ORBITAL RADIUS OF A HYDROGEN-LIKE MESON IN S-, P- AND D-STATES

Abstract

Radial probability density function of a heavy quark–light quark [Formula: see text] system in the states S, P and D, is studied numerically. It is found that the maximum of this function at r=a0 and the light quark energy (Eq) are related through [Formula: see text], where l is the orbital angular momentum, Z=0.446/ξ, and ξ is the strength of the color Coulomb potential. Phenomenology predicts that to difference of the hydrogen atom of QED, the "color atomic number" is such that Z≤1. This can be thought of as due to an anti-screening effect from the gluons. The respective expectation value for the radial coordinate in these states is found to be [Formula: see text] These results are valid for ξ in the range 0.446<ξ<0.646 and a light quark mass in the range 0<m<300 MeV. The above relations coincide with the maximum value of the slope of the Isgur–Wise at zero recoil point in the following way [Formula: see text] The relations found in the present work imply that [Formula: see text], from which we argue that the value of ξ′(1) is very sensitive to the color Coulomb-like interaction U=-ξ/r.