Local analytic sector subtraction at NNLO

Abstract

We present a new method for the local subtraction of infrared divergences at next-tonext-to-leading order (NNLO) in QCD, for generic infrared-safe observables. Our method attempts to conjugate the minimal local counterterm structure arising from a sector partition of the radiation phase space with the simplifications following from analytic integration of the counterterms. In this first implementation, the method applies to final-state massless particles. We show how our method compactly organises infrared subtraction at NLO, we deduce in detail the general structure of the subtraction terms at NNLO, and we provide a proof of principle with a complete application to a simple process at NNLO.

Numerical Loop-Tree Duality: contour deformation and subtraction

“…Traditionally, the computation of these two components is performed using very different approaches and the deep connection relating their degenerate infrared degrees of freedom is only realised through dimensional regularisation [3][4][5] at the very end of the computation. Indeed, real-emission contributions are typically computed numerically through the introduction of subtraction counterterms [6][7][8][9][10][11][12][13][14][15][16][17] or some form of phase-space slicing [18][19][20][21][22][23][24][25], whereas the evaluation of their virtual counterparts is mostly carried out purely analytically, thus realising the cancellation of infrared singularities at the integrated level. A notable exception is the computation of inclusive Higgs production at N 3 LO accuracy [26], which was performed through reverse-unitarity [27,28].…”

Factorisation and subtraction beyond NLO

“…We now provide a brief description of a subtraction procedure at NLO and NNLO, for the case of massless coloured particles in the final state, identifying the local counterterms required in this case. Our goal here is to present the general structure of the procedure, which is sufficient for the purposes of the present paper: a detailed construction of a complete subtraction algorithm for this case is presented in [73].…”

“…The paper is organised as follows: in Section 2, we briefly review the infrared factorisation of multi-parton scattering amplitudes for massless gauge theories; then, in Section 3, we present a basic outline of the subtraction problem at NLO and NNLO: a companion paper [73] is devoted to a detailed construction of a full subtraction algorithm for final-state singularities; in Sections 4 and 5, we present our definitions for soft and collinear local counterterms, valid to all to all orders in perturbation theory; in Section 6, we briefly illustrate the definitions by showing how they reconstruct the well-understood structure of final-state infrared subtraction at NLO; in Section 7 we apply our general results to the problem of NNLO subtraction, and we provide precise expressions for all the local counterterms required for hadronic massless final states; finally, we discuss future developments in Section 8.…”

A subtraction scheme for massive QED

“…Recent years have seen a huge effort towards the development of universal schemes for nextto-next-to-leading order (NNLO) calculations (see e.g. [5][6][7][8][9][10][11][12]). Typically, these schemes were designed with QCD calculations in mind.…”