Abstract
In this paper, we examine the effect of nonzero quark masses on the renormalization of gauge-invariant nonlocal quark bilinear operators, including a finite-length Wilson line (called Wilson-line operators). These operators are relevant to the definition of parton quasi-distribution functions, the calculation on the lattice of which allows the direct nonperturbative study of the corresponding physical parton distribution functions. We present our perturbative calculations of the bare Green's functions, the renormalization factors in RI' and MSbar schemes, as well as the conversion factors of these operators between the two renormalization schemes. Our computations have been performed in dimensional regularization at one-loop level, using massive quarks. The conversion factors can be used to convert the corresponding lattice nonperturbative results to the MSbar scheme, which is the most widely used renormalization scheme for the analysis of experimental data in high-energy physics. Also, our study is relevant for disentangling the additional operator mixing which occurs in the presence of nonzero quark masses, both on the lattice and in dimensional regularization.
Highlights
Parton quasidistribution functions are nowadays widely employed in the nonperturbative study of hadron structure in lattice QCD. They are directly related to the matrix elements of gauge-invariant nonlocal fermion bilinear operators, including a finite-length Wilson line, which are called Wilson-line operators
parton distribution functions (PDFs) are an essential tool for studying the quark and gluon structure of hadrons, as they describe the distributions of momentum and spin of constituent partons inside a hadron, in the infinite momentum frame
Comparing the massive and the massless cases, the effect of finite mass on the renormalization of Wilson-line operators becomes significant for strange quarks, as well as for heavier quarks. These are features of massive quasi-PDFs, which must be taken into account in their future nonperturbative study
Summary
Parton quasidistribution functions (quasi-PDFs) are nowadays widely employed in the nonperturbative study of hadron structure in lattice QCD. Even in the absence of quark masses, bare Green’s functions of Wilson-line operators may contain finite, regulator-dependent contributions that cannot be removed by a simple multiplicative renormalization; as a consequence, an appropriate (i.e., regularization-independent) choice of renormalization prescription for RI’ necessitates the introduction of mixing matrices for certain pairs of operators [16], both in the continuum and on the lattice. Comparing the massive and the massless cases, the effect of finite mass on the renormalization of Wilson-line operators becomes significant for strange quarks, as well as for heavier quarks These are features of massive quasi-PDFs, which must be taken into account in their future nonperturbative study. A table of Feynman parameter integrals, which appear in the expressions of our results, is relegated to Appendix B
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