Renormalization group coefficients and the S-matrix

TL;DR

This paper introduces a novel on-shell unitarity method to compute renormalization group coefficients like beta functions and anomalous dimensions using form factors and phase-space integrals, linking the dilatation operator to the S-matrix phase.

Contribution

It presents a new technique connecting S-matrix phases to anomalous dimensions through form factors, applicable to various quantum field theories at one-loop and higher levels.

Findings

Dilatation operator equals minus the S-matrix phase over pi.

Method successfully applied to Yang-Mills, QCD, and Yukawa theories.

Provides a unified framework for calculating RG coefficients using on-shell methods.

Abstract

We show how to use on-shell unitarity methods to calculate renormalization group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.