Polarized twist-three distributions $g_T$ and $h_L$ and the role of intrinsic transverse momentum

TL;DR

The paper addresses how intrinsic quark transverse momentum affects twist-three polarized distributions $g_T(x)$ and $h_L(x)$. By decomposing these distributions into twist-two (Wandzura-Wilczek) parts, quark-mass terms, and interaction-dependent pieces encoded in quark-gluon-quark correlators, it reveals the substantial role of transverse momentum and nonlocal matrix elements. It derives Burkhardt-Cottingham-type sum rules for $g_2$ and a similar rule for $h_2$, and demonstrates how the interaction-dependent components enter observable quantities. The authors compute polarized DIS and DY processes at ${\\cal O}(1/Q)$, showing that intrinsic $k_T$ and quark-gluon correlations can significantly modify the LT asymmetry $A_{LT}$ in DY, with bag-model estimates indicating sizable departures from zero-$k_T$ expectations, highlighting the necessity of including transverse momentum effects in twist-three analyses.

Abstract

In a nonstandard way we split up the polarized quark distributions $g_T$ and $h_L$ into their twist-two, quark-mass, and interaction-dependent parts, emphasizing the sensitivity to quark intrinsic transverse momentum. We show how to derive the Burkhardt-Cottingham sum rule in this approach and derive a similar sum rule for the chiral-odd distribution $h_2$. The effect of intrinsic transverse momentum in experimental observables is illustrated in the calculation of the ${\cal O}(1/Q)$ double-spin asymmetry $A_{LT}$ in Drell-Yan scattering.

Figures (12)

• Figure 1: The blob representing the quark-quark correlation function $\Phi_{\alpha\beta}(PS;k)$.
• Figure 2: The quark-gluon-quark correlation function ${\cal M}^i_{\alpha\beta}(PS;k,p)$.
• Figure 3: The physical area in the $\sigma\tau$-plane for $x=1/2$. The lower boundary is given by the line $\tau=\sigma-1$, the upper by $\tau=x\sigma-x^2$.
• Figure 4: Distribution function $g_T(x)$ for a massless quark in the bag (solid line), its twist-two Wandzura-Wilczek part $\int_x^1 dy[g_1(y)/y]$ (dotted) and its interaction-dependent part $\tilde{g}_T(x)-\int_x^1 dy [\tilde{g}_T(y)/y]$ (dashed) jaff91a. The dot-dashed line is $\tilde{g}_T(x)$ which diverges like $1/x$ for $x\rightarrow 0$.
• Figure 5: $h_2$ (solid curve) in the bag is twice $g_2$ (dashed).