The Mathematica package TopoID and its application to the Higgs boson production cross section

Jens Hoff

doi:10.1088/1742-6596/762/1/012061

Abstract

We present the Mathematica package TopoID which aims at the automation of several steps in multiloop calculations. The algorithm which lies at the very core of the package is described and illustrated with an example. The main features of TopoID are stated and some of them are briefly demonstrated for NLO or NNLO Higgs boson production.

Highlights

With the LHC running in the coming years at 14 TeV, the experimental precision for observables will further improve
Some quantities under consideration presently are for example the Higgs boson production cross section at N3LO [1, 2], the four-loop MS-OS relation [3, 4], the four-loop cusp anomalous dimension [5] or the five-loop β-function [6]
The integrals within each topology are subject to integrationby-parts identities (IBPs) [12] which allow for a systematic reduction to “master integrals”

Summary

Introduction

With the LHC running in the coming years at 14 TeV, the experimental precision for observables will further improve. Some quantities under consideration presently are for example the Higgs boson production cross section at N3LO [1, 2], the four-loop MS-OS relation [3, 4], the four-loop cusp anomalous dimension [5] or the five-loop β-function [6]. All these calculations are based on the evaluation of Feynman diagrams which usually suffers from a factorial growth of complexity with higher orders. The complexity involved in algebraic operations on the coefficients of integrals in reduction relations or in the function classes for master integrals, is a different and still open subject

Example

Features of TopoID

Conclusion