Nucleon Electromagnetic Form Factors in the Continuum Limit from 2+1+1-flavor Lattice QCD

Abstract

Results are presented for the nucleon isovector electromagnetic form factors using 11 ensembles generated by the MILC collaboration using the 2+1+1-flavors HISQ action. They span 4 lattice spacings $a\sim$ 0.06, 0.09, 0.12 and 0.15~fm and 3 values of $M_{\pi }\sim 135,225$ and 315 MeV. High-statistics estimates are used to perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses. The $Q^2$ dependence over the range 0.05-1.4 ${\mathrm{GeV}}^2$ is investigated using both the $z$-expansion and the dipole form. Final $z$-expansion estimates for the isovector r.m.s. radius are $r_E=0.769(27)(30)$ fm $r_M=0.671(48)(76)$ fm and ${\mu }^{p-n}=3.939(86)(138)$ Bohr magneton. The first error is the combined uncertainty from the leading-order analysis, and the second is an estimate of the additional uncertainty due to using the leading order chiral-continuum-finite-volume fits. The dipole estimates, $r_E=0.765(11)(8)$ fm, $r_M=0.704(21)(29)$ fm and ${\mu }^{p-n}=3.975(84)(125)$, are consistent with those from the $z$-expansion but with smaller errors. Our analysis highlights three points. First, all data from the eleven ensembles and existing lattice data on, or close to, physical mass ensembles from other collaborations collapses more clearly onto a single curve when plotted versus $Q^2/M_N^2$ as compared to $Q^2$ with the scale set by quantities other than $M_N$. The difference between these two analyses is indicative of discretization errors, some of which presumably cancel when the data are plotted versus $Q^2/M_N^2$. Second, the size of the remaining deviation of this common curve from the Kelly curve is small and can be accounted for by statistical and possible systematic uncertainties. Third, to improve lattice estimates, high statistics data for $Q^2<0.1$ ${\mathrm{GeV}}^2$ are needed.

51 pages, 38 figures

References in corpus (17)

• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High-precision determination of the electric and magnetic form factors of the proton
• Nucleon Electromagnetic Form Factors
• Model independent extraction of the proton charge radius from electron scattering
• Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
• Proton and neutron electromagnetic form factors and uncertainties
• Defining the Proton Radius: a Unified Treatment
• Proton and neutron electromagnetic form factors from lattice QCD
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Extraction of the Neutron Magnetic Form Factor from Quasi-Elastic 3He(pol)(e(pol),e') at Q^2 = 0.1 - 0.6 (GeV/c)^2
• Nucleon electromagnetic form factors using lattice simulations at the physical point
• Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass
• Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
• Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
• Proton root-mean-square radii and electron scattering
• Proton rms-radii from low-q power expansions?
• The Proton Form Factor Ratio Measurements at Jefferson Lab

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