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

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.

💡 Research Summary

The paper presents a comprehensive theoretical study of the isospin‑2 Σ_c^{++}π^{+} and its heavy‑flavor counterpart Σ_b^{+}π^{+} systems, focusing on low‑energy scattering observables and femtoscopic correlation functions (CFs). Two distinct strong‑interaction frameworks are employed. The first is an SU(4)‑symmetric approach that uses the leading‑order Weinberg‑Tomozawa (WT) chiral interaction as the kernel of an on‑shell Bethe‑Salpeter equation (BSE). A sharp momentum cutoff Λ regularizes the loop integrals; Λ is fixed by reproducing the masses of the Λ_c(2595) and Λ_b(5912) resonances, yielding Λ≈650 MeV for the charm sector and Λ≈653 MeV for the bottom sector. The second framework augments the WT interaction with an explicit constituent‑quark‑model (CQM) state exchanged in the Σ_cπ channel. Here the loop function is split into a finite part and a UV‑divergent part; only the divergent piece is regularized, which reduces cutoff artefacts. The CQM parameters (coupling d_c and bare mass) are tuned together with Λ to reproduce the Λ_c(2595) pole, leading to two representative sets: (d_c=0.69, Λ=650 MeV) and (d_c=1.15, Λ=400 MeV).

Both models predict a repulsive interaction in the I=2 channel because the WT coefficient C_WT=+2. The differences between the models arise solely from the regularization scheme: the SU(4)‑WT loop function shows a stronger momentum dependence above ~200 MeV, while the WT + CQM scheme yields a smoother behaviour. Consequently, the S‑wave phase shift δ(p) is nearly identical at low momenta but diverges modestly at higher momenta, with the SU(4)‑WT giving slightly larger phases.

Coulomb repulsion between the two positively charged hadrons is incorporated using relativistic Coulomb wave functions. Its impact on the scattering length and effective range is modest (≈0.1 fm increase). However, in the femtoscopic CF the Coulomb effect dominates: the CF is strongly suppressed (values below ~0.5) and the sensitivity to the underlying strong interaction is dramatically reduced. When only the strong force is considered, the CF clearly distinguishes between the two models; once the Coulomb interaction is added, the discriminating power essentially disappears.

The analysis is repeated for the Σ_b^{+}π^{+} system. By fixing the UV cutoff to the Λ_b(5912) resonance, the authors find that scattering lengths, effective ranges, and CF shapes in the bottom sector closely mirror those in the charm sector, in line with expectations from heavy‑quark flavor symmetry (HQFS). This similarity reinforces the notion that HQFS can be used to relate charm and bottom hadron interactions.

Overall, the work provides detailed predictions for phase shifts, low‑energy parameters, and femtoscopic correlation functions for two experimentally accessible channels. It highlights how the choice of UV regularization influences strong‑interaction observables, while also demonstrating that electromagnetic repulsion can mask these effects in CF measurements. The results serve as a benchmark for future experimental studies at the LHC or other high‑luminosity facilities, where measuring Σ_c^{++}π^{+} and Σ_b^{+}π^{+} CFs could test the theoretical frameworks, probe the role of UV renormalization, and assess the validity of heavy‑quark symmetry in the non‑perturbative regime.