The exotic particles such as the pentaquarks are to strengthen understanding of important interactions and the principle of QCD in which pentaquarks contain two heavy- valence quarks. The structure of two bodies including an antiquark and two-diquark is introduced. A new potential for quark interaction is suggested which includes the logarithm potential, the linear potential, and the spin-spin interaction. The suggested potential is included in the framework of spinless of Bethe-Salpeter equation. A comparison with other works is presented which provides a good description of pentaquarks.

In this paper, the new analytic–exact energy eigenvalues and eigenfunctions are obtained in the fractional forms by using the extended Nikiforov–Uvarov approach in which the heavy diquark systems are described. We have recalculated the mass spectra and fractional radial wave of heavy tetraquarks. The mass spectra are compared to the experimental data. The present results show a good agreement with the experimental data and are improved in comparison with other studies. We conclude that the fractional models play a good role in the heavy tetraquark masses.

Masses and decay width for some heavy baryons are studied within Isgur–Wise formalism. The extended Cornell potential is employed. The hyper-radial Schrödinger equation with extended Cornell potential is solved to obtain eigenvalues of energy and baryonic wave function by using the extended iteration method. Masses and the rate of decay width for some heavy baryons are calculated. The present results are improved in comparison with other recent works and are in a good agreement with experimental data.

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