Abstract
We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs. We present the results of our calculations of the one-loop corrections for the bilocal Gμα(z) overset{sim }{G} λβ (0) correlator of gluonic fields. Expressions are given for a general situation when all four indices are arbitrary, and also for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF. We study the evolution properties of these matrix elements, and derive matching relations between Euclidean and light-cone Ioffe-time distributions. These relations are necessary for extraction of the polarized gluon distributions from the lattice data.
Highlights
DefinitionsTo extract polarized gluon distributions of a nucleon, we consider matrix elements of bilocal operators Gμα(z)Gλβ(0) composed of two gluon fields, with the dual field defined by
We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs
Expressions are given for a general situation when all four indices are arbitrary, and for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF
Summary
To extract polarized gluon distributions of a nucleon, we consider matrix elements of bilocal operators Gμα(z)Gλβ(0) composed of two gluon fields, with the dual field defined by. The matrix elements are specified by mμα;λβ(z, p) ≡ p, s| Gμα(z) E(z, 0; A)Gλβ(0)|p, s ,. The standard definition of the polarized gluon PDFs [34] uses the contracted amplitude gαλmμα;λβ, but we will keep all four indices μ, α, λ, β non-contracted. To simplify further formulas, we normalize sμ by s2 = −m2, where m is the nucleon mass. This means that our polarization vector sμ is related by sμ = mSμ to the usual polarization vector Sμ which is normalized by S2 = −1
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