Pion mass difference from vacuum polarization

TL;DR

This paper computes the electromagnetic contribution to the pion mass difference using lattice QCD with overlap fermions, achieving a precise determination of $24(100) \,\mathrm{MeV}^2$ and extracting related low-energy constants.

Contribution

It provides a first-principles lattice QCD calculation of the pion mass difference in the chiral limit using overlap fermions, ensuring systematic error control.

Findings

Electromagnetic pion mass difference: 1024(100) MeV^2

Determined pion decay constant $f_$ and low-energy constant $L_{10}^r$

Validated the use of overlap fermions for systematic error control

Abstract

We calculate the electromagnetic contribution to the pion mass difference, $\Delta m^2_\pi=m^2_{\pi^+}-m^2_{\pi^0}$, in the chiral limit through the $VV-AA$ type vacuum polarization using Das-Guralnik-Mathur-Low-Young (DGMLY) sum rule. The calculation is made with two-flavors of dynamical overlap fermions on a $16^3\times 32$ lattice at $a\sim$0.12 fm. The exact chiral symmetry of the overlap fermion is essential to control the systematic error in the difference $VV-AA$. We obtain $\Delta m_\pi^2 = 1024(100) {\rm MeV^2}$ combining the lattice data with the perturbative contribution in the high momentum region evaluated by the operator product expansion. By analyzing the momentum dependence of the vacuum polarization, we also obtain pion decay constant $f_\pi$ and the low-energy constants $L_{10}^r$ in the chiral limit.