LIGHT QUARK ORBITAL RADIUS OF A HEAVY QUARK–LIGHT QUARK SYSTEM IN AN S-STATE

Abstract

Radial probability density function of a heavy quark–light quark [Formula: see text] system in an S-state is analyzed numerically. It is found that the maximum of this function at r=a0 and the light quark energy (Eq) are related through the relation Eq=Z/a0, where Z=c0/c, c is the strength of the color Coulomb potential and c0=0.446. Z<1 can be thought of as due to a color anti-screening effect. The respective expectation value for r in this state is [Formula: see text]. These results are valid for c in the range c0≤ c≤0.7 and a light quark mass in the range 0≤ m≤ 300 MeV. As a result of these patterns of regularity, bounds on the mass of the heavy quarks are imposed. These give mc=1.3±0.33 GeV and mb=4.6±0.3 GeV. It is also shown that Eq is not directly an "inertia" parameter, as it has been called by the heavy quark effective theory, but a physical quantity that needs to be measured. The relations found in the present work coincide with the maximum value that the slope of the Isgur–Wise function at zero recoil can take, in either way [Formula: see text] or [Formula: see text].