Gluonic Pole Cross Sections and Single Spin Asymmetries in Hadron-Hadron Scattering

TL;DR

This paper develops a formalism to describe single spin asymmetries in hadron-hadron scattering using gluonic pole cross sections, which arise from process-dependent gauge-links in TMD correlators. By decomposing TMDs into tilde (T-even) and gluonic-pole (T-odd) parts with diagram-dependent gluonic pole strengths C_G, the authors show how SSA can be written as convolutions with gluonic pole cross sections across quark and gluon channels. They provide the complete set of gluonic pole factors for 2→2 processes and illustrate the method with back-to-back pion production in polarized pp collisions, highlighting how Sivers- and Collins-type effects couple to the hard parts via C_G. The framework clarifies the role of color flow and gauge-links in SSA, offering a calculable, tree-level approach that can guide predictions for hadron-hadron experiments (e.g., RHIC), while noting the need for factorization proofs in these more complex processes.

Abstract

The gauge-links connecting the parton field operators in the hadronic matrix elements appearing in the transverse momentum dependent distribution functions give rise to T-odd effects. Due to the process-dependence of the gauge-links the T-odd distribution functions appear with different pre-factors. A consequence is that in the description of single spin asymmetries the parton distribution and fragmentation functions are convoluted with gluonic pole cross sections rather than the basic partonic cross sections. In this paper we calculate the gluonic pole cross sections encountered in single spin asymmetries in hadron-hadron scattering. The case of back-to-back pion production in polarized proton-proton scattering is worked out explicitly. It is shown how T-odd gluon distribution functions originating from gluonic pole matrix elements appear in twofold.

Figures (5)

• Figure 1: The gauge-link structure in the correlator $\Phi$ in (a) SIDIS: $\mathcal{U}^{[+]}$ and (b) DY: $\mathcal{U}^{[-]}$.
• Figure 2: We encounter three different types of gluonic pole matrix elements (GPME's): the quark-GPME $\Phi_G{=}(\Phi_G)_{rs}^a(t^a)_{sr}{=}\mathop{\mathrm{Tr}}\nolimits[\Phi_G^at^a]$ and the two gluon-GPME's $\Gamma_G^{(f)}{=}\Gamma_G^{abc}(t^a)_{cb}{=}\Gamma_G^{abc}if^{abc}$ and $\Gamma_G^{(d)}{=}\Gamma_G^{abc}d^{abc}$. The $d^{abc}$ and $f^{abc}$ are the symmetric and antisymmetric structure constants of $SU(3)$: $t^at^b{=}\frac{T_F}{N}\delta^{ab} {+}\frac{1}{2}\left(d^{abc}{+}if^{abc}\right)t^c$.
• Figure 3: A contribution to $qg{\rightarrow}qg$ scattering (a) and some collinear gluon insertions (b)-(d).
• Figure 4: Ratios of gluonic pole cross sections and partonic cross sections for some gluonic pole cross sections associated with quarks. They are plotted as functions of the variable $y{\equiv}{-}\hat{t}/\hat{s}$ for $N{=}3$ (solid line) and $N{\rightarrow}\infty$ (dashed line).
• Figure 5: The leading order contribution to the cross section of $H_1{+}H_2\rightarrow h_1{+}h_2{+}X$.