Single transverse-spin asymmetries at large $x$

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.

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 be the amplitudes squared 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 $x$.