Real-virtual contributions to the inclusive Higgs cross-section at N3LO

Charalampos Anastasiou,Franz Herzog,Falko Dulat,Claude Duhr,Bernhard Mistlberger

doi:10.1007/jhep12(2013)088

Charalampos Anastasiou, Franz Herzog + Show 3 more

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https://doi.org/10.1007/jhep12(2013)088

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Abstract

Abstract We compute the contributions to the N3LO inclusive Higgs boson cross-section from the square of one-loop amplitudes with a Higgs boson and three QCD partons as external states. Our result is a Taylor expansion in the dimensional regulator ϵ, where the coefficients of the expansion are analytic functions of the ratio of the Higgs boson mass and the partonic center of mass energy and they are valid for arbitrary values of this ratio. We also perform a threshold expansion around the limit of soft-parton radiation in the final state. The expressions for the coefficients of the threshold expansion are valid for arbitrary values of the dimension. As a by-product of the threshold expansion calculation, we have developed a soft expansion method at the integrand level by identifying the relevant soft and collinear regions for the loop-momentum.

Highlights

In ref. [9] as a threshold expansion around the limit of soft-parton emissions
We focus on a different contribution to the N3LO cross-section, the integration over phase-space of the squared one-loop amplitudes for partonic processes for Higgs production in association with a quark or gluon in the final-state
In method (Ia), we reduce the one-loop amplitudes to bubble and box master integrals and find appropriate representations of the box master integrals which allow for a trivial integration over phase-space order by order in the threshold expansion

Summary

Introduction

In ref. [9] as a threshold expansion around the limit of soft-parton emissions. An important ingredient for the threshold expansion of the Higgs boson cross-section with both real and virtual radiation, the two-loop soft current, was presented in refs. [10, 11]. We focus on a different contribution to the N3LO cross-section, the integration over phase-space of the squared one-loop amplitudes for partonic processes for Higgs production in association with a quark or gluon in the final-state. We denote these squared real-virtual contributions as (RV). Method (III) identifies counterterms for combined loop and phase-space integrals and proceeds with an expansion in ǫ followed by a direct integration over phase-space variables This is made possible by embedding the classical polylogarithms that arise in the ǫ expansion into a larger space of multiple polylogarithms where the integration over phase space is trivial.

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