be safely evaluated numerically in four-dimensions. We show numerically that the subtraction term correctly approximates the matrix elements in the various single unresolved configurations.
Highlights
In hadronic collisions, the most basic form of the strong interaction at short distances is the scattering of a coloured parton off another coloured parton
Summing over the different final-final, initial-final and initial-initial configurations, we find that the explicit poles in dσNRVNLO are removed by 1 dσNS,Na LO to yield an integrand free from explicit infrared poles over the whole region of integration
As stated in the introduction, the aim of this paper is to construct the subtraction term for the real-virtual contribution such that the (m + 1)-parton contribution to the m-jet rate is free from explicit ǫ-poles over the whole of phase space and the subtracted integrand is well behaved in the single unresolved regions of phase space
Summary
The most basic form of the strong interaction at short distances is the scattering of a coloured parton off another coloured parton. 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. DσNS NLO denotes the subtraction term for the (m+2)-parton final state which behaves like the double real radiation contribution dσNRRNLO in all singular limits. Subtraction term was shown to reproduce the singular behaviour present in dσNRRNLO in all of the single and double unresolved limits It is the purpose of this paper to construct the appropriate subtraction term dσNT NLO to render the leading colour five-gluon contribution dσNRVNLO explicitly finite and numerically well behaved in all single unresolved limits. Appendix C contains a modified form for the wide angle soft subtraction terms present in dσNS NLO, while formulae relating to the mass factorisation contribution are given in appendix D
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