Scattering and Femtoscopic Correlation Functions of the $\hat{I}{\pounds }_c^{++}\ddot{I}{€}^{+}$, $\hat{I}{\pounds }_c^0\ddot{I}{€}^{-}$ and $\hat{I}{\pounds }_b^{+}\ddot{I}{€}^{+}$ Systems

Abstract

We present predictions for scattering observables and femtoscopic correlation functions (CFs) of the $I=2$ $\hat{I}{\pounds }_c^{++}\ddot{I}{€}^{+}$, $\hat{I}{\pounds }_c^0\ddot{I}{€}^{-}$ systems and its heavy-flavor counterpart $\hat{I}{\pounds }_b^{+}\ddot{I}{€}^{+}$. In both heavy-quark 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, $\hat{I}{›}_c(2595)$ and $\hat{I}{›}_b(5912)$, respectively. While the $\hat{I}{\pounds }_c^0\ddot{I}{€}^{-}$ pair is governed solely by the strong interaction, electrostatic contributions are included in the other two channels involving charged particles through 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 $\hat{I}{\pounds }_c^{++}\ddot{I}{€}^{+}$ and $\hat{I}{\pounds }_b^{+}\ddot{I}{€}^{+}$ 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. Thus, the $\hat{I}{\pounds }_c^0\ddot{I}{€}^{-}$ CF-being free from Coulomb effects-provides the most suitable observable for constraining the strong dynamics of the isotensor $\hat{I}{\pounds }_c\ddot{I}€$ system.

13 pages, 9 figures, 1 table, discussion extended including the $\hat{I}{\pounds }_c^0\ddot{I}{€}^{-}$ channel, accepted version for publication in Physics Letters B