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$η-η^{\prime}$ Mixture in Chiral Bag

The $η-η^{\prime}$ mixture is discussed in the chiral bag model to calculate the pseudoscalar octet-singlet mixing angle consistent with the experimental data. The color anomaly is taken into account with the modified boundary conditions, which shows the relation between the $η^{\prime}$ mass and the gluon condensate inside the chiral bag. We show, however, that $η-η^{\prime}$ mixing angle can follow the Cheshire Cat Principle, i.e., insensitivity to the bag radius.