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In this article, we review recent lattice calculations on the $x$-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of some of the approaches for the transverse-momentum-dependent PDFs (TMD PDFs). This new direction of lattice calculations is particularly interesting for phenomenological fits on experimental data sets, as the lattice results can help to improve the constraints on the distribution functions.
We present the first calculation of the $x$-dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-
We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the
We present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the
This work presents the first calculation in lattice QCD of three moments of spin-averaged and spin-polarized generalized parton distributions in the proton. It is shown that the slope of the associated generalized form factors decreases significantly
We present a high-statistics lattice QCD determination of the valence parton distribution function (PDF) of the pion, with a mass of 300 MeV, using two very fine lattice spacings of $a=0.06$ fm and 0.04 fm. We reconstruct the $x$-dependent PDF, as we