Single transverse-spin asymmetry for $D$-meson production in semi-inclusive deep inelastic scattering

TL;DR

This paper demonstrates that the single-transverse spin asymmetry (SSA) for open charm production in SIDIS, at sufficiently large transverse momentum, is directly proportional to the diagonal tri-gluon correlation function $T_G(x,x)$ within the QCD collinear factorization framework. It derives the twist-three gluonic contribution to the SSA, revealing both derivative and non-derivative hard parts and showing that soft-pole dynamics select $x_1=x_2=x$, with potential inclusion of a secondary correlator $\tilde{T}_G(x,x)$ depending on color neutralization. Using a simple model $T_G(x,x)=\lambda_g G(x)$, the authors estimate SSAs for COMPASS and eRHIC kinematics, finding sizable asymmetries (order 5–10%), a minimum near $z_h\approx0.5$, and characteristic dependence on $z_h$ and $P_{h\perp$; they also discuss extracting information on both $T_G$ and $\tilde{T}_G$ by comparing $D$ and $\bar{D}$ production. The work highlights SIDIS as a clean probe of gluon transverse-spin structure beyond conventional PDFs, with implications for understanding multi-parton correlations in hadrons and guiding future experimental extractions of tri-gluon dynamics.

Abstract

We study the single-transverse spin asymmetry for open charm production in the semi-inclusive lepton-hadron deep inelastic scattering. We calculate the asymmetry in terms of the QCD collinear factorization approach for $D$ mesons at high enough $P_{h\perp}$, and find that the asymmetry is proportional to the twist-three tri-gluon correlation function in the proton. With a simple model for the tri-gluon correlation function, we estimate the asymmetry for both COMPASS and eRHIC kinematics, and discuss the possibilities of extracting the tri-gluon correlation function in these experiments.

Figures (7)

• Figure 1: Kinematics of the SIDIS process in hadron frame.
• Figure 2: A typical diagram that gives a non-vanishing contribution to the SSA.
• Figure 3: Feynman diagrams that give the twist-three contribution to the spin-dependent cross section. The short bar indicates the propagator that produces the pole. The letters, $A,B$ and $C$, represent the color of the initial-state gluons.
• Figure 4: The fully differential unpolarized cross section for $D^0$ production in SIDIS for COMPASS kinematics. The curves represent: $\sigma_0^U$(solid), $\sigma_1^U$(dashed), and $\sigma_2^U$(dotted) in Eq. (\ref{['angulardis']}).
• Figure 5: The fully differential unpolarized cross section for $D^0$ production in SIDIS at the future eRHIC. The curves represent: $\sigma_0^U$(solid), $\sigma_1^U$(dashed), and $\sigma_2^U$(dotted) in Eq. (\ref{['angulardis']}).