Five-body systems with Bethe-Salpeter equations

In a paper led by Gernot Eichmann (Graz U., co-PI), in collaboration with Maria Teresa Peña (IST Lisbon) and Raul Torres (IST Lisbon), we extend the Bethe-Salpeter formalism to systems composed of five valence particles. To make the calculations manageable, we implement properties of the permutation group S5 and construct an approximation based on intermediate two- and three-body poles. We extract the five-body ground and excited states, along with the spectra obtained from the two-, three-, and four-body equations. In the limit of a massless exchange particle, the two-, three-, four-, and five-body states coexist within a certain range of the coupling strength, while for heavier exchange particles, the five-body system becomes Borromean. Our study serves as a foundational step for calculating pentaquark properties using functional methods.

Papers: Phys. Lett. B 866 (2025), 139525; Phys. Rev. D 111 (2025), 094008