Based on the analysis of both Borel and Finite-Energy QCD sum rules, t
he inclusion of finite mesonic widths leads to a dramatic effect on th
e predictions for the momentum dependence of the rho - omega mixing ma
trix element, It is shown that the rho - omega mixing matrix element t
raditionally discussed in the literature, has the same sign and simila
r magnitude in the space-like region as its on-shell value, This contr
asts the zero-width result where the mixing matrix element is typicall
y of opposite sign in the space-like region.