Abstract

MANZOOR, R.; AHMED, J.  and  RAYA, A.. A new variational approach and its application to heavy quarkonia. Rev. mex. fis. [online]. 2021, vol.67, n.1, pp.33-53.  Epub Jan 31, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.67.33.

By combining the variational principle with Heisenberg uncertainty principle in an effective Hamiltonian for heavy flavored mesons, we introduce a framework to estimate masses and radii of these states from an analytical constraint. In a novel manner, a model for quark velocity and a model for quark momentum width are introduced. These kinematical model parameters are obtained as analytical functions of inter quark separation in heavy quarkonia. The values of such quark parameters are then used in the calculation of S-wave annihilation decay rates of $c\overline{c}$ and $b\overline{b}$. To test the accuracy of our technique we first calculate the spin averaged masses, scalar radii and annihilation decay rates of charmonium and bottomonium without and with relativistic corrections by solving the Schrödinger wave equation with the appropriate parametrization of the Song-Lin potential. The Schrödinger wave equation is solved numerically with the matrix Numerov method and we observe a good agreement with the experimental measurements and other theoretical calculations and extract strong running coupling constant for $c\overline{c}$ and $b\overline{b}$ systems. In non-relativistic settings, heavy meson spectra have been obtained and extended to rather higher excited states within our framework by using bare masses of c and b quarks which we have extracted from analysis of experimental data.

Keywords : Non-relativistic potential model; charmonium and bottomonium; variational principle.

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