Quasi-Parton Distribution Function in Lattice Perturbation Theory

Understand

Large momentum effective field theory provides a new direction for lattice QCD calculations of hadronic structure functions, such as parton distribution functions (PDFs), meson distribution amplitudes, and so on, directly with $x$-dependence.

• In the framework of Lattice Perturbation Theory (LPT), we compute the one-loop quark-in-quark quasi-PDF with the na\"ive fermion action ($\tilde{q}^{\mathrm{nv}}$) and quasi-PDF with Wilson-Clover action ($\tilde{q}^{\mathrm{WC}}$) and show that $\tilde{q}^{\mathrm{nv}}$ reduces to the continuum quasi-PDF in the continuum limit.
• We point out, however, that the continuum limit and massless quark limit do not commute.
• We find that the condition to recover the same collinear divergence that the quasi-PDF has in continuum QCD is $aP_3^2\approx m$ and $m\ll P_3$, while the condition to fully recover the continuum quasi-PDF is $aP_{3}^{2}\ll m\ll P_{3}$, where $P_3$ is the momentum in the direction of the quark's motion (longitudinal direction).