Accessing tri-gluon correlations in the nucleon via the single spin asymmetry in open charm production

TL;DR

This paper investigates single transverse-spin asymmetries (SSAs) in open charm production in polarized proton-proton collisions using the QCD collinear twist-3 framework. It includes both twist-3 quark-gluon and tri-gluon correlation functions, derives LO hard parts, and shows that quark-gluon contributions alone yield negligible asymmetries in current RHIC kinematics, making any observed SSA a signal of tri-gluon correlations. By modeling the tri-gluon functions with simple forms $T_G^{(f,d)}(x,x)=\lambda_{f,d} G(x)$, the authors predict sizable $A_N$, with strong dependence on rapidity, transverse momentum, and the relative signs of $\lambda_f$ and $\lambda_d$, and differences between $D$ and $\bar{D}$ production. They argue that measuring SSAs for both $D$ and $\bar{D}$ offers a promising way to disentangle the two tri-gluon correlators and to map multi-gluon spin correlations in the polarized proton, connecting to the gluon Sivers function in the TMD picture and motivating future experimental constraints.

Abstract

We calculate the single transverse-spin asymmetry for open charm production in $pp$ collisions within the QCD collinear factorization approach. We include contributions from both twist-three quark-gluon and tri-gluon correlation functions. We find that the quark-gluon correlation functions alone generate only a very small asymmetry for open charm production in the kinematic region of current interest at RHIC, so that the observation of any significant single-spin asymmetry would be a clear indication of the presence of tri-gluon correlations inside a polarized proton. We furthermore demonstrate that the tri-gluon contribution could be very different for the production of $D$ and $\bar{D}$ mesons. These features make the single spin asymmetry in open charm production in polarized $pp$ collisions at RHIC an excellent probe of tri-gluon correlation functions.

Figures (7)

• Figure 1: Lowest order Feynman diagram for light quark-antiquark annihilation (a) and for gluon-gluon fusion to a pair of heavy quarks.
• Figure 2: Feynman diagrams that give the twist-3 contribution to the spin-dependent cross section in the quark-antiquark annihilation channel: initial-state interaction (a), (b), and final-state interaction (c), (d). The short bar indicates the propagator that produces the unpinched pole.
• Figure 3: Feynman diagrams that give the twist-3 contribution to the spin-dependent cross section in the gluon-gluon fusion channel: initial-state interaction (a), (b), and final-state interaction (c), (d). The short bar indicates the propagator that produces the pole.
• Figure 4: The SSA as a function of rapidity $y$ for $D^0$ meson (left) and $\bar{D}^0$ meson production (right) at $\sqrt{s}=200$ GeV and $P_{h\perp}=2$ GeV. The curves are: solid ($\lambda_f=\lambda_d=0.07$ GeV), dashed ($\lambda_f=\lambda_d=0$), dotted ($\lambda_f=-\lambda_d=0.07$ GeV).
• Figure 5: Same as Fig. \ref{['y_dep']}, but as a function of Feynman-$x_F$.