Tri-meson bound state $BB{B}^{\ast }$ via delocalized $\pi$~Bond

Abstract

During the last decades, numerous exotic states which cannot be explained by the conventional quark model have been observed in experiment. Some of them can be understood as two-body hadronic molecules, such as the famous $X(3872)$, analogous to deuteron in nuclear physics. Along the same line, the existence of the triton leaves an open question whether there is a bound state formed by three hadrons. Since, for a given potential, a system with large reduced masses is more easier to form a bound state, we study the $BB{B}^{\ast }$ system with the one-pion exchange potential as an exploratory step by solving the three-body Schrödinger Equation. We predict that a tri-meson molecular state for the $BB{B}^{\ast }$ system is probably existent as long as the molecular states of its two-body subsystem $B{B}^{\ast }$ exist.

20 pages, 20 figures