Spectroscopy and femtoscopic correlation function of the $B\bar{D}$, $B=(N, Δ)$ system in quark delocalization color screening model

TL;DR

The paper addresses the spectroscopy and scattering of pentaquark states composed of $qqqq\bar{c}$ in the $B\bar{D}$ sector using the quark delocalization color screening model (QDCSM) combined with the resonating-group method (RGM). It computes effective baryon–meson potentials, identifies bound and resonance states across isospin $I=0,1,2$ and spins $J^P=1/2^-,3/2^-,5/2^-$, and translates those predictions into low-energy scattering parameters and femtoscopic correlation functions via the CATS framework. Key findings include a bound $I(J^P)=0(1/2^-)$ state from channel coupling, several $\Delta\bar{D}$ and $\Delta\bar{D}^*$ resonances in the $I(J^P)=1(3/2^-)$ and $1(1/2^-)$ sectors, and pronounced spin-dependent structures in the $I=2$ sector, all of which leave distinctive imprints in the $N\bar{D}$ correlation signals. The results offer concrete predictions for future experiments at ALICE and LHCb and demonstrate a framework to connect quark-level dynamics to femtoscopy observables in heavy-flavor multiquark systems.

Abstract

In this work, we systematically investigate the pentaquark systems with quark contents $qqqq\bar{c}$ with the analyzed total spin and parity quantum numbers of $J^{P}=\frac{1}{2}^{-}$, $J^{P}=\frac{3}{2}^{-}$ and $J^{P}=\frac{5}{2}^{-}$, in the I=0, I=1 and I=2 isospin channels. The effective potentials between baryon and meson clusters are given, and the possible bound states are also investigated. Also, the study of the scattering process of the open channels is performed to identify possible resonance states. Our estimations indicate that several possible bound states and narrow baryon-meson resonances are found from corresponding the calculation processes. Furthermore, to bridge the gap between theoretical predictions and experimental measurement, we also extract the low-energy scattering parameters and compute the femtoscopic correlation functions for the $N\bar{D}$ system using the CATS framework. The results demonstrate that the predicted $I=0$ bound state manifests as a significant enhancement at low momentum accompanied by a characteristic suppression. In contrast, the $I=1$ correlations remain relatively flat as the predicted resonances are kinematically distant from the threshold. The $I=2$ sector exhibits strong spin dependence, where the bound state signal in the $J=1/2^{-}$ channel is largely masked by repulsive components in spin-averaged observables. This cancellation effect suggests that future experimental searches at ALICE and LHCb may require spin-selective measurements to identify such states. These predictions provide crucial theoretical guidance for future experiments.

Figures (9)

• Figure 1: The effective potentials of the $B\bar{D}$ system in QDCSM, and (a) $I=0$, (b) $I=1$, (c) $I=2$.
• Figure 2: The $N\bar{D}$$S-$wave phase shifts with two-channel coupling for the $I(J^{P})=1(\frac{1}{2}^{-})$ system.
• Figure 3: The $N\bar{D}$$S-$wave phase shifts with three-channel coupling for the $I(J^{P})=1(\frac{1}{2}^{-})$ system.
• Figure 4: The $N\bar{D}^{\ast}$$S-$wave phase shifts with two-channel coupling for the $I(J^{P})=1(\frac{3}{2}^{-})$ system.
• Figure 5: The $N\bar{D}^{\ast}$$S-$wave phase shifts with three-channel coupling for the $I(J^{P})=1(\frac{3}{2}^{-})$ system.