The charmonium and bottomonium mass spectroscopy with a simple approximaton of the kinetic term

Abstract

In this paper we propose a particular description of meson spectroscopy, with emphasis in heavy bound states like charmonia and bottomonia, after working on the main aspects of the construction of an effective potential model. We use the prerogatives from ``soft QCD'' to determine the effective potential terms, establishing the asymptotic Coulomb term from one gluon exchange approximation. At the same time, a linear confinement term is introduced in agreement with QCD and phenomenological prescription. The main aspect of this work is the simplification in the calculation, consequence of a precise and simplified description of the kinetic term of the Hamiltonian. With this proposition we perform the calculations of mass spectroscopy for charmonium and bottomonium mesons and we discuss the real physical possibilities of developing a generalized potential model, its possible advantages relative to experimental parameterization and complexity in numerical calculations.