Weak Mixing Angles as Dynamical Degrees of Freedom

In an analogy to the case of axion, which converts the $\Theta$-angle into a dynamical degree of freedom, we are trying to imagine a situation where the quark mixing angles turn out to be dynamical degrees of freedom (pseudo-Goldstone bosons), and their vacuum expectation values are obtained from the minimization of the vacuum energy. We present an explicit supersymmetric model with horizontal symmetry, where such a mechanism can be realized. It implies one relation between the quark masses and the CKM mixing angles: $s_{13}s_{23}/s_{12}=(m_s/m_b)^2$, which is fulfilled within present experimental accuracy. We believe, however, that the idea might be more general than this concrete model, and it can be implemented in more profound frameworks.