Chiral Logarithms Tamed

TL;DR

This paper introduces a recursive method to efficiently compute and sum leading chiral logarithms in effective field theories, applicable beyond chiral perturbation theory to other non-renormalizable theories.

Contribution

It develops non-linear recursion relations for leading chiral logarithms, enabling rapid calculations and summation in various non-renormalizable effective field theories.

Findings

33-loop contribution computed in seconds

Method applicable to other non-renormalizable theories

Provides a powerful summation tool for LLs

Abstract

We derive non-linear recursion relations for the leading chiral logarithms (LLs). These relations not only provide a very efficient method of computation of LLs (e.g. the 33-loop contribution is calculated in a dozen of seconds on a PC) but also equip us with a powerful tool for the summation of the LLs. Our method is not limited to the chiral perturbation theory only, it is pertinent for any non-renormalizable effective field theory such as, for instance, the theory of critical phenomena, the low-energy quantum gravity, etc.