Single Transverse-Spin Asymmetries at Large-x

TL;DR

This work develops a perturbative QCD-based power-counting framework to determine the large-$x$ behavior of transverse-momentum dependent quark distributions. By analyzing leading-tree diagrams with three-quark Fock states and accounting for orbital angular momentum interferences, it shows that $k_ot$-even TMDs scale as $(1-x)^3$ while $k_ot$-odd (including Sivers and Boer-Mulders) scale as $(1-x)^4$, with the Sivers function $q_T$ explicitly suppressed by one power relative to the unpolarized distribution. The analysis also clarifies the relation between TMDs and GPDs, compares with GPD $E$, and extends the results to pion distributions, providing concrete guidelines for phenomenological parameterizations. Evolution effects are neglected, but the results highlight the endpoint dynamics and the role of orbital angular momentum in generating SSAs at large $x$. Overall, the paper offers a systematic large-$x$ power-counting map for TMDs that constrains nonperturbative inputs and informs phenomenology of SSAs in SIDIS and related processes.

Abstract

The large-$x$ behavior of the transverse-momentum dependent quark distributions is analyzed in the factorization-inspired perturbative QCD framework, particularly for the naive time-reversal-odd quark Sivers function which is responsible for the single transverse-spin asymmetries in various semi-inclusive hard processes. By examining the dominant hard gluon exchange Feynman diagrams, and using the resulting power counting rule, we find that the Sivers function has power behavior $(1-x)^4$ at $x \to 1$, which is one power of $(1-x)$ suppressed relative to the unpolarized quark distribution. These power-counting results provide important guidelines for the parameterization of quark distributions and quark-gluon correlations.

Figures (4)

• Figure 1: Typical Feynman diagram contributing to the large-x quark distribution in nucleon. The blobs at the left and right sides represent the three-quark light-cone wave function distribution amplitudes of the nucleon.
• Figure 2: Leading diagrams contributing to the $k_\perp$-even quark distributions at large-x: left half of the relevant diagrams are shown. The contributions will the amplitudes square of these diagrams, including the interference between them. These diagrams also contribute to the $k_\perp$-odd and naive time-reversal-odd TMD quark distributions.
• Figure 3: Leading Feynman diagrams contributing to the naive time-reversal-odd TMD quark distributions at large-x.
• Figure 4: Feynman diagrams contribution to the transverse-momentum-dependent quark distribution in Pion at large-x.