Squeezed condensate of gluons and $η-η'$ mass difference

Abstract

We consider a mechanism to create the $η- η'$ mass difference by the gluon anomaly in a squeezed vacuum. We find that the mass shift of the $η_0$ governing this mass difference is determined by the magnetic part of the gluon condensate. For the squeezed vacuum this magnetic part coincides with the total gluon condensate, so that we get a relation between the gluon condensate and the mass shift of the $η_0$ as a function of the strong coupling constant $α_s$. The values of the gluon condensate obtained through this relation are compared with the value by Shifman, Vainshtein and Zakharov and the recent update values by Narison.