RMS and charge radii in a potential model

Abstract

The Dalgarno's method of perturbation is used to solve the Schrodinger's equation with the Cornell potential V (r) = − 4αs 3r + br + c. The short range and long range effect of the potential is incorporated in the same wave function by using two scales r S and r L as an integration limit. With the wave function then the results for bounds on r.m.s. radii of various heavy flavored mesons are reported. We have also showed the relation between r.m.s. and charge radius of mesons.

Isgur–Wise function and a new approach to potential model

“…The input parameters in the numerical calculations used are m u = 0.336GeV , m s = 0.483GeV , m c = 1.55GeV , m b = 4.95GeV and b = 0.183GeV 2 and α s values 0.39 and 0.22 for charmonium and bottomonium scale respectively, are same with the previous work [15,31].…”

“…In general, it is expected that a constant term 'c' in the potential should not affect the wave function of the system while applying the perturbation theory. But in our previous work [15] it is seen that whether the term 'c' is in parent or perturbed part of the Hamiltonian, it always appears in the total wave function which is inconsistent with the quantum mechanical idea that a constant term 'c' in the potential can at best shift the energy scale, but should not perturb the wave function i.e. a Hamiltonian H with such a constant and another H without it should give rise to the same wave functions.…”

2S and 3S State Masses and decay constants of heavy-flavour mesons in a non-relativistic QCD potential model with three-loop effects in V-scheme

“…The most common perturbative method is Dalgarno's perturbation theory (DPT) [21,[23][24][25], which is a stationary static perturbation theory. The non-relativistic potential model has been found successful for heavy-heavy B, η c and η b families.…”

“…One aim of the present work is to make an analysis of the contribution of three-loop effects in the improved strong coupling constant α V ( 1 r ) in V -scheme, which in turn contributes to the spin-spin interaction [27][28][29] term present in the expression of mass and decay constant of the heavy-flavour meson. In addition, the non-relativistic binding energy effect between the two quark-antiquark composition of the heavyflavour meson is newly incorporated in the expression of PSM mass, which was absent in our some previous works [23][24][25]37,39,41].…”

Charge radii of heavy flavored mesons in a potential model

“…it is based on the two kinds of asymptotic behaviors: ultraviolet at short distance (Coulomb like) and infrared at large distance (linear confinement term). In the potential (1), - 4 3 is due to the color factor, α s is the strong coupling constant, r is the inter-quark distance, b is the confinement parameter and 'c' is a constant scale factor which is a phenomenological constant and is needed to reproduce correct masses of heavy-light meson bound state.…”