An effective model for quark masses and mixings

Abstract

By analogy with an effective model of charged-lepton mass matrix that, with the inputs of $m^{exp}_e $ and $m^{exp}_μ$, predicts (in a perturbative zero order) $m_τ= 1776.80 $ MeV close to $m^{exp}_τ= 1777.03^{+0.30}_{-0.26}$ MeV, we construct such a model for quark mass matrices reproducing consistently the bulk of experimental information on quark masses and mixings. In particular, the model predicts $|V_{u b}| = 0.00313$, $γ= - \arg V_{u b} = 63.8^\circ$ and $|V_{t d}| = 0.00785$, $β= - \arg V_{t d} = 20.7^\circ$ (i.e., $\sin 2β= 0.661$ to be compared with the BaBar value $\sin 2β^{exp} = 0.59 \pm 0.14$), if the figures $|V^{exp}_{u s}| = 0.2196$, $|V^{exp}_{c b}| = 0.0402$ and $m^{exp}_{s} = 123$ MeV, $m^{exp}_{c} = 1.25$ GeV, $m^{exp}_{b} = 4.2$ GeV are used as inputs. Also the rest of CKM matrix elements is predicted consistently by the experimental data. Here, quark masses and CKM matrix elements (ten independent quantities) are parametrized by eight independent model constants, what gives two independent predictions, e.g. for $|V_{ub}|$ and $β$. The considered model deals with the fundamental-fermion Dirac mass matrices, so that the neutrino Majorana mass matrix is outside the scheme. Some foundations of the model are collected in Appendix.