Nonrelativistic quark model for mass spectra and decay constants of heavy-light mesons using conformable fractional derivative and asymptotic iteration method

Abstract

In this paper, we use the concept of conformable fractional derivative to study the nonrelativistic radial Schrödinger equation. We suggest an extended version of the Cornell potential as the quark–antiquark interaction of light and heavy mesons. We generalize the asymptotic iteration method to the fractional domain. The latter is used to calculate the energy eigenvalues, as well as the effect of the fractional order [Formula: see text] on energy spectra. To test the applicability of our model, we use the obtained results to reproduce the mass spectra of some light and heavy mesons such as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] quarks. The mass spectra are obtained at different values of the fractional order parameter [Formula: see text] and were compared with experimental results and other relevant theoretical works. Using the wave function, we calculated the decay constants for heavy-light [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] mesons. Our results are found to be in good agreement with the experimental data, and improved in comparison with other theoretical previsions.