Gluon PDF of the proton using twisted mass fermions

In this paper, we present lattice QCD results for the x dependence of the unpolarized gluon parton distribution functions (PDFs) for the proton. We use one ensemble of Nf = 2 + 1 + 1 maximally twisted mass fermions with a clover improvement, and the Iwasaki improved gluon action. The quark masses are tuned to produce a pion with a mass of 260 MeV. The ensemble has a lattice spacing of a = 0.093 fm and a spatial extent of 3 fm. We employ the pseudodistribution approach, which relies on matrix elements of nonlocal operators that couple to momentum-boosted hadrons. In this work, we use five values of the momentum boost between 0 and 1.67 GeV. The gluon field-strength tensors of the nonlocal operator are connected with straight Wilson lines of varying length z. The light-cone Ioffe time distribution (ITD) is extracted utilizing data with z up to 0.56 fm and a quadratic parametrization in terms of the Ioffe time at fixed values of z. We explore systematic effects, such as the effect of the stout smearing for the gluon operator, excited states effects, and the dependence on the maximum value of z entering the fits to obtain the gluon PDF. Also, for the first time, the mixing with the quark singlet PDFs is eliminated using matrix elements with nonlocal quark operators that were previously analyzed within the quasi-PDF framework on the same ensemble. Here, we expand the dataset for the quark singlet and reanalyze within the pseudoPDFs method eliminating the corresponding mixing in the gluon PDF.