Near-threshold Isospin Violation in the Pion Form Factor from Chiral Perturbation Theory

TL;DR

This paper investigates isospin violation in the pion form factor near threshold using Chiral Perturbation Theory, finding it to be very small, around 10^-4, at threshold compared to larger effects in the resonance region.

Contribution

It provides a next-to-leading order calculation of isospin violation in the pion form factor near threshold within Chiral Perturbation Theory, highlighting its minimal size.

Findings

Isospin violation near threshold is of order 10^-4.

Isospin violation is much smaller near threshold than in the resonance region.

Next-to-leading order contributions are essential for capturing the first nonvanishing isospin violation.

Abstract

We examine the isospin violation in the timelike pion form factor near threshold at next-to-leading order in the chiral expansion using the techniques of Chiral Perturbation Theory. This next-to-leading order contribution contains the first nonvanishing isospin violation. This isospin violation is found to be very small near threshold. In particular, the isospin violation at threshold is found to be of order 10^-4, which should be compared with the few percent level seen in the vector meson resonance region.