Single Spin Asymmetry Scaling in the Forward Rapidity Region at RHIC

TL;DR

The paper addresses forward-region hadron production and single transverse spin asymmetries at RHIC within a color-glass-condensate framework. It combines spin-averaged cross sections that exhibit geometric scaling with a Collins-function–driven SSA to model $A_N$, deriving scaling forms and bounding the asymmetries with current transversity and Collins constraints. The study finds that forward RHIC data show scaling in $P_{h\top}^2/Q_s^2(x_2)$, and that the Collins mechanism within CGC can generate sizable $A_N$, with a double ratio $A_N^{pA}/A_N^{pp}$ at small $P_{h\top}$ providing a probe of the nuclear saturation scale. These results offer a practical framework to extract the saturation scale and to constrain quark transversity and Collins-function evolution using RHIC forward data and, potentially, LHC measurements.

Abstract

We investigate the scaling properties in inclusive hadron production and the associated single transverse spin asymmetry in the forward rapidity region at RHIC. We find that the spin-averaged experimental data in both $pp$ and $dAu$ collisions demonstrates a transverse-momentum-dependent geometric scaling. We introduce the transverse momentum dependent Collins fragmentation function to study the scaling of the single transverse spin asymmetries. The general feature of the scaling analysis is consistent with the experimental observations, in particular, for the transverse momentum dependence of the spin asymmetries at RHIC energy. We further propose to probe the saturation scale of nucleus by measuring the spin asymmetry normalized by that in $pp$ scattering at low transverse momentum.

Figures (4)

• Figure 1: Geometric scaling of the differential cross sections (left) and the nuclear modification factor $R_{\rm dAu}$ (right) plotted as a function of $P_{h\perp}^2/Q_s^2$. Data are from BRAHMS Arsene:2004ux and STAR Adams:2006uz Collaborations at RHIC.
• Figure 2: Left: $P_{h\perp}$-dependence of the single spin asymmetry. We use Eq. (\ref{['lowpt']}) to fit the STAR experimental data :2008qbDrachenberg:2009nd. Right: We plot $A_N e^{\delta^2P_{h\perp}^2/Q_s^4} e^{(1+2\lambda)y}$ as a function of $x_F$ - the generalized $x_F$-scaling for the single spin asymmetry according to Eq. (\ref{['xfscaling']}). We have chosen $\delta=0.16$ GeV to demonstrate the scaling. The data is from STAR :2008qb.
• Figure 3: The comparison with the STAR experimental data at $\sqrt{s}=200$ GeV for rapidity $y_h=3.3$ (left) and $y_h=3.7$ (right). The solid lines are using the transversity from Martin:1997rzVogelsang:2005cs and the Collins function from Yuan:2008tvVogelsang:2005cs. The dashed curves are the upper bound as explained in the text.
• Figure 4: The comparison with BRAHMS experimental data at $\sqrt{s}=200$ GeV. The curves are the same as explained in Fig. \ref{['starxf']}.