On QCD and $\omega-\rho$ mixing

TL;DR

This paper refines the calculation of the $ ho- ho$ mixing parameters by removing continuum contributions and questioning vacuum saturation assumptions, leading to a more reliable estimate of the mixing parameter $eta$.

Contribution

It introduces a method to eliminate continuum contributions in sum rule calculations and challenges the vacuum saturation hypothesis for dimension 6 condensates.

Findings

Continuum contributions can be effectively removed to reduce uncertainties.

The vacuum saturation hypothesis is inadequate for estimating certain condensates.

The estimated value of the $eta$ parameter is 0.25.

Abstract

The evaluation of sum rules and vacuum condensates used in the calculation of the mixing parameters of the $\omega -\rho$ 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 $\beta$ which governs the off-shell variation of the $\omega -\rho$ mixing is $\beta=.25$.