Abstract
We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-$x$ dependence of a momentum-dependent quasi-distribution is calculated on the lattice and matched to the ordinary lightcone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.
Highlights
Parton distribution functions (PDFs) are probability densities of quarks and gluons seen by an observer moving at the speed of light relative to the hadron
This property makes it possible to carry out a nonperturbative renormalization of the quasi-PDF in the regularization-invariant momentum-subtraction scheme (RI/MOM) [46] that has been widely used for quark operators on the lattice
We have carried out a nonperturbative renormalization of the quasi-PDF in the RI/MOM scheme in lattice QCD
Summary
Parton distribution functions (PDFs) are probability densities of quarks and gluons seen by an observer moving at the speed of light relative to the hadron. Ji [17,18] proposed a new approach for the direct computation of parton physics, large-momentum effective field theory (LaMET) According to this approach, in order to get the normal PDF, one can start by calculating a “quasi-PDF,” which is defined as a spatial correlation of partons along, say the z direction, in a moving nucleon, Z q~ ðx; Pz; μ~ Þ 1⁄4. The one-loop matching kernels were calculated in the continuum theory for the isovector quark distributions in a transverse-momentum cutoff scheme in Ref. This property makes it possible to carry out a nonperturbative renormalization of the quasi-PDF in the regularization-invariant momentum-subtraction scheme (RI/MOM) [46] that has been widely used for quark operators on the lattice. We present lattice results for the nonperturbatively renormalized quasi-PDF in RI/MOM scheme for the isovector unpolarized case, and match it to the MS PDF at one-loop order in perturbative QCD. Summarize our results and discuss possible directions for further studies
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