Hidden Bottom Pentaquark in the SU(5) Version of the Flavor-Spin Model

Abstract

We generalize to five distinct flavors the flavor-spin hyperfine interaction introduced previously for four flavors and used in the study of \(uudc{\overline{c}}\) pentaquark. As a particular case here we study the lowest states of the pentaquark \(uudb{\overline{b}}\), of either positive or negative parity, in a constituent quark model with linear confinement and the presently extended hyperfine interaction. The positive parity states have one unit of angular momentum located in the subsystem of four quarks and are described by translationally invariant states of orbital permutation symmetry \([31]_O\) which requires the configuration \(s^3 p\). The negative parity states are described by the configuration \(s^4\) of permutation symmetry \([4]_O\). We show that the lowest state has the quantum numbers \(J^P\) = \(1/2^+\) or \(3/2^+\) and I = 1/2 and is located below the \(\Sigma _b B\) threshold by \(-\) 132 MeV. We present a comparison between the spectra of \(uudc{\overline{c}}\) and \(uudb{\overline{b}}\) pentaquarks.