Leading isospin breaking effects on the lattice

TL;DR

This paper introduces a lattice method to evaluate leading isospin breaking effects from quark mass differences and QED, providing precise results for pion mass splitting, quark masses, and symmetry breaking parameters.

Contribution

The paper proposes a general lattice-based expansion method to compute isospin breaking effects due to quark mass differences and QED interactions, applicable to various hadronic observables.

Findings

Pion mass splitting: 1.44(13)(16) x 10^3 MeV^2

Quark mass difference: 2.39(8)(17) MeV

Quark mass ratio: 0.50(2)(3)

Abstract

We present a method to evaluate on the lattice the leading isospin breaking effects due to both the small mass difference between the up and down quarks and the QED interaction. Our proposal is applicable in principle to any QCD+QED gauge invariant hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameters (m_d - m_u)/Lambda_{QCD} and alpha_{em}, where m_f is the renormalized quark mass and alpha_{em} the renormalized fine structure constant. In this paper we discuss in detail the general strategy of the method and the conventional, although arbitrary, separation of QCD from QED isospin breaking corrections. We obtain results for the pion mass splitting, M_{pi+}^2-M_{pi0}^2= 1.44(13)(16) x 10^3 MeV^2, for the Dashen's theorem breaking parameter epsilon_{gamma}= 0.79(18)(18), for the light quark masses, [m_d - m_u](MSbar,2 GeV)= 2.39(8)(17) MeV, [m_u / m_d](MSbar,2 GeV)= 0.50(2)(3) and for the flavour symmetry breaking parameters R and Q. We also update our previous results for the QCD isospin breaking corrections to the Kl2 decay rate and for the QCD contribution to the neutron-proton mass splitting.