Proton and neutron electromagnetic form factors from lattice QCD in the continuum limit

Abstract

We compute the electromagnetic form factors of the proton and neutron using lattice QCD. We employ $N_{\mathrm{f}}$=2+1+1 twisted mass clover-improved fermions with quark masses tuned to their physical values. Three ensembles with lattice spacings of $a$=0.080 fm, 0.068 fm, and 0.057 fm, and approximately the same physical volume allow us to obtain the continuum limit directly at the physical pion mass. For each ensemble, we use several values of the sink-source time separation, ranging from 0.5 fm to 1.5 fm, to allow for a thorough analysis of excited state effects via multi-state fits. The disconnected contributions are also analyzed using high statistics combined with techniques to mitigate stochastic noise in the estimation of the fermion loop. These techniques include low-mode deflation, dilution in the color and spin components, and hierarchical probing. We study the momentum transfer dependence of the form factors using the $z$-expansion and dipole Ansätze, thereby enabling the extraction of the electric and magnetic radii and the magnetic moments, as well as the Zemach and Friar radii in the continuum limit. Results for the proton and neutron electric and magnetic mean square radii are $\sqrt{⟨r_E^2{⟩}^p}=0.860(38)(23)$ fm, $⟨r_E^2{⟩}^n=-0.147(48)$ fm${}^2$, $\sqrt{⟨r_M^2{⟩}^p}=0.870(53)(15)$ fm and $\sqrt{⟨r_M^2{⟩}^n}=0.913(67)(19)$ fm, and for the proton and neutron magnetic moments ${\mu }^p=2.849(92)(52)$ and ${\mu }^n=-1.819(76)(29)$, respectively. In all cases, the first error is statistical and the second systematic, where the latter includes an estimate of the error from the fits to the momentum dependence of the form factors and from the continuum extrapolation.

32 pages, 26 figures, and 20 tables; v2: published version

References in corpus (13)

• Model independent extraction of the proton charge radius from electron scattering
• Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions
• Proton and neutron electromagnetic form factors and uncertainties
• The nucleon spin and momentum decomposition using lattice QCD simulations
• The RMS Charge Radius of the Proton and Zemach Moments
• 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
• Improved information criteria for Bayesian model averaging in lattice field theory
• First moments of the nucleon transverse quark spin densities using lattice QCD
• Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD
• Electromagnetic form factors of the nucleon from $N_f=2+1$ lattice QCD
• $N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors
• Zemach and Friar radii of the proton and neutron from lattice QCD