Leading isospin-breaking corrections to meson masses on the lattice

D. Giusti; V. Lubicz; G. Martinelli; F. Sanfilippo; S. Simula; N. Tantalo; C. Tarantino

doi:10.1051/epjconf/201817506002

paper

Leading isospin-breaking corrections to meson masses on the lattice

arXiv:1710.06633 · doi:10.1051/epjconf/201817506002

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 $(m_{d} - m_{u}) / Λ_{QC D}$ and $α_{e m}$ , where $m_{f}$ is the renormalized quark mass and $α_{e m}$ the renormalized fine structure constant. We obtain results for the pion, kaon and $D$ -meson mass splitting; for the Dashen's theorem violation parameters $ε_γ(\overline{\mathrm{MS}}, 2~\mbox{GeV})$, $ε_{π^{0}}$ , $ε_{K^0}(\overline{\mathrm{MS}}, 2~\mbox{GeV})$; for the light quark masses $(\widehat{m}_d - \widehat{m}_u)(\overline{\mathrm{MS}}, 2~\mbox{GeV})$, $(\widehat{m}_u / \widehat{m}_d)(\overline{\mathrm{MS}}, 2~\mbox{GeV})$; for the flavour symmetry breaking parameters $R(\overline{\mathrm{MS}}, 2~\mbox{GeV})$ and $Q(\overline{\mathrm{MS}}, 2~\mbox{GeV})$ and for the strong IB effects on the kaon decay constants.

8 pages, 2 figures, talk delivered at the XXXV International Symposium on Lattice Field Theory, Granada (Spain), 18-24 June 2017

Leading isospin-breaking corrections to meson masses on the lattice

Abstract

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