Isospin breaking effects due to the up-down mass difference in Lattice QCD

TL;DR

This paper introduces a novel lattice QCD method to precisely evaluate isospin breaking effects caused by the up-down quark mass difference, applicable to various hadronic observables.

Contribution

The authors develop a new expansion-based approach for high-precision calculation of isospin breaking effects in lattice QCD, applicable to multiple physical quantities.

Findings

Computed leading isospin breaking effects on kaon masses and decay constants.

Quantified neutron-proton mass splitting due to up-down quark mass difference.

Validated the method's applicability to semileptonic decay form factors.

Abstract

We present a new method to evaluate with high precision isospin breaking effects due to the small mass difference between the up and down quarks using lattice QCD. Our proposal is applicable in principle to any hadronic observable which can be computed on the lattice. It is based on the expansion of the path-integral in powers of the small parameter md-mu. In this paper, we apply this method to compute the leading isospin breaking effects for several physical quantities of interest: the kaon meson masses, the kaon decay constant, the form factors of semileptonic Kl3 decays and the neutron-proton mass splitting.