Radial Regge trajectories and leptonic widths of the isovector mesons

摘要

It is shown that two physical phenomena are important for high excitations: (i) the screening of the universal gluon-exchange potential and (ii) the flattening of the confining potential owing to creation of quark loops, and both effects are determined quantitatively. Taking the first effect into account, we predict the masses of the ground states with l = 0, 1, 2 in agreement with experiment. The flattening effect ensures the observed linear behavior of the radial Regge trajectories M-2(n) = m(0)(2) + n(r)mu(2) GeV2, where the slope mu(2) is very sensitive to the parameter gamma, which determines the weakening of the string tension sigma(r) at large distances. For the rho trajectory the linear behavior starts with n(r) = 1 and the values mu(2) = 1.40(2) GeV2 for gamma = 0.40 and mu(2) = 1.34(1) GeV2 for gamma = 0.45 are obtained. For the excited states the leptonic widths Gamma(ee)(rho(775)) = 7.0(3) keV, Gamma(ee)(rho(1450)) = 1.7(1) keV, Gamma(ee)(rho(1900)) = 1.0(1) keV, Gamma(ee)(rho(2150)) = 0.7(1) keV, and Gamma(ee)(1(3)D(1)) = 0.26(5) keV are calculated, if these states are considered as purely q (q) over bar states. The width Gamma(ee)(rho(1700) increases if rho(1700) is mixed with the 23S 1 state, giving for a mixing angle theta = 21 degrees almost equal widths: Gamma(ee)(rho(1700)) = 0.75(6) keV and Gamma(ee)(1450) = 1.0(1) keV.