We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N f =2+1+1 ensembles having pion masses of 213 MeV and 373 MeV each at a different value of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 17 N f =2+1+1 ensembles generated at three values of the lattice spacing, a. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of O(a 2 )-terms. The moments of the generalized parton distributions are given in the MS scheme at a scale of µ = 2 GeV. We compare with recent results obtained using different discretization schemes. The implications on the spin content of the nucleon are also discussed.

We present a dedicated analysis of the influence of excited states on the calculation of nucleon matrix elements. This calculation is performed at a fixed value of the lattice spacing, volume and pion mass that are typical of contemporary lattice computations. We focus on the nucleon axial charge, g A , for which we use about 7,500 measurements, and on the average momentum of the unpolarized isovector parton distribution, x u−d , for which we use about 23,000 measurements. All computations are done employing N f = 2 + 1 + 1 maximally-twisted-mass Wilson fermions and using nonperturbatively calculated renormalization factors. Excited state effects are shown to be negligible for g A , whereas they lead to an O(10%) downward shift for x u−d .

We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-tonoise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.

We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light (u,d), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound can be provided. The present calculation which is performed at only one value of the lattice spacing and pion mass serves as a technical feasibility study for a future computation of the scalar quark content of the nucleon with a detailed analysis of the systematics.

We perform a detailed numerical investigation of the approximate moduli space metric proposed by Diakonov and Petrov [1] for a confining model of dyons. Our findings strongly indicate that only for a small number of dyons at sufficiently low density this metric is positive definiteand, therefore, a valid moduli space metric -throughout a considerable part of configuration space. This poses strong limitations on results obtained by an unrestricted integration over collective coordinates in this model. It also indicates that strong correlations between collective coordinates will be essential for the physical content of a dyon model, which could be exhibited by a suitable simulation algorithm.