Target Mass Effects in Parton Quasi-Distributions

TL;DR

Addressing how finite nucleon mass affects parton quasi-distributions, the paper develops a VDF/TMD framework to separate kinematic target-mass effects from dynamical higher-twist contributions. It derives explicit twist-2 relations between Q(y,P) and the PDF f(y) and shows that $M^2/P^2$ corrections are smaller than standard higher-twist effects, with a kinematic dependence entering through $k_\perp^2+x^2 M^2$ in the TMDs. Using Gaussian and simple non-Gaussian TMD models, it demonstrates that for $p_3 \gtrsim 2M$ the $M^2$ corrections to PQDs become negligible within lattice uncertainties. The results justify neglecting target-mass corrections in practical lattice extractions of PDFs from PQDs and offer a modeling pathway for including $M^2$ effects when needed.

Abstract

We study the impact of non-zero (and apparently large) value of the nucleon mass $M$ on the shape of parton quasi-distributions $Q(y,p_3)$, in particular on its change with the change of the nucleon momentum $p_3$. We observe that the usual target-mass corrections induced by the $M$-dependence of the twist-2 operators are rather small. Moreover, we show that within the framework based on parametrizations by transverse momentum dependent distribution functions (TMDs) these corrections are canceled by higher-twist contributions. We identify a novel source of kinematic target-mass dependence of TMDs and build models corrected for such dependence. We find that resulting changes may be safely neglected for $p_3 \gtrsim 2M$.

Figures (5)

• Figure 1: Structure of parton-hadron matrix element.
• Figure 2: Twist-2 part of $Q(y,P)$ for $P/M =0.5,\ 1, \ 2$ (from bottom to top at $y=0.1$) compared to the limiting PDF $f(y) = (1-y)^3 \theta (0<y<1)$.
• Figure 3: Evolution of $Q(y,P)$ in the Gaussian model for $P/\Lambda =3,5,10$ (from bottom to top at $y=0.1$) compared to the limiting PDF $f(y) = (1-y)^3 \theta (y)$.
• Figure 4: Comparison of QPDs $Q(y,P;M)$ for $M=3 \Lambda$ and $M=0$ at $P=M$.
• Figure 5: Comparison of QPDs $Q(y,P;M)$ for $M=3 \Lambda$ and $M=0$ at $P=2M$.