Probing $ φ$N interaction through bound states of $ φ\textrm{N-}α$ system

TL;DR

This work investigates the existence of φN–α bound states within a three-body φN–α cluster framework, contrasting single-channel φN potentials from lattice QCD with coupled-channel φN interactions from chiral Lagrangians. By constructing φα potentials through a single-folding procedure and an optical-model approach, and modeling Nα with Gaussian and Woods–Saxon forms, the authors solve the three-body problem using hyperspherical harmonics. They find that a φNα bound state is possible under a pure single-channel φN interaction, with central binding energies up to about $B_3\sim$10–25 MeV depending on channel, but the vector-baryon coupled-channel dynamics consistent with experimental φp data eliminates the bound state. This indicates that coupled-channel effects are essential in predicting mesic nuclei and must be incorporated in interpretations of φ-meson binding in nuclei. The results provide guidance for future experiments targeting φ-mesic systems and underscore the sensitivity of few-body bound states to the underlying two-body interaction structure.

Abstract

The possible bound state of the $ φN α$ system is explored within the framework of the three-body cluster model. The calculations are done by employing the state-of-the-art $ φ$N interactions obtained from the analysis of the pure elastic scattering and the coupled-channel in the $φp$ correlation functions. The $ φα$ potentials are constructed by two methods: the single-folding potential (SFP) method for the given spin-averaged $ φ$N potentials in coordinate space, and the optical model potential (OMP) approximation within the multiple-scattering framework for the given scattering length of the $ φ$N interaction. It is found that, when only the single-channel $ φN$ interactions are employed, the $ φN α$ system could be bound with a binding energy in the interval [3-26] MeV. However, the coupled-channel $φp$ interaction, which is most consistent with experimental measurements, does not yield any bound state, even when the spin-averaged $φN$ potential is employed, and this potential is found to be more attractive than the corresponding coupled-channel counterpart. It is essential to consider the contributions from the dynamics of the vector-baryon coupled channels $φp$ interaction. This effect is capable of playing a decisive role in the existence of mesic nuclei.

Figures (3)

• Figure 1: The Jacobi T-coordinate system used to describe the $_{\phi}^{6}\textrm{He}$ mesic nuclei as $\phi\textrm{N-}\alpha$.
• Figure 2: The spin-averaged $\phi$N potential in Eq. \ref{['eq:spin-ave']}, as a function of separation $r$ for lattice Euclidean times $t/a= 12$ (blue solid line), and $14$ (red dashed lines) by the parameters given in Table \ref{['tab:Fit_para']}.
• Figure 3: The spin-averaged $\phi \alpha$ potential in Eq. \ref{['eq:ws-fit']} as a function of separation $r$ for lattice Euclidean time $t/a= 12$ (blue solid line), and $14$ (red dashed lines) by the parameters given in Table \ref{['tab:phi-alpha-para']}. The $\phi \alpha$ potential, obtained from the OMP approximation as given by Eq. \ref{['eq:optical_pot_final']}, is based on $a_{0} = 0.85$ fm (dotted purple lines) extracted by the ALICE collaboration in PhysRevLett.127.172301 and on $a_{0} = 0.272$ fm (dash-dotted green lines) obtained from the theoretical coupled-channel approach within the chiral Lagrangian method FeijooPRD2025.