Heavy flavor baryons containing single and double charm (beauty) quarks with light flavor combinations are studied using the hypercentral description of the three-body problem. The confinement potential is assumed as hypercentral Coulomb plus power potential with power index e???. The ground state masses of the heavy flavor, $J^{P} = dfrac{1}{2}^{+}$ and $dfrac{3}{2}^{+}$ baryons are computed for different power indices, e??? starting from 0.5 to 2.0. The predicted masses are found to attain a saturated value in each case of quark combinations beyond the power index e??? = 1.0.
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