Chiral perturbation theory for three-flavour lattice QCD with isospin splitting

TL;DR

This paper extends chiral perturbation theory to include isospin splitting effects in three-flavour lattice QCD, providing next-to-leading order mass expansions for pseudoscalar mesons considering lattice spacing and quark mass differences.

Contribution

It derives next-to-leading order mass formulas for pseudoscalar mesons in twisted mass lattice QCD with isospin splitting, incorporating lattice spacing and quark mass difference effects.

Findings

Derived mass expansions up to order $m_q^2$, $\Delta m^2$, and $a^2$.

Includes effects of up-down quark mass difference.

Provides theoretical tools for analyzing lattice QCD simulations with isospin splitting.

Abstract

An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In Wilson chiral perturbation theory the effects of the finite lattice spacing $a$ are taken into account. In recent years the effects of isospin splitting on the masses of hadrons have been investigated in Monte Carlo simulations. Correspondingly, in this article we derive the expansions of the masses of the pseudoscalar mesons in chiral perturbation theory at next-to-leading order for twisted mass lattice QCD with three light quark flavours, taking the mass difference between the up and down quarks into account. The results include terms up to orders $m_q^2$ in the quark masses, $\Delta m^2$ in the mass splitting between up- and down quarks, and $a^2$ in the lattice spacing, respectively.