Single spin asymmetry in forward pA collisions: Phenomenology at RHIC

Abstract

We confront the theoretical result of single spin asymmetry (SSA) AN in forward pA collisions p ↑ A → hX including the gluon saturation effect with the recent preliminary experimental data from the PHENIX and STAR collaborations at RHIC. While we find overall reasonable agreement with the STAR data, our results indicate that the strong nuclear suppression of the asymmetry AN ∼ A −1/3 observed by the PHENIX collaboration cannot be explained within the present understanding of this problem.

Nuclear Dependence of the Transverse Single-Spin Asymmetry in the Production of Charged Hadrons at Forward Rapidity in Polarized p+p , p+Al , and Aidala1, Akiba2, Alfred3 et al. 2019Phys. Rev. Lett.

“…The dynamics of gluons in the small-x regime, where the gluon density is predicted to increase drastically, can be described by the color-glass condensate (CGC) formalism [39] at the saturation scale Q s , where Q 2 sA ∝ A 1/3 for the target nucleus [40,41]. In recent years, substantial attention has been given to an interplay between small-x physics and spin physics by studying TSSAs in transversely-polarized proton and ion collisions (p ↑ +A) and gluon saturation effects in a nucleus are taken into account for various calculations of TSSAs in p ↑ +A collisions [40][41][42][43][44][45][46][47][48][49][50][51]. An A-dependence of TSSAs can arise from the A-dependence of Q s when the probe is at or below Q s , while TSSAs are expected to be A-independent at higher scales [42,43,[49][50][51].…”

“…The recent efforts to calculate A N in p ↑ +p and p ↑ +A collisions, accounting for gluon saturation effects [30,[49][50][51] suggested that A N could be A-independent or A −1/3dependent for the different contributions to A N in the region where p T < Q s . However, p T ∼ 2.9 GeV/c in our results is much larger than the saturation scale in the Au nucleus (Q Au s ∼ 0.9 GeV) for the kinematics of this measurement and would lead to no strong A dependence of TSSAs under these models, as calculated in Ref.…”

Exact relations for twist-3 gluon distribution and fragmentation functions from operator identities

“…This relation is independent from (15) and (22), and the three relations (15), (22) and (28) allow one to solve ∆G 3T (x), ∆H 3T (x) and ∆G (1) T (x) in terms of ∆G(x) and the dynamical functions. Here we comment on the relations obtained from operator identities other than (23).…”

“…As we found in previous subsections, eqs. (15), (22) and (28) constitute a complete set of the independent relations among the twist-3 intrinsic, kinematical and dynamical DFs. Here we provide a solution for the intrinsic and kinematical functions in terms of the twist-2 and dynamical twist-3 DFs.…”

“…Actually we can make a short cut. Since they are in parallel with (15), (22) and (28) for the gluon distributions ∆G 3T (x), ∆G (1) T (x) and ∆H 3T (x), we can read off the desired results from (34), (35) and (36) by a simple replacement. The results read…”