A New Mechanism for Generating a Single Transverse Spin Asymmetry

TL;DR

The study addresses the origin of single transverse spin asymmetries (STSA) in high-energy polarized hadron collisions by introducing a mechanism within the Color Glass Condensate framework in which a transversely polarized quark splits to a quark and gluon, $q^{\uparrow} \to qG$, and interacts with the target via a $C$-odd odderon exchange alongside a $C$-even interaction. The authors derive general expressions for STSA in quark, gluon, and photon production, showing that a nonzero asymmetry requires both $C$-odd and $C$-even exchanges and that the effect vanishes for prompt photons. In a quasi-classical evaluation, they find qualitative agreement with observed trends—STSA is non-monotonic in transverse momentum $k_T$, peaks near the saturation scale $Q_s$, and grows with the projectile’s $x_F$—and predict a strong suppression of STSA in proton-nucleus relative to proton-proton collisions. The work highlights a distinct, odderon-driven mechanism for STSA, offering a potential path to direct odderon observations while outlining necessary phenomenological refinements and higher-order corrections for quantitative comparisons.

Abstract

We propose a new mechanism for generating a single transverse spin asymmetry (STSA) in polarized proton-proton and proton-nucleus collisions in the high-energy scattering approximation. In this framework the STSA originates from the q->q G splitting in the projectile (proton) light-cone wave function followed by a perturbative (C-odd) odderon interaction, together with a C-even interaction, between the projectile and the target. We show that some aspects of the obtained expression for the STSA of the produced quarks are in qualitative agreement with experiment: STSA decreases with decreasing projectile x_F and is a non-monotonic function of the transverse momentum k_T. In our framework the STSA peaks at k_T near the saturation scale Q_s. Our mechanism predicts that the quark STSA in proton-nucleus collisions should be much smaller than in proton-proton collisions. We also observe that in our formalism the STSA for prompt photons is zero.

Figures (16)

• Figure 1: A sketch of the geometry of polarized scattering: the incoming transversely-polarized projectile is moving along the $+z$-axis, while its spin is pointing along the $+x$-axis. The positive $y$-axis points to the right of the beam.
• Figure 2: Experimental data on the pion single transverse spin asymmetry $A_N$ as a function of Feynman-$x$ reported by E581 and E704 collaborations (graphically reconstructed from Adams:1991cs, shown in the left panel) for $0.7 \le k_T \le 2.0$ GeV/c, and as a function of the pion transverse momentum $k_T$ collected by the STAR collaboration Abelev:2008qb (right panel).
• Figure 3: Sketch of the three potential sources of asymmetry: in the parton distribution function via the Sivers effect, via partonic interaction, or in the fragmentation function via the Collins effect.
• Figure 4: Recent preliminary data from the STAR collaboration (graphically reconstructed from Poljak:2010tm) for the $\pi^0$ asymmetry within final-state jets as a function of the angle $\gamma$ between the outgoing pion and the jet thrust axis. The Collins contribution is proportional to the slope of the data, and is consistent with zero.
• Figure 5: Transversely polarized quark scattering in the field of the nucleus producing either a quark ($q$), gluon ($G$), or a prompt photon ($\gamma$) along with extra hadrons denoted by $X$: $q^{\uparrow} + A \rightarrow (q, \, G, \, \gamma) + X$.