Solution of the Harmonic Plus Modified Yukawa-Kratzer Potential and Mass Spectra of Hidden Charm and Hidden Strange Tetraquark

The approximate solution of the Schrödinger equation in D-Dimensions for Harmonic plus Modified Yukawa-Kratzer potential (HMYKP) is investigated using the Nikiforove-Uvarov (N-U) method. This method is based on solving the second-order linear differential equation by reducing it to a generalized equation hypergeometric type by a suitable variable change. We studied the four-quark systems with the \(cs\bar{c}\bar{s}\) , \(cq\bar{c}\bar{q}\) quark structures within the framework of the non-relativistic quark model. The HMYKP is written as 1 \(\begin{aligned} V(r)= a_1r^2+\frac{a_2 e^{-2\alpha r}}{r^2} -\frac{a_3 e^{-\alpha r}}{r}+a+D_e-\left( \frac{A_1}{r}-\frac{A_2}{r^2}\right) \end{aligned}\) Using HMYKP new analytical exact energy eigenvalue and eigenfunction were obtained in fractional form using the N-U approach. We have used a heavy-light tetraquark system to verify the method’s applicability and we have recalculated their mass spectra and fractional radial wave. The obtained mass spectra have been compared to experimental data and also found to improve in another comparison with other studies apart from that we also calculate heavy-heavy and heavy-light flavored meson mass spectra. We conclude that the N-U method plays a good role in hadron physics.