Unpolarized transverse momentum dependent parton distributions of the nucleon from lattice QCD

We present a first lattice QCD calculation of the unpolarized nucleon 's isovector transverse-momentum dependent parton distribution functions (TMDPDFs), which are essential to predict observables of multiscale, semi-inclusive processes in the standard model. We use a N f 1 / 4 2 + 1 + 1 MILC ensemble with valence clover fermions on a highly improved staggered quark (HISQ) sea to compute the quark momentum distributions in a large-momentum nucleon on the lattice. The state-of-the-art techniques in renormalization and extrapolation in the correlation distance on the lattice are adopted. The perturbative kernel up to next-to-next-to-leading order is taken into account, and the dependence on the pion mass and the hadron momentum is explored. Our results are qualitatively comparable with phenomenological TMDPDFs, which provide an opportunity to predict high energy scatterings from first principles.