Light quark orbital radius of a heavy Quark-Light quark system in an S-state

摘要

Radial probability density function of a heavy quark-light quark (Q,q-bar) system in an S-state is analyzed numerically. It is found that the maximum of this function at r = a_0 and the light quark energy (E_q) are related through the relation E_q = Z/a_0, where Z = c_0/c, c is the strength of the color Coulomb potential and c_0 = 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 = 6/5a_0. These results are valid for c in the range c_0 < = 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 m_c = 1.3 +- 0.33 GeV and m_b = 4.6 +- 0.3 GeV. It is also shown that E_q 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 #xi#'(1)_(max) = -a_0/ = -5/6 or E_q = -6/5 (Z#si#'(1)_(max))/a_0.