Lattice QCD exploration of pseudo-PDFs

Kostas Orginos; Anatoly Radyushkin; Joseph Karpie; Savvas Zafeiropoulos

paper

Lattice QCD exploration of pseudo-PDFs

arXiv:1706.05373

Abstract

We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element $M (P z_{3}, z_{3}^{2})$ as a function of the Ioffe time $ν = P z_{3}$ and the distance $z_{3}$ . The next step is to divide $M (P z_{3}, z_{3}^{2})$ by the rest-frame density $M (0, z_{3}^{2})$ . Our lattice calculation shows a linear exponential $z_{3}$ -dependence in the rest-frame function, expected from the $Z (z_{3}^{2})$ factor generated by the gauge link. Still, we observe that the ratio $M (P z_{3}, z_{3}^{2}) / M (0, z_{3}^{2})$ has a Gaussian-type behavior with respect to $z_{3}$ for 6 values of $P$ used in the calculation. This means that $Z (z_{3}^{2})$ factor was canceled in the ratio. When plotted as a function of $ν$ and $z_{3}$ , the data are very close to $z_{3}$ -independent functions. This phenomenon corresponds to factorization of the $x$ - and $k_{⊥}$ -dependence for the TMD $F (x, k_{⊥}^{2})$ . For small $z_{3} \leq 4 a$ , the residual $z_{3}$ -dependence is explained by perturbative evolution, with $α_{s} / π = 0.1$ .

arXiv comment12 pages, 18 figures, to appear in Phys. Rev. D

Lattice QCD exploration of pseudo-PDFs

Abstract

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