Leading isospin breaking effects on the lattice

By G. Divitiis, R. Frezzotti, V. Lubicz, G. Martinelli, R. Petronzio, G. Rossi, F. Sanfilippo, S. Simula, N. Tantalo. 2013

146 citations recorded by the source corpus.

We present a method to evaluate on the lattice the leading isospin breaking effects due to both the small mass difference between the up and down quarks and the QED interaction. Our proposal is applicable in principle to any QCD+QED gauge invariant hadronic observable that can be computed on the lattice. It is based on the expansion of the path integral in powers of the small parameters (md-mu)/ΛQCD and αem, where mf is the renormalized quark mass and αem the renormalized fine structure constant. In this paper we discuss in detail the general strategy of the method and the conventional, although arbitrary, separation of QCD from QED isospin breaking corrections. We obtain results for the pion mass splitting, Mπ+2-Mπ02=1.44(13)(16)×103 MeV2, for the Dashen’s theorem breaking parameter eγ=0.79(18)(18), for the light quark masses, [md-mu](MS ,2 GeV)=2.39(8)(17) MeV, [mu/md](MS ,2 GeV)=0.50(2)(3), and for the flavor symmetry breaking parameters R and Q. We also update our previous results for the QCD isospin breaking corrections to the Kl2 decay rate and for the QCD contribution to the neutron-proton mass splitting. The numerical results of this paper have been obtained by using the gluon field configurations produced by the ETMC Collaboration with nf=2 dynamical quarks. We treated the dynamical quarks as electrically neutral particles (electroquenched approximation) and neglected a disconnected diagram in the charged and neutral pion mass splitting. We provide all the formulas necessary to remove these approximations and discuss in detail the estimate of the associated systematic uncertainties.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2ffbda1d74421bc2751bb62eefb93167f84e0807

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Citations in the corpus

Leading hadronic contribution to the muon magnetic moment from lattice QCD (2020, methodology): “Green squares are lattice results: this work’s result, denoted by BMWc’20 and represented by a filled symbol at the top of the figure, is followed by Mainz’19 [30], FHM’19 [31], ETM’19 [32], RBC’18 [19] and our earlier work BMWc’17 [14].”
Scattering processes and resonances from lattice QCD (2017, background): “…realistic, with up, down, strange and charm quark masses tuned to their correct physical values, and even some including the relatively small effects due to QED (Aoki et al., 2012b; Blum et al., 2007, 2010; Borsanyi et al., 2015; de Divitiis et al., 2013; Duncan et al., 1996; Horsley et al., 2016).”
Review of lattice results concerning low-energy particle physics (2016, methodology): “The reason for this unphysical parameter choice is that there are only few simulations of SU (2) isospin-breaking effects in lattice QCD, which is ultimately the cleanest way for predicting these effects [16,103,104,110,115,167,206,207].”