Possibly stable configurations of $Θ^+_5$ in the flux-tube model

Abstract

In this work, following the literature, we investigate the semi-classical picture where various spatial configurations for $Θ^+_5$ were suggested by several authors. We use the flux tube model where the effective Column coefficient and string tension are extracted from the lattice QCD calculations, to obtain the interactions among the constituent quarks, which is later to be taken as an effective potential. It is reasonable to assume that keeping the simple spatial shape, only the breathing mode is considered, thus the whole system is much simplified and described by only one variable. Substituting the potential into the Schrödinger equation, we evaluate the binding energy of the system. We find that each of the configuration has higher symmetries and corresponds to a local minimum of energy and one of them results in a mass which is smaller than the others. It is interesting to notice that with such a very simplified semi-classical picture the minimal value corresponds to a mass of 1530 to 1554 MeV for $Θ^+_5$. The good agreement with the LEPS' data may indicate that such simplified picture indeed reflects physical reality in some sense.