Tools for calculations in color space

TL;DR

This paper discusses tools and software packages for performing exact calculations in QCD color space, crucial for accurate predictions at the LHC across various computational methods.

Contribution

It introduces new computational tools, ColorMath and ColorFull, for efficient and exact color structure calculations in QCD, including a general method for constructing orthogonal multiplet bases.

Findings

ColorMath simplifies color calculations in Mathematica.

ColorFull enables demanding calculations and interfacing with event generators.

The tools improve the accuracy and efficiency of QCD color space computations.

Abstract

Both the higher energy and the initial state colored partons contribute to making exact calculations in QCD color space more important at the LHC than at its predecessors. This is applicable whether the method of assessing QCD is fixed order calculation, resummation, or parton showers. In this talk we discuss tools for tackling the problem of performing exact color summed calculations. We start with theoretical tools in the form of the (standard) trace bases and the orthogonal multiplet bases (for which a general method of construction was recently presented). Following this, we focus on two new packages for performing color structure calculations: one easy to use Mathematica package, ColorMath, and one C++ package, ColorFull, which is suitable for more demanding calculations, and for interfacing with event generators.