Abstract
We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such ‘long-link’ operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributions.
Highlights
We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory
Parton distribution functions (PDFs) provide important information on the quark and gluon structure of hadrons; at leading twist, they give the probability of finding a specific parton in the hadron carrying certain momentum and spin, in the infinite momentum frame
There are several obstacles which need to be overcome before a transparent picture of PDFs can emerge via Ji’s approach; one such obstacle is clearly the intricate renormalization behavior, which is the object of our present study
Summary
Parton distribution functions (PDFs) provide important information on the quark and gluon structure of hadrons; at leading twist, they give the probability of finding a specific parton in the hadron carrying certain momentum and spin, in the infinite momentum frame. Ji, involving the computation of quasi-distribution functions, which are accessible in Lattice QCD. Exploratory studies of the quasi-PDFs reveal promising results for the non-singlet operators for the unpolarized, helicity and transversity cases. A standard way of extracting quasi-distribution functions in lattice simulations involves computing hadronic matrix elements of certain gauge-invariant nonlocal operators; these are made up of a product of an anti-quark field at position x, possibly some Dirac gamma matrices, a path-ordered exponential of the gauge field (Wilson line) along a path joining points x and y, and a quark field at position y. There are several obstacles which need to be overcome before a transparent picture of PDFs can emerge via Ji’s approach; one such obstacle is clearly the intricate renormalization behavior, which is the object of our present study. We provide a prescription for estimating the linear divergence using non-perturbative data and extending arguments from perturbation theory. A long write-up of our work, together with an extended list of references, can be found in [1] (see the companion paper [2])
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