Abstract
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 improve the constraints on the distribution functions.
Highlights
The quest for an in-depth understanding of hadrons and their interactions dates back to the mid-20th century
It is difficult to disentangle the strange-quark parton distribution functions (PDFs) from the down-quark PDF. This results in large ambiguities in its extraction, and, for example, global analysis of Deep Inelastic Scattering (DIS) + SIDIS data sets gives different sign for the strange-quark helicity PDF, s, for different fragmentation functions [108,109]
The kinematical ones are the first moments of transverse momentum dependent (TMD) two-parton PDFs, and the dynamical ones from matrix elements with quark-gluon-quark non-local operators
Summary
The quest for an in-depth understanding of hadrons and their interactions dates back to the mid-20th century. X is the Bjorken scaling variable, and Q2 represents the scale of the hard interaction. HDIS is the hard part, which is process-dependent and calculable in perturbative QCD. In the case of the unpolarized DIS, the relevant distribution function is the spin-averaged (or unpolarized) PDF for the ith type of partons. Both functions HDIS and fi are given in the MS scheme. The dependence of the distribution functions on the factorization scale can be effectively eliminated using the evolution equations, resulting in process-independent functions. The dependence on the renormalization scale does not pose difficulties, as the data sets can be evolved to the same scale using perturbation theory. The PDFs, GPDs, and TMD PDFs are light-cone correlation functions and cannot be accessed from the Euclidean
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