We report on our exploratory study for the direct evaluation of the parton distribution functions from lattice QCD, based on a recently proposed new approach. We present encouraging results using N f ¼ 2 þ 1 þ 1 twisted mass fermions with a pion mass of about 370 MeV. The focus of this work is a detailed description of the computation, including the lattice calculation, the matching to an infinite momentum and the nucleon mass correction. In addition, we test the effect of gauge link smearing in the operator to estimate the influence of the Wilson line renormalization, which is yet to be done.

We present results of lattice QCD simulations with mass-degenerate up and down and mass-split strange and charm (N f = 2 + 1 + 1) dynamical quarks using Wilson twisted mass fermions at maximal twist. The tuning of the strange and charm quark masses is performed at two values of the lattice spacing a ≈ 0.078 fm and a ≈ 0.086 fm with lattice sizes ranging from L ≈ 1.9 fm to L ≈ 2.8 fm. We measure with high statistical precision the light pseudoscalar mass m PS and decay constant f PS in a range 270 m PS 510 MeV and determine the low energy parameters f 0 andl 3,4 of SU(2) chiral perturbation theory. We use the two values of the lattice spacing, several lattice sizes as well as different values of the light, strange and charm quark masses to explore the systematic effects. A first study of discretisation effects in light-quark observables and a comparison to N f = 2 results are performed.

The masses of the low lying baryons are evaluated using a total of ten ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values. The light sea quarks correspond to pseudo scalar masses in the range of about 210 MeV to 430 MeV. We use the Iwasaki improved gluonic action at three values of the coupling constant corresponding to lattice spacing a = 0.094 fm, 0.082 fm and 0.065 fm determined from the nucleon mass. We check for both finite volume and cut-off effects on the baryon masses. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. We performed a chiral extrapolation of the forty baryon masses using SU(2) χPT. After taking the continuum limit and extrapolating to the physical pion mass our results are in good agreement with experiment. We provide predictions for the mass of the doubly charmed Ξ * cc , as well as of the doubly and triply charmed Ωs that have not yet been determined experimentally.

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.