QCD Amplitudes: new perspectives on Feynman integral calculus

TL;DR

This paper explores the algebraic structures and differential equations governing QCD scattering amplitudes, emphasizing unitarity, master integrals, and advanced solution techniques like Magnus series.

Contribution

It introduces new perspectives on the decomposition of amplitudes and the differential equations they satisfy, highlighting the role of unitarity and integrand reduction methods.

Findings

Unveiled algebraic patterns in QCD amplitudes

Connected unitarity to master integral decomposition

Applied Magnus exponential series to solve differential equations

Abstract

I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter obey. In particular, I discuss the key role played by unitarity for the decomposition in terms of master integrals, by means of generalized cuts and integrand reduction, as well as for solving the corresponding differential equations, by means of Magnus exponential series.