Heavy-quark bound states in potentials with the Bethe-Salpeter equation

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The spinless Bethe—Salpeter equation is solved for three attractive static quark-antiquark potentials of the form V(r)=−ar−β+brβ+c, 0<β≤1, and the effective non-Coulombic power-law potential of the formV(r)=ar 0.1+c to obtain the spin-averaged energy levels in bottomonium ϒ(b \(\bar b\) ) and charmonium ψ(c \(\bar c\) ) families. The shifted 1/N expansion technique is used. Calculations of the energy eigenvalues are carried out up to third order and parameters of each potential are adjusted to obtain the best agreement with the experimental spin-averaged data (SAD). Flavor-dependent and flavor-independent cases are considered in this work.