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Spectrum of Binding System for Heavy Quark (Q) with an Anti-sbottom or for a Sbottom and Anti–sbottom Pair

Since long-lived light bottom squark (sbottom) and its anti-particle with a mass close to the bottom quark have not been excluded by experiments so far, so we would like to consider such a sbottom to combine with its anti-particle to form a color singlet meson-like bound state or to combine with a common anti-quark to form a fermion-like one, or accordingly their anti-particles to form an anti-particle bound system. Namely we calculate the low-lying spectrum of the systems specifically based on QCD inspired potential model. To be relativistic as much as possible, we start with the framework of Bethe–Salpeter (BS) equation even for non-relativistic binding systems. Finally, we obtain the requested spectrum by constructing general forms of the BS wave functions and solving the BS equations under instantaneous approximation.