Leading isospin-breaking corrections to meson masses on the lattice

¹ Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
³ Dipartimento di Fisica and INFN, Università degli Studi di Roma "La Sapienza", Piazzale Aldo Moro 5, I-00185 Rome, Italy
⁴ Dipartimento di Fisica and INFN, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Rome, Italy

^* Speaker, e-mail: davide.giusti@uniroma3.it

Published online: 26 March 2018

Abstract

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with N_f = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters $\left({\stackrel{⌢}{m}}_d-{\stackrel{⌢}{m}}_u\right)/{\Lambda }_{QCD}$ and α_em, where ${\stackrel{⌢}{m}}_f$ is the renormalized quark mass and α_em the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen’s theorem violation parameters ϵ_γ(MM, 2 GeV), ϵ_π⁰ ϵ_K⁰(MS, 2 GeV) for the light quark masses $\left({\stackrel{⌢}{m}}_d-{\stackrel{⌢}{m}}_u\right)\left(\overline{\text{MS}},2\text{GeV}\right),\left({\stackrel{⌢}{m}}_u/{\stackrel{⌢}{m}}_d\right)\left(\overline{\text{MS}},2\text{GeV}\right);$ for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.