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In this paper, we examine the effect of nonzero quark masses on therenormalization of gauge-invariant nonlocal quark bilinear operators, includinga finite-length Wilson line (called Wilson-line operators). These operators arerelevant to the definition of parton quasi-distribution functions, thecalculation on the lattice of which allows the direct nonperturbative study ofthe corresponding physical parton distribution functions. We present ourperturbative calculations of the bare Green's functions, the renormalizationfactors in RI' and MSbar schemes, as well as the conversion factors of theseoperators between the two renormalization schemes. Our computations have beenperformed in dimensional regularization at one-loop level, using massivequarks. The conversion factors can be used to convert the corresponding latticenonperturbative results to the MSbar scheme, which is the most widely usedrenormalization scheme for the analysis of experimental data in high-energyphysics. Also, our study is relevant for disentangling the additional operatormixing which occurs in the presence of nonzero quark masses, both on thelattice and in dimensional regularization.

Renormalization of Wilson-line operators in the presence of nonzero quark masses