Charm Sivers function at the EicC

The Electron-Ion Collider in China (EicC) is pivotal in enhancing our knowledge of the internal structure of nucleons and nuclei, particularly through the study of transverse momentum-dependent parton distributions (TMDs). Among the leading-twist TMDs, the Sivers function is of particular interest, as it provides crucial insights into the spin and momentum structure of hadrons and plays a significant role in describing transverse single-spin asymmetries (SSAs) in high-energy scatterings. In this study, we focus on the theoretical framework and phenomenological implications of the Sivers function in the context of small-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> physics, where it is intricately connected to the spin-dependent QCD odderon, demonstrating that the SSA can be expressed in terms of transverse momentum-dependent factorization within the Color Glass Condensate effective theory. Furthermore, we present simulation results using PythiaeRHIC to assess the feasibility of measuring the charm quark Sivers function at the EicC. The simulation outcomes suggest that the EicC, with its unique kinematic coverage, offers distinct advantages for probing the Sivers function, which would provide compelling evidence for the existence of the elusive spin-dependent odderon.