Pion valence quark distribution from current-current correlation in lattice QCD

Abstract

We extract the pion valence quark distribution q π v ðxÞ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted q π v ðxÞ and that obtained from experimental data across the entire x range. Further, we demonstrate that the oneloop matching coefficient relating the LQCD matrix computed in position space to the q π v ðxÞ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD-calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

Isovector parton distribution functions of the proton on a superfine lattice

“…Based on these theoretical developments, unpolarized and polarized nucleon PDFs have been calculated on the lattice [24,[26][27][28][29][30][31][32][33]. Furthermore, lattice calculations of the valence pion PDF have also appeared [34][35][36][37][38]. The status of this field is well summarized in recent review papers [39][40][41][42].…”

An analysis of parton distribution functions of the pion and the kaon with the maximum entropy input

“…And the analysis from current-current correlation in LQCD [14] predicts α v = 0.78 (11)(3) at Q 2 = 4 GeV 2 . The PDFs of the pion and the kaon determined in this work are consistent with the predictions of Regge theory [63,64] and LQCD approach [14][15][16].…”

“…Another recent LQCD calculation using the reduced Ioffe-time pseudodistributions predicts β v = 1.08(41)(11) at Q 2 = 4 GeV 2 [15]. However β v = 2.12(56)(14) at Q 2 = 4 GeV 2 is predicted from the current-current correlation in LQCD [14]. From perturbative QCD, β for the valence quark distribution is 2 in the asymptotic region [36][37][38].…”

“…The large-x behavior of valence quark distribution is an interesting topic in theory, which can be calculated with LQCD [14][15][16], quark number counting rule [62,63], and perturbative QCD predictions [36][37][38]. The large-x behavior is usually described by,…”

“…Parton distribution functions (PDFs) display the longitudinal momentum structure of the quarks and gluons in the infinite momentum frame. In theory, there are quite a lot of methods giving pion and kaon PDFs, such as lattice QCD (LQCD) [12][13][14][15][16], Dyson-Schwinger Equations (DSE) [17][18][19], holographic QCD [20], light-front quantization [21], and the constituent quark model [22][23][24].…”