Scattering and Femtoscopic Correlation Functions of the $Σ_c^{++}π^{+}$ and $Σ_b^{+}π^{+}$ Systems

Abstract: We present predictions for scattering observables and femtoscopic correlation functions (CFs) of the $I=2$ $Σ_c^{++}π^{+}$ system and its heavy-flavor counterpart $Σ_b^{+}π^{+}$. In both sectors, the strong interaction is formulated within two distinct theoretical frameworks, each constrained to reproduce the lowest-lying odd-parity isoscalar spin-$1/2$ resonances, $Λ_c(2595)$ and $Λ_b(5912)$, respectively. Electrostatic contributions are incorporated by means of relativistic Coulomb wave functions. We show that the differences observed in the scattering observables between the two strong-interaction models arise mainly from the specific ultraviolet regularization schemes employed. The inclusion of Coulomb effects induces only a very small increase in both the scattering length and the effective range. The resulting CFs in the charm and bottom sectors display analogous global features, in agreement with expectations from heavy-quark flavor symmetry. Both, the $Σ_c^{++}π^+$ and $Σ_b^{+}π^{+}$ CFs, when computed including only the strong interaction, exhibits substantial discriminating power among the different models. However, once Coulomb effects are incorporated, the CFs become largely affected by the repulsive electrostatic interaction, which diminishes their sensitivity to the details of the underlying strong dynamics, thereby reducing the capability to differentiate between theoretical descriptions.