Electromagnetic mass splittings of the low lying hadrons and quark masses from2+1flavor latticeQCD+QED

Abstract

2 Results computed in lattice QCD+QED are presented for the electromagnetic mass splittings of the low lying hadrons. These are used to determine the renormalized, non-degenerate, light quark masses. It is found that m M S u = 2.24 (10) (34), m M S d = 4.65 (15) (32), and m M S s = 97.6 (2.9) (5.5) MeV at the renormalization scale 2 GeV, where the first error is statistical and the second systematic.We find the lowest order electromagnetic splitting (m π + − m π 0 ) QED = 3.38 (23) MeV, the splittings including next-to-leading order, (m π + − m π 0 ) QED = 4.50 (23) MeV, (m K + − m K 0 ) QED = 1.87(10) MeV, and the m u = m d contribution to the kaon mass difference, (m K + − m K 0 ) (mu−m d ) = −5.840(96) MeV. All errors are statistical only, and the next-to-leading order pion splitting is only approximate in that it does not contain all next-to-leading order contributions. We also computed the proton-neutron mass difference, including for the first time, QED interactions in a realistic 2+1 flavor calculation. We find (m p − m n ) QED = 0.383 (68) MeV, (m p − m n ) (mu−m d ) = −2.51(14) MeV (statistical errors only), and the total m p − m n = −2.13(16)(70) MeV, where the first error is statistical, and the second, part of the systematic error. The calculations are carried out on QCD ensembles generated by the RBC and UKQCD collaborations, using domain wall fermions and the Iwasaki gauge action (gauge coupling β = 2.13 and lattice cutoff a −1 ≈ 1.78 GeV). We use two lattice sizes, 16 3 and 24 3 ( (1.8 fm) 3 and (2.7 fm) 3 ), to address finite volume effects. Non-compact QED is treated in the quenched approximation.The valence pseudo-scalar meson masses in our study cover a range of about 250 to 700 MeV, though we use only those up to about 400 MeV to quote final results.We present new results for the electromagnetic low energy constants in SU(3) and SU(2) partially-quenched chiral perturbation theory to the next-to-leading order, obtained from fits to our data. Detailed analysis of systematic errors in our results and methods for improving them are discussed. Finally, new analytic results for SU(2) L × SU(2) R -plus-kaon chiral perturbation theory, including the one-loop logs proportional to α em m, are given. 3

Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei

“…It is worth re-emphasizing that in forming these estimates of the QED power-law corrections, exponential corrections of the form e −mπL have been neglected. 8 When comparing with previous results one should note that the squared mass shift of the π + , as an example, due to FV QED is…”

“…In some instances, the up-and down-quark masses and quenched Quantum Electrodynamics (QED) have been included in an effort to precisely post-dict the observed isospin splittings in the spectrum of hadrons [4,[6][7][8][9][10][11][12][13]. While naively appearing to be a simple extension of pure LQCD calculations, there are subtleties associated with including QED.…”

Two-particle elastic scattering in a finite volume including QED

“…The operator O E * when acting on the two-particle operator simply yields the non-relativistic center-of-mass energy, E * . 3 The power counting in the EFT is manifest in the PDS scheme [46,47]. Here for simplicity we use M S, which obscures the strong power counting, but does not change it.…”

“…In particular, hadronic spectra and other hadronic observables are now being calculated in the presence of both isospin violation from the light-quark masses and Quantum Electrodynamics (QED) [1][2][3][4][5][6][7][8][9][10][11]. QED plays a critical role in the stability and structure of nuclei, and therefore first principles calculations of nuclear structure require the inclusion of the electromagnetic (EM) interactions among quarks.…”

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

“…[1], particularly in the past few years, leading to recent determinations of the electromagnetic mass splitting of light pseudoscalar mesons and light baryons, see refs. [2][3][4][5][6][7][8][9] for recent works on the subject. All these works rely on finite-volume formulations of QED obtained by quenching some Fourier modes of the gauge field.…”