Heavy-Quark Spin Symmetry Violation effects in Charmed Baryon Production

In this work, we investigate the Heavy-Quark Spin Symmetry (HQSS) exhibited in the effective Lagrangians governing the three-point interactions of $D$ mesons, charmed baryons, and nucleons. We first construct the effective Lagrangians, and there are 12 distinct terms. As a result, we observe that the invariant Lagrangian under HQSS manifests exclusively in the pseudoscalar $D$ mesons coupling to nucleons and $\Lambda_c$ baryons, whereas nucleons and $\Sigma_c$ ($\Sigma_c^*$) baryons only couple with vector $D$ mesons. By taking into account the violated heavy-quark spin transformation, one can recover all interactions from the effective Lagrangians. Furthermore, we compute the differential cross-sections of the $p\bar p \to Y_c\bar{Y}_c'$ scatterings, where $Y_c,\bar{Y_c}' = \Lambda_c,~\Sigma_c,~\Sigma_c^*$, to reveal the residue of the violating HQSS (VHQSS) on charmed baryon production. Ultimately, by accounting for VHQSS, we aim for precise predictions of production rates, which are essential for the High-Energy Storage Ring (HESR) experiments at the Facility for Antiproton and Ion Research (FAIR).