Proton isovector helicity PDF at NNLO and the twist-3 moment d ˜ 2 from lattice QCD at physical quark masses

Le résumé fourni par la source

We present a lattice quantum chromodynamics calculation of the x -dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the d ˜ 2 moment of the twist-3 PDF g T ( x ) for the first time in the MS ¯ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing a = 0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta P z = { 0 , 0.25 , 1.02 , 1.53 } GeV . We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for g T ( x ) , we obtain d ˜ 2 u − d ( 2 GeV ) = 0.0024 ( 46 ) at next-to-leading order in MS ¯ . Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the x -space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the MS ¯ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region x ∈ [ 0.25 , 0.75 ] . The end-point regions are then parametrized, combined with the LaMET prediction at moderate x , and fitted to the short-distance matrix elements in coordinate space.

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