Scale Dependence of Twist-3 Quark-Gluon Operators for Single Spin Asymmetries

Abstract

We derive the scale dependence of twist-3 quark-gluon operators, or ETQS matrix elements, at one-loop. These operators are used to factorize transverse single spin asymmetries, which are studied intensively both in experiment and theory. The scale dependence of two special cases are particularly interesting. One is of soft-gluon-pole matrix elements, another is of soft-quark-pole matrix elements. From our results the evolutions in the two cases can be obtained. A comparison with existing results of soft-gluon-pole matrix elements is made.

Figures (4)

• Figure 1: A set of diagrams of one-loop corrections to $T_{\pm} (x_1,x_2)$ from the $qg$-contribution. This set only contains the self-energy corrections represented by black dots, and corrections with one gluon emission from a gauge link.
• Figure 2: Another set of diagrams for one-loop corrections of $T_{\pm}$ from the $qg$-contribution.
• Figure 3: One-loop diagrams in the light-cone gauge for $T_{\pm}(x_1,x_2)$ from the $q\bar{q}$-contribution.
• Figure 4: The one-loop diagrams for $T_{\pm}(x_1,x_2)$ from the $gg$-contribution. The gluons from the bottom are labeled as, the left gluon is with $p_1$, the middle one is with $p_2$, both are incoming. The right one is with $p$ as an outgoing gluon.