Geometric approach to asymptotic expansion of Feynman integrals

110

162

Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.

Section: Jhep12(2016)121mentioning

confidence: 99%

Non-abelian factorisation for next-to-leading-power threshold logarithms

Bonocore

Laenen

Magnea

et al. 2016

110

162

“…To implement the asymptotic expansion for χ → 0 we use the program asy.m [43]. It provides scaling rules for the alpha parameters for the various regions which have to be considered.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Double-Higgs boson production in the high-energy limit: planar master integrals

Davies

Mishima

Steinhauser

et al. 2018

“…(3.14), reproduce the same expansions as one can obtain from an expansion in Feynman parameter space by the methods of ref. [45,46]. Combined with the expansion of the phase-space measure discussed at the beginning of this section, we have therefore obtained a machinery to compute the threshold expansion of the coefficient functions C (1) ij→klH (z, ǫ).…”

Section: Jhep08(2015)051mentioning

confidence: 99%

“…Note that the eikonal approximation of the loop integrals depends on the specific orientation with which it enters the soft phase-space integrals, or equivalently, which invariants become soft. We have explicitly evaluated all loop integrals in the eikonal approximation by determining the scaling of the Feynman parameters in the limit using the package asy.m [45,46]. We find that in all cases, except for one pentagon integral, the remaining parametric integrations can be perfomed in closed form to all orders in the dimensional regulator ǫ.…”

Section: The Soft Regionmentioning

confidence: 99%

Soft expansion of double-real-virtual corrections to Higgs production at N3LO

Anastasiou

Duhr

Dulat

et al. 2015

102

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N 3 LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N 3 LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.