Virtual photons in the pion form factors and the energy-momentum tensor

TL;DR

This paper calculates electromagnetic corrections to pion form factors and the energy-momentum tensor using chiral perturbation theory, revealing small but significant effects on pion radii and form factors.

Contribution

It provides a next-to-leading order analysis of virtual photon effects on pion form factors and the energy-momentum tensor within two-flavor chiral perturbation theory.

Findings

Electromagnetic corrections are consistent with expected sizes for vector form factors.

Photon corrections reduce the vector radius by about 1%.

Isospin-breaking effects decrease the neutral pion scalar radius by 2%.

Abstract

We evaluate the vector and scalar form factor of the pion in the presence of virtual photons at next-to-leading order in two-flavor chiral perturbation theory. We also consider the scalar and tensor pion form factors of the energy-momentum tensor. We find that the intrinsic electromagnetic corrections are of the expected size for the vector form factor and very small for the charged pion scalar form factor. Detector resolution independent photon corrections reduce the vector radius by about one percent. The scalar radius of the neutral pion is reduced by two percent by isospin-breaking contributions. We perform infrared regularization by considering electron-positron annihilation into pions and the decay of a light Higgs boson into a pion pair. We discuss the detector resolution dependent contributions to the various form factors and pion radii.