Quantum electrodynamics for vector mesons

Quantum electrodynamics for $\rho$ mesons is considered. It is shown that, at tree level, the value of the gyromagnetic ratio of the $\rho^+$ is fixed to 2 in a self-consistent effective quantum field theory. Further, the mixing parameter of the photon and the neutral vector meson is equal to the ratio of electromagnetic and strong couplings, leading to the mass difference $M_{\rho^0}-M_{\rho^\pm}\sim 1 {\rm MeV}$ at tree order.Comment: 4 pages, 2 figures, REVTeX 4, accepted for publication in PR

Proton and neutron electromagnetic radii and magnetic moments from lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. The $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron, as well as the Zemach radius of the proton. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC).Comment: 7 pages, 3 figures, contribution to the 16th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2023), October 15th-20th, 2023, Mainz, Germany. arXiv admin note: substantial text overlap with arXiv:2401.0540

Electromagnetic form factors of the nucleon from Nf=2+1N_f = 2 + 1 lattice QCD

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton's electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values $\langle r_E^2 \rangle^p = (0.672 \pm 0.014$ (stat)${} \pm 0.018$ (syst)$)$ fm${}^2$, $\langle r_M^2 \rangle^p = (0.658 \pm 0.012$ (stat)${} \pm 0.008$ (syst)$)$ fm${}^2$, and $\mu_M^p = 2.739 \pm 0.063$ (stat)${} \pm 0.018$ (syst). The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent $ep$-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 $ep$-scattering experiment.Comment: 48 pages, 10 figure

Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD

We present lattice-QCD results for the electromagnetic form factors of the proton and neutron including both quark-connected and -disconnected contributions. The parametrization of the $Q^2$-dependence of the form factors is combined with the extrapolation to the physical point. In this way, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain at the physical pion mass and in the continuum and infinite-volume limit $\sqrt{\langle r_E^2 \rangle^p} = 0.820(14)$ fm, $\sqrt{\langle r_M^2 \rangle^p} = 0.8111(89)$ fm, and $\mu_M^p = 2.739(66)$, where the errors include all systematics.Comment: 7 pages, 3 figures; for the accompanying paper, see arXiv:2309.06590 [hep-lat]. arXiv admin note: substantial text overlap with arXiv:2309.0659

Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass

We describe details of the renormalization of two-loop integrals relevant to the calculation of the nucleon mass in the framework of manifestly Lorentz-invariant chiral perturbation theory using infrared renormalization. It is shown that the renormalization can be performed while preserving all relevant symmetries, in particular chiral symmetry, and that renormalized diagrams respect the standard power counting rules. As an application we calculate the chiral expansion of the nucleon mass to order O(q^6).Comment: Version accepted for publication in Nucl. Phys. A, missing one-loop diagram added, minor changes in notation, discussion of results improve