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We present a comprehensive analysis of the electromagnetic form factors of the nucleon from a lattice simulation with two flavors of dynamical -improved Wilson fermions. A key feature of our calculation is that we make use of an extensive ensemble of lattice gauge field configurations with four different lattice spacings, multiple volumes, and pion masses down to . We find that by employing Kelly-inspired parametrizations for the dependence of the form factors, we are able to obtain stable fits over our complete ensemble. Dirac and Pauli radii and the anomalous magnetic moments of the nucleon are extracted and results at light quark masses provide evidence for chiral nonanalytic behavior in these fundamental observables.
In this paper we present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED, concentrating particularly on violations of isospin symmetry. We calculate the π+-π0 splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in [1]. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the u and d quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen’s theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as \( \overline{M\ S} \), in which Dashen’s theorem for neutral mesons is violated.
By considering a flavor expansion about the flavor symmetric point, we investigate how flavor blindness constrains octet baryon matrix elements after is broken by the mass difference between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavor symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line-disconnected terms in the three-point correlation functions is also given. As we consider Wilson cloverlike fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavor-conserving matrix elements of the vector first-class form factors.