Cabibbo angle and quark mass spectrum

Abstract

We propose that the light quarks $\mathcal{P}$, $\mathfrak{N}$, and $\lambda$ are massless when the weak interaction is switched off. Because of the mass degeneracy between the $\mathfrak{N}$ and $\lambda$ fields the Cabibbo angle $\theta$ is undefined. When the weak interaction is switched on the light quarks manage to acquire masses by undergoing weak radiative processes involving heavy quarks (such as the charm quark), thus lifting the mass degeneracy. By identifying appropriate linear combinations of the $\mathfrak{N}$ and $\lambda$ fields as the physical $\mathfrak{N}$ and $\lambda$ states one in effect determines the Cabibbo angle. In this view, the orientation between the strong and weak interactions is controlled by the structure of the weak interaction. We assume strong interactions to be asymptotically free. The implementation of this program leads us to consider a "vector-like" weak interactiontheory which involves six quarks and right-handed currents and which has been discussed on phenomenological grounds elsewhere. (One feature of this program is that the smallness of the neutral kaon mass difference is ensured without further adjustments.) The Cabibbo angle $\theta$ and the mass ratio $\frac{m_{\mathfrak{N}}}{m_{\lambda }}$ (which measures the extent of chiral symmetry breaking) are thus fixed in terms of some of the other parameters appearing in the theory, namely the mass ratio of the two positively charged heavy quarks and various mixing angles, for instance, the analog of $\theta$ in the right-handed current. These parameters are all measurable in principle. Our knowledge of $\theta$ and $\frac{m_{\mathfrak{N}}}{m_{\lambda }}$ then enables us to make various predictive statements about these ratios and consequently the structure of the weak interaction at higher energies. Our point of view also leads naturally to an intimate connection between zero $\theta$ and exact chiral SU(2) symmetry.