Leading isospin-breaking corrections to meson masses on the lattice

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 $(\widehat{m}_d - \widehat{m}_u)/\Lambda_{QCD}$ and $\alpha_{em}$, where $\widehat{m}_f$ is the renormalized quark mass and $\alpha_{em}$ the renormalized fine structure constant. We obtain results for the pion, kaon and $D$-meson mass splitting; for the Dashen's theorem violation parameters $\epsilon_\gamma(\overline{\mathrm{MS}}, 2~\mbox{GeV})$, $\epsilon_{\pi^0}$, $\epsilon_{K^0}(\overline{\mathrm{MS}}, 2~\mbox{GeV})$; 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.

[1]  N. Tantalo,et al.  Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions , 2017, 1704.06561.

[2]  P. Boyle,et al.  Electromagnetic Corrections to Meson Masses and the HVP , 2016, 1612.05962.

[3]  T. Lippert,et al.  Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED. , 2016, Physical review letters.

[4]  D. Pleiter,et al.  QED effects in the pseudoscalar meson sector , 2015, 1509.00799.

[5]  T. Lippert,et al.  Ab initio calculation of the neutron-proton mass difference , 2014, Science.

[6]  V. Lubicz,et al.  Up, down, strange and charm quark masses with Nf=2+1+1 twisted mass lattice QCD , 2014, 1403.4504.

[7]  S. Gottlieb,et al.  Review of lattice results concerning low-energy particle physics , 2016, The European Physical Journal C.

[8]  R. Petronzio,et al.  Leading isospin breaking effects on the lattice , 2013, 1303.4896.

[9]  T. Lippert,et al.  Systematic errors in partially-quenched QCD plus QED lattice simulations , 2012, 1201.2787.

[10]  R. Petronzio,et al.  Isospin breaking effects due to the up-down mass difference in lattice QCD , 2011, 1110.6294.

[11]  V. Cirigliano,et al.  A note on isospin violation in Pl2(gamma) decays , 2011, 1102.0563.

[12]  I. Montvay,et al.  Light hadrons from Nf=2+1+1 dynamical twisted mass fermions , 2011, 1101.0518.

[13]  T. Lippert,et al.  Electromagnetic corrections to light hadron masses , 2010, 1011.4189.

[14]  M. Antonelli,et al.  An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays , 2010, 1005.2323.

[15]  I. Montvay,et al.  Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks , 2010, 1004.5284.

[16]  M. Hayakawa,et al.  QED in Finite Volume and Finite Size Scaling Effect on Electromagnetic Properties of Hadrons , 2008, 0804.2044.

[17]  I. Scimemi,et al.  Electromagnetic corrections in hadronic processes , 2003, hep-ph/0305260.

[18]  Duncan,et al.  Electromagnetic splittings and light quark masses in lattice QCD. , 1996, Physical review letters.

[19]  J. Bijnens.  Violations of Dashen's theorem , 1993, hep-ph/9302217.

[20]  H. Leutwyler,et al.  Light Quarks at Low Temperatures , 1987 .

[21]  Heinrich Leutwyler,et al.  Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark , 1985 .

[22]  R. Dashen.  CHIRAL SU(3) x SU(3) AS A SYMMETRY OF THE STRONG INTERACTIONS. , 1969 .