Leading isospin-breaking corrections to meson masses on the lattice

Davide Giusti,Guido Martinelli,Cecilia Tarantino,Silvano Simula,Vittorio Lubicz,Francesco Sanfilippo,Nazario Tantalo,M Della Morte,P Fritzsch,C Pena Ruano,E Gámiz Sánchez

doi:10.1051/epjconf/201817506002

Davide Giusti, Guido Martinelli + Show 9 more

Open Access

https://doi.org/10.1051/epjconf/201817506002

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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 Nf = 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 [see formula in PDF] and αem, where [see formula in PDF] is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen’s theorem violation parameters ϵγ(MM, 2 GeV), ϵπ0 ϵK0(MS, 2 GeV) for the light quark masses [see formula in PDF] 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.

Highlights

In the last few years the determination of several observables in flavour physics by lattice QCD reached such a precision that both electromagnetic (e.m.) effects and strong isospin breaking corrections, generated by the light-quark mass difference, cannot be neglected any more
Typical examples are the calculations of the leptonic decay constants fK and fπ relevant for K 2 and π 2 decays, and the determination of the vector form factor at zero fourmomentum transfer f+(0) appearing in semileptonic K 3 decays
These quantities are used to extract the CKM entries |Vus| and |Vus|/|Vud| from the experimental decay rates, and they have been computed on the lattice with a precision at the few per mille level [1]

Summary

Introduction

In the last few years the determination of several observables in flavour physics by lattice QCD reached such a precision that both electromagnetic (e.m.) effects and strong isospin breaking corrections, generated by the light-quark mass difference (md −mu), cannot be neglected any more (see e.g. Ref. [1] and references therein). Typical examples are the calculations of the leptonic decay constants fK and fπ relevant for K 2 and π 2 decays, and the determination of the vector form factor at zero fourmomentum transfer f+(0) appearing in semileptonic K 3 decays These quantities are used to extract the CKM entries |Vus| and |Vus|/|Vud| from the experimental decay rates, and they have been computed on the lattice with a precision at the few per mille level [1]. [6, 7], consists in an expansion of the lattice path-integral in powers of the two small parameters (md − mu) and αem, namely αem ≈ (md − mu)/ΛQCD ≈ 1% Since it suffices to work at leading order in the perturbative expansion, the attractive feature of the RM123 method is that the small values of the two expansion parameters are factorized out, so that one can get relatively large numerical signals for the slopes of the corrections with respect to the two expansion parameters.

Simulation details

Evaluation of the IB corrections

Results