Abstract
Within the framework of large momentum effective theory (LaMET), genenaralized parton distributions (GPDs) can be extracted from lattice calculations of quasi-GPDs through a perturbative matching relation, up to power corrections that are suppressed by the hadron momentum. In this paper, we focus on isovector quark GPDs, including the unpolarized, longitudinally and transversely polarized cases, and present the one-loop matching that connects the quasi-GPDs renormalized in a regularization-independent momentum subtraction (RI/MOM) scheme to the GPDs in MS scheme. We find that the matching coefficient is independent of the momentum transfer squared. As a consequence, the matching for the quasi-GPD with zero skewness is the same as that for the quasi-PDF. Our results provide a crucial input for the determination of quark GPDs from lattice QCD using LaMET.
Highlights
Understanding the internal structure of nucleons has been an important goal of hadron physics
III, we present a rigorous derivation of the factorization formula for the isovector quark quasi-generalized parton distributions (GPDs) based on operator product expansion (OPE)
When the hadron momentum Pz is much greater than M and ΛQCD, the regularizationindependent momentum subtraction (RI/MOM) quasi-GPD can be matched onto the MS GPD through the factorization formula [55,58]
Summary
Understanding the internal structure of nucleons has been an important goal of hadron physics. As a generalization of the PDFs to off-forward kinematics, the GPDs contain a wealth of new information on nucleon structure They naturally encompass the FFs, PDFs as well as the distribution amplitudes (DAs), and offer a description of the correlations between the transverse position and longitudinal momentum of quarks and gluons inside the nucleon, thereby giving access to quark and gluon orbital angular momentum contributions to the nucleon spin. A multiplicative renormalization of both the quark [40,43,44] and gluon [69,70] quasiPDFs has been established in coordinate space This allows for a nonperturbative renormalization in the regularizationindependent momentum subtraction (RI/MOM) scheme [88]. We reconsider the one-loop matching for isovector quark quasi-GPDs in the RI/MOM scheme.
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