A model calculation of the CKM matrix

Abstract

We propose a strategy to compute the CKM matrix based on the conjecture, recently put forward in the literature, according to which elementary particle masses are not generated like in the standard Higgs scenario, but emerge from a non-perturbative mechanism triggered by the presence in the fundamental Lagrangian of ``irrelevant'' chiral breaking operators of the Wilson type of dimension $d\geq 6$ scaled by $d-4$ powers of the UV cutoff. Non-perturbatively generated quark masses have the form $m_q\sim C_q(\alpha) \Lambda_{RGI}$ where $\Lambda_{RGI}$ is the RGI scale of the theory and $C_q(\alpha)$ is a function of the gauge couplings. For the (elementary) fermion $q$ the $C_q(\alpha)$ leading behaviour is $C_q(\alpha)={\mbox{O}}(\alpha^{1+(d_q-4)/2})$. The dependence of the gauge coupling power behaviour from the dimension $d_q$ of the Wilson-like operators associated with the fermion $q$ can be exploited to construct hierarchically organized up and down ''proto-mass matrices'' for ''proto-flavours'', the diagonalization of which yields flavoured quarks with definite masses and a first principle construction of the CKM matrix.