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.

Figures (9)

• Figure 1: Real (top) and imaginary (bottom) parts of $G_{\Sigma_c\pi}(s)$ as functions of the total CM energy $\sqrt{s}$ (lower x-axis) and the CM momentum $p$ (upper x-axis). The solid lines represent the loop functions obtained within the SU(4)-WT (green) and the $\Sigma_c\pi$ [WT $\&$ CQM] (orange) renormalization schemes without Coulomb interaction (denoted by $G_{\Sigma_c\pi}(s)$), while the dashed lines show the corresponding results including the repulsive Coulomb interaction (denoted by $G^{\mathrm{Cb}}_{\Sigma_c\pi}(s)$). We take the UV cutoff $\Lambda=650$ MeV in the $\Sigma_c\pi$ [WT $\&$ CQM] case, similar to the one obtained for the SU(4)-WT model ($\Lambda=653$ MeV).
• Figure 2: Strong isotensor $\Sigma_c\pi$$S$-wave phase shift as a function of CM momentum. Orange (green) solid line: predictions of the $\Sigma_c\pi$ [WT $\&$ CQM] model with $\Lambda = 650~\mathrm{MeV}$ (SU(4)-WT model with $\Lambda = 653~\mathrm{MeV}$). Shaded band: phase shift range for the $\Sigma_c\pi$ [WT $\&$ CQM] model when the UV cutoff is varied from 400 to 650 MeV.
• Figure 3: $\Sigma_c^{++} \pi^+$$S$-wave strong phase shift in presence of the Coulomb interaction as a function of CM momentum. Darker orange (green) solid lines: $\Sigma_c\pi$ [WT $\&$ CQM] model with $\Lambda = 650~\mathrm{MeV}$ (SU(4)-WT model with $\Lambda = 653~\mathrm{MeV}$). Shaded band: variation of the $\Sigma_c\pi$ [WT $\&$ CQM] phase shift for UV cutoffs 400–650 MeV. Lighter orange and green lines: phase shifts without Coulomb effects.
• Figure 4: The $\Sigma_c^{++} \pi^+$ CF as a function of the CM momentum, calculated within the $\Sigma_c\pi$ [WT $\&$ CQM] (orange) and SU(4)-WT (green) models, including only the strong interaction, for a source radius of $R = 1~\mathrm{fm}$. For the $\Sigma_c\pi$ [WT $\&$ CQM] model with $\Lambda = 650~\mathrm{MeV}$ in the calculation of the on-shell amplitude, the CFs for source radii $R = 2~\mathrm{fm}$ (dashed) and $R = 5~\mathrm{fm}$ (dotted) are also shown. The band reflects the variations of the $\Sigma_c\pi$ [WT $\&$ CQM] CF, calculated for $R = 1~\mathrm{fm}$, arising from the ambiguities in the on-shell amplitude discussed in Figs. \ref{['fig:PS']} and \ref{['fig:PS_conC']}.
• Figure 5: The same as in Fig. \ref{['fig:CF_sinC']} but including the Coulomb interaction. In addition, we also display the CF for $R=1~\mathrm{fm}$ obtained when only the Coulomb interaction is included (blue curve).