Abstract
We show that the correct way to extract parton distribution functions from the reduced Ioffe-time distribution (RITD), a ratio of the Ioffe-time distribution for a moving hadron and a hadron at rest, is through a factorization formula. This factorization exists because, at small distances, forming the ratio does not change the infrared behavior of the numerator, which is factorizable. We illustrate the effect of such a factorization by applying it to results in the literature.
Highlights
One of the most important goals of QCD is to understand the structure of hadrons in terms of their fundamental constituents—quarks and gluons
The pseudodistribution proposal is equivalent to the quasidistribution calculation in the large momentum effective theory (LaMET), in the sense that similar factorization formulas exist for both approaches and that large nucleon momentum is required in both cases to extract the information on the leading-twist parton distribution functions (PDFs) [29]
The authors of Ref. [56] determined the PDFs based on an approximate scaling in z2 observed in the lattice data of the reduced Ioffe-time distribution (RITD), where z is the distance between the two quark fields defining the equal-time quark correlator
Summary
One of the most important goals of QCD is to understand the structure of hadrons in terms of their fundamental constituents—quarks and gluons. The pseudodistribution proposal is equivalent to the quasidistribution calculation in the LaMET, in the sense that similar factorization formulas exist for both approaches and that large nucleon momentum is required in both cases to extract the information on the leading-twist PDF [29]. [56] determined the PDFs based on an approximate scaling in z2 observed in the lattice data of the RITD, where z is the distance between the two quark fields defining the equal-time quark correlator. They highlighted the remaining z2-dependence of the RITD and studied its evolution with z2
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