Soft-fermion-pole contribution to single-spin asymmetry for pion production in pp collisions

Abstract

We study the single transverse spin asymmetry for the inclusive pion production in the nucleon-nucleon collision, p^\uparrow p\toπX, based on the twist-3 mechanism in the collinear factorization. We derive the soft-fermion-pole (SFP) contribution to the twist-3 single-spin-dependent cross section associated with the twist-3 quark-gluon correlation functions in the polarized nucleon. We find that the SFP can give rise to a large effect to the asymmetry A_N owing to the large partonic hard cross sections with the large color factor, if the SFP function has a similar magnitude as the soft-gluon-pole (SGP) function, in spite of the absence of the "derivative term" for the SFP function unlike for the SGP function.

Figures (9)

• Figure 1: General structure of the cut diagrams for the twist-3 cross section for $p^\uparrow p\to\pi X$ associated with the twist-3 quark-gluon correlation function in the polarized nucleon. Left (right) diagram represents contribution with the unpolarized quark (gluon) distribution in the unpolarized nucleon.
• Figure 2: Typical examples of the cut diagrams for the SFP hard part, $S_\alpha^{\rm SFP}$ in (\ref{['sfpformula']}). In (a), two quark-lines coming from the polarized nucleon are in the opposite side of the cut, while in (b) they are in the same side of the cut. The bared internal line in each diagram generates SFP. Momentum for each line is defined as in Fig. 1 with $k_i=x_ip$. In this example, the coherent gluon line can attach at three different places of each diagram without it, and those three are represented by a single one shown in the right where the positions of the gluon-attachment are represented by the numbered dots (1),(2) and (3).
• Figure 3: Diagrams for the SFP contribution of the type shown in Fig. 2(a) in the quark (or anti-quark) fragmentation channel with the unpolarized quark (or anti-quark) distribution. The propagator with a bar gives an SFP. The parton $c$ fragments into the final pion. The solid vertical line without an arrow represents the final state cut. The mirror diagrams also contribute.
• Figure 4: Diagrams for the SFP contribution of the type shown in Fig. 2(b) in the quark (or anti-quark) fragmentation channel with the unpolarized quark (or anti-quark) distribution. See the caption to Fig. 3.
• Figure 5: Diagrams for the SFP contribution of the type shown in Fig. 2(b) in the gluon fragmentation channel with the unpolarized quark (or anti-quark) distribution. See the caption to Fig. 3.