Electromagnetic self-energies of the neutral pions: Contributions from vector resonances

TL;DR

This paper calculates the electromagnetic self-energy of neutral pions using vector meson dominance, highlighting the contribution of vector resonances to pion mass differences within a QCD context.

Contribution

It provides a finite estimate of the electromagnetic self-energy of neutral pions from vector resonances, incorporating chiral anomaly effects and comparing with other mass contributions.

Findings

Electromagnetic self-energy from vector resonances is finite and smaller than other contributions.

The calculated self-energy can be compared with short-distance QCD effects.

The approach confirms the role of vector mesons in pion mass differences.

Abstract

By employing vector meson dominance to establish the electromagnetic interactions of hadrons, the electromagnetic self-energy of the neutral pions, which receives the contributions from the vector resonances due to chiral anomaly, is evaluated. This part of the electromagentic mass, which can contribute to the mass difference of $\pi^\pm-\pi^0$, is finite and as expected, is smaller than the contributions due to isospin symmetry breaking and electromagnetic chiral logs corrections, however, could be compared with the contribution from the short distance QCD.