ar X iv : h ep - p h / 99 03 22 3 v 1 2 M ar 1 99 9 On QCD and ω − ρ mixing

The evaluation of sum rules and vacuum condensates used in the calculation of the mixing parameters of the ω − ρ system involve dangerous cancellations of large numbers. In this note the contribution of the continuum is eliminated in order to avoid such a large source of uncertainty. It is also seen that the hypothesis of vacuum saturation used in the estimate of the dimension 6 condensate is inadequate. The value obtained for the parameter β which governs the off-shell variation of the ω − ρ mixing is β=.25 . Since Shifman,Vainshtein and Zakharov [1] first applied QCD sum rules to the problem of ω-ρ mixing in order to probe the mechanism of isotopic symmetry breaking several attempts have been made to obtain the ω-ρ mixing parameters in terms of the quark masses and the various quark and gluon field condensates [2], [3], [4]. The values obtained for the mixing parameters vary widely in the literature. The reason for this instability is easily found: the sum rules for the problems are integrals over the difference of two nearly equal contributions, the one of the 2π intermediate states dominated by the ρ − meson and the one of the 3π intermediate states dominated by the ω-meson. The integrals being the difference of large numbers it is not surprising that the various approximations used, which do not necessarily evenly effect each contribution, can result in large perturbations in the values obtained. The same applies to the estimate of the vacuum condensates of the operator product expression which are themselves differences of nearly equal numbers and for the evaluation of which it is certainly overoptimistic to trust the vacuum saturation hypothesis as has been done in the literature. In this note no attempt will be made to estimate the contribution of the continuum, this contribution will rather be eliminated by an appropriate choice of a damping factor in the sum rules. It will also be shown that the vacuum saturation hypothesis must necessarily be relaxed in the determination of the dimension-6 condensate which will treated as an unknown. ∗e-mail: [email protected]