On the factorization of chiral logarithms in the pion form factors

TL;DR

This paper investigates the factorization of chiral logarithms in pion form factors, confirming its validity at two loops, extending to all orders for some diagrams, and identifying its breakdown at three loops.

Contribution

It explains the all-order factorization property of chiral logarithms in pion form factors and identifies the loop order where it fails.

Findings

Factorization holds at two loops in pion form factors.

All-order factorization is valid for a subclass of diagrams.

Factorization breaks down at three loops.

Abstract

The recently proposed hard-pion chiral perturbation theory predicts that the leading chiral logarithms factorize with respect to the energy dependence in the chiral limit. This claim has been successfully tested in the pion form factors up to two loops in chiral perturbation theory. In the present paper we explain this factorization property at two loops and even show that it is valid to all orders for a subclass of diagrams. We also demonstrate that factorization is violated starting at three loops.