Chiral Symmetry Breaking and the Cabibbo Angle

Abstract

The proposal of Oakes linking the pion mass and the strangeness-changing weak interactions in investigated in the (8,8) symmetry breaking of $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$. This leads to a determination of the Cabibbo angle and the $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay rates which are in agreement with the earlier results in the $(3,\overline{3})\ensuremath{\bigoplus}(\overline{3},3)$ model. The connection between cancellations in the leading weakinteraction divergences and the Cabibbo angle, however, does not hold in the (8,8) scheme.