Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

TL;DR

This paper develops a general recursive method to compute leading infrared logarithms in massless effective field theories using fundamental principles like unitarity, analyticity, and crossing symmetry, avoiding complex loop calculations.

Contribution

It introduces non-linear recursion equations for infrared logarithms derived solely from fundamental amplitude properties, enabling high-order calculations efficiently.

Findings

Recursion equations derived for infrared logarithms

Method applicable to multiple dimensions and theories

Validated on various effective field theory examples

Abstract

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.