Down-sector quark masses and flavor mixing radiatively generated from the up sector.

Abstract

We present a model of quark mass generation where the observed intergeneration mass hierarchy, large ratio $\frac{{m}_{t}^{2}}{{m}_{b}^{2}}\ensuremath{\gg}1$, and flavor mixing can all arise naturally. The basic assumption is that only the charge ⅔ quarks (${u}_{i};i=1,2,3$) couple to heavy fermions $F$ by emission and reabsorption of bosons $S$. The generation-index dependence of the shape of the form factors at these $S\overline{F}{u}_{i}$ couplings is responsible for the up-sector mass hierarchy. The ${W}^{\ifmmode\pm\else\textpm\fi{}}$ gauge bosons are assumed to have a generation-index-independent anomalous-magnetic-moment-type correction to the standard $V\ensuremath{-}A$ coupling to quarks. This correction enables the charge -⅓ quarks to acquire masses by coupling to the up-sector charge ⅔ quarks, which provides a natural explanation for ${m}_{t}^{2}\ensuremath{\gg}{m}_{b}^{2}$. Because the charge ⅔ quark self-energy matrix is probed here at a non-negligible momentum, the down-sector mass matrix turns out to be significantly different from the up-sector mass matrix, thus producing naturally smaller intergeneration mass ratios as well as flavor mixing and $\mathrm{CP}$ violation if the form factors are complex. In order to exhibit the remarkable properties of the above scheme, we use a concrete model for the form factors. We find for the particular scenarios ${M}_{F}\ensuremath{\gg}\ensuremath{\Lambda}$ or ${M}_{F}\ensuremath{\ll}\ensuremath{\Lambda}$ (where $\ensuremath{\Lambda}$ is a characteristic mass scale common to all form factors) simple analytical expressions for the mass matrices. Excellent 4 to 6 parameter fits to the 10 observables in the quark sector are obtained. All dimensionless input parameters are of order 1 and do not require fine-tuning. An interesting scenario within our scheme with top-driven ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{Y}$ breaking as well as some possible extensions of the model to include mass generation for leptons are briefly discussed.