Multiplicative renormalizability of quasi-parton operators

TL;DR

This paper proves that quasi-gluon operators in lattice QCD can be multiplicatively renormalized to all orders, extending previous results for quasi-quark operators, thus strengthening the theoretical basis for extracting PDFs from lattice calculations.

Contribution

It extends the proof of multiplicative renormalizability from quasi-quark to quasi-gluon operators, ensuring a solid theoretical foundation for lattice QCD PDF extraction.

Findings

Quasi-gluon operators can be multiplicatively renormalized to all orders.

Using a gauge-invariant UV regulator is essential for the renormalization proof.

The results support the QCD collinear factorization approach for lattice QCD calculations.

Abstract

Extracting parton distribution functions (PDFs) from lattice QCD calculation of quasi-PDFs has been actively pursued in recent years. We extend our proof of the multiplicative renormalizability of quasi-quark operators in Ref. [1] to quasi-gluon operators, and demonstrated that quasi-gluon operators could be multiplicatively renormalized to all orders in perturbation theory, without mixing with other operators. We find that using a gauge-invariant UV regulator is essential for achieving this proof. With the multiplicative renormalizability of both quasi-quark and quasi-gluon operators, and QCD collinear factorization of hadronic matrix elements of there operators into PDFs, extracting PDFs from lattice QCD calculated hadronic matrix elements of quasi-parton operators could have a solid theoretical foundation.