Abstract
In this note we reexamine the possibility of extracting parton distribution functions from lattice simulations. We discuss the case of quasi-parton distribution functions, the possibility of using the reduced Ioffe-time distributions and the more recent proposal of directly making reference to the computation of the current-current $T$-product. We show that in all cases the process of renormalization hindered by lattice momenta limitation represents an obstruction to a direct Euclidean calculation of the parton distribution function.
Highlights
The publication of Ref. [1] has prompted a substantial investment in attempts to compute parton distribution functions (PDFs) from first principle lattice simulations
The possibility of extracting PDFs from lattice QCD simulations of the hadronic matrix elements of a bilocal operator2 has been analyzed critically in Ref. [4], where it was observed that, despite the fact that such latticederived quantities can be made UV finite by an appropriate multiplicative renormalization, moments are plagued by UV power divergencies, so that the resummed expression provided by lattice simulations does not yield the correct PDF, as the moments of the physical PDF are instead finite and experimentally measured quantities
Equation (15) becomes a relation involving the moments of the physical PDF after sending Pz → ∞
Summary
The publication of Ref. [1] has prompted a substantial investment in attempts to compute parton distribution functions (PDFs) from first principle lattice simulations.. [4], where it was observed that, despite the fact that such latticederived quantities can be made UV finite by an appropriate multiplicative renormalization, moments are plagued by UV power divergencies, so that the resummed expression provided by lattice simulations does not yield the correct PDF, as the moments of the physical PDF are instead finite and experimentally measured quantities In spite of these difficulties a large number of papers have appeared which addressed the (perturbative) calculation of matching and renormalization coefficients, reported the lattice data of matrix elements of bilocal operators and enlarged the set of lattice quantities that can possibly be used for the purpose of extracting PDFs. In this paper we start in Sec. II by reexamining the theoretical foundation of the Ji proposal of Ref.
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