Possibility of the antibottom-strange molecular pentaquarks near $BΣ$ and $B^*Σ$ thresholds

Abstract: The molecular states in coupled channel system of $B_s^0N- BΛ- B^*Λ- BΣ- B<sup>*Σ$ are investigated within one-boson-exchange model that includes $S$-$D$ wave mixing and a tunable short-range $δ(r)$ term. Bound, resonant, and virtual states are searched by analytically continuing the $S$ matrix in the complex energy plane. In the single-channel analysis, the $BΣ$ and $B<sup>*Σ$ systems with $J<sup>P=1/2<sup>-$ and $3/2^-$ are found to be attractive and form three bound states with reasonable cutoff region, corresponding to $1/2^-( BΣ)$, $1/2^-( B^*Σ)$, and $3/2^-( B^*Σ)$. When coupled-channel dynamics is included, these states evolve into near-threshold poles that produce enhancements in the $B_s<sup>0N$, $BΛ$, and $B<sup>*Λ$ invariant mass spectra. The pole below the $B<sup>*Σ$ threshold in the $J<sup>P=1/2<sup>-$ system depends strongly on the treatment of the short-range $δ(r)$ term and becomes a virtual state when this contribution is removed, while the other two resonant poles and their line shapes are only moderately affected. For representative parameter region, the predicted masses of these states lie in the $6.44-6.52$ GeV region and have widths of a few to several MeV. The pole coupling and partial-width analyses indicate that the poles are generated mainly by the $BΣ$ and $B<sup>*Σ$ channels interaction, and their observable signals are expected mainly in the lower open channels $B_s<sup>0N$, $BΛ$, and $B<sup>*Λ$. These results support the existence of near-threshold molecular pentaquark $P_{ \bar b s}$ and provide useful guidance in future experimental searches.

• The paper employs a coupled-channel OBE model to predict antibottom-strange molecular pentaquarks near BΣ and B*Σ thresholds.
• The study shows that the B̅Σ state is robustly bound via long-range meson exchange, while B̅*Σ states are highly sensitive to short-range contact dynamics.
• The predicted masses (6.44–6.52 GeV) and narrow widths indicate observable threshold enhancements in high-luminosity collider experiments.

Antibottom-Strange Molecular Pentaquarks Near $\bar B\Sigma$ and $\bar B^*\Sigma$ Thresholds

Introduction and Motivation

This work performs a detailed theoretical analysis of the possibility of antibottom-strange molecular pentaquark states, denoted as $P_{\bar b s}$, in the energy region near the thresholds of the $\bar B\Sigma$ and $\bar B^*\Sigma$ two-hadron systems. The motivation is grounded in the recent experimental discovery of near-threshold hidden-charm pentaquark states and the mounting evidence for hadronic molecules in the heavy-flavor sector. Since the binding of heavy meson–baryon systems is theoretically more favorable in the bottom sector due to the increased reduced mass, the search for bottom-strange molecular pentaquarks serves as a stringent test of the universality of the molecular interpretation and coupled-channel dynamics in QCD.

Theoretical Framework

Coupled-Channel OBE Model

The coupled-channel system of $B_s^0N$, $\bar B\Lambda$, $\bar B^*\Lambda$, $\bar B\Sigma$, and $\bar B^*\Sigma$ is systematically analyzed using the nonrelativistic Schrödinger equation. The hadron-hadron interactions are modeled by an effective one-boson-exchange (OBE) potential, derived from heavy-quark spin symmetry and SU(3) flavor constraints. The exchanges include the full set of scalar, pseudoscalar, and vector light mesons, with coupling constants determined from phenomenological and experimental data.

A key feature of this study is the explicit inclusion of a short-range $\bar B^*\Sigma$0 (contact) term, whose weight is governed by a tunable dimensionless parameter $\bar B^*\Sigma$1. This allows the assessment of the dependence of near-threshold pole positions and residues on unresolved short-range QCD dynamics and regularization ambiguities.

$\bar B^*\Sigma$2-$\bar B^*\Sigma$3 Mixing and Analytical Continuation

All channels and partial waves relevant for $\bar B^*\Sigma$4 and $\bar B^*\Sigma$5 are included, with special attention to $\bar B^*\Sigma$6-$\bar B^*\Sigma$7 wave mixing that can impact the binding or resonance behavior. Possible bound, virtual, and resonant states are identified by analytic continuation of the coupled-channel $\bar B^*\Sigma$8-matrix into the complex energy plane. The nature of each pole is assessed by its Riemann sheet location, residue structure, and associated channel couplings.

Numerical Results

Single Channel Analysis

The $\bar B^*\Sigma$9 channel with $P_{\bar b s}$0 supports a bound state whose binding mechanism is almost entirely insensitive to the contact parameter $P_{\bar b s}$1, confirming the dominance of long-range (Yukawa-type) meson exchange. In contrast, the $P_{\bar b s}$2 states with both $P_{\bar b s}$3 and $P_{\bar b s}$4 display strong sensitivity to the short-range dynamics controlled by $P_{\bar b s}$5, with the $P_{\bar b s}$6 state becoming shallow or even dissolving depending on the value of $P_{\bar b s}$7.

Coupled-Channel Spectroscopy and Pole Structure

Upon coupling all channels, three near-threshold poles are consistently identified:

• $P_{\bar b s}$8: Appears as a bound state on the physical sheet, predominantly generated by $P_{\bar b s}$9 attraction.
• $\bar B\Sigma$0: Emerges as a state near the $\bar B\Sigma$1 threshold; its existence and nature (resonance vs. virtual state) are highly sensitive to the short-range $\bar B\Sigma$2 term. As $\bar B\Sigma$3 increases (contact repulsion is enhanced), the pole migrates toward the unphysical Riemann sheet, manifesting as a threshold cusp rather than a Breit-Wigner resonance.
• $\bar B\Sigma$4: Also appears as a narrow near-threshold structure, with main component from the $\bar B\Sigma$5 channel. Its decay patterns and amplitude behavior are consistent with $\bar B\Sigma$6-wave molecular dynamics, with significant $\bar B\Sigma$7-wave contributions in coupled decay channels.

The predicted masses of these states lie robustly in the $\bar B\Sigma$8–$\bar B\Sigma$9 GeV range, with widths ranging from a few to several MeV, depending on the regularization and short-range prescription.

Decay Patterns, Partial Widths, and Observability

The detailed residue analysis indicates that while each pole is dominated by its primary forming channel ($\bar B^*\Sigma$0 or $\bar B^*\Sigma$1), the experimentally accessible decay modes are the open lower-threshold channels: $\bar B^*\Sigma$2, $\bar B^*\Sigma$3, and $\bar B^*\Sigma$4. For the $\bar B^*\Sigma$5 state, $\bar B^*\Sigma$6 and $\bar B^*\Sigma$7 are the dominant decay channels, while the higher-mass $\bar B^*\Sigma$8 and $\bar B^*\Sigma$9 decay predominantly to $B_s^0N$0 and $B_s^0N$1.

These features imply that the predicted states should be observable as narrow enhancements or nontrivial line-shape distortions in the invariant-mass spectra of the above channels, particularly in prompt production scenarios at LHC energies, since the predicted mass range lies above all established ground-state bottom hadrons, precluding observation via weak decays.

Implications and Outlook

This work substantiates the theoretical expectation that bottom-strange molecular pentaquarks are plausible and should be searched for near the $B_s^0N$2 and $B_s^0N$3 thresholds. The quantitative sensitivity to short-range physics, encoded via the $B_s^0N$4 parameter, underscores the necessity for rigorous treatment of contact terms and form factors in future hadronic molecule studies. The results support the universality of the heavy-hadron molecular picture in QCD and extend the coupled-channel analysis methodology to the antibottom-strange sector.

On the theoretical side, these findings motivate further studies using alternative models—such as chiral unitary approaches, lattice QCD, or unitarized effective field theory—in order to reduce uncertainties related to phenomenological regularization and short-range dynamics. On the experimental side, targeted searches for threshold enhancements or line-shape distortions in $B_s^0N$5, $B_s^0N$6, and $B_s^0N$7 channels at high-luminosity hadron colliders (e.g., LHCb, CMS, ATLAS) are clearly warranted.

Conclusion

A comprehensive coupled-channel OBE analysis reveals strong theoretical support for the existence of narrow antibottom-strange molecular pentaquarks near the $B_s^0N$8 and $B_s^0N$9 thresholds. The structures are robust against moderate changes in long-range dynamics but can be sensitive to the modeling of short-range QCD effects. The predicted masses and dominant decay modes provide targeted benchmarks for upcoming experimental searches. This work significantly advances the understanding of heavy-flavor hadron spectroscopy and the molecular interpretation of exotic QCD states.