Flavor Democracy in Standard Models at High Energies

Abstract

It is possible that the standard model (SM) is replaced around some transition energy $\E_{tr}$ by a new, possibly Higgsless, ``flavor gauge theory'' such that the Yukawa (running) parameters of SM at $E \sim \E_{tr}$ show up an (approximate) flavor democracy (FD). We investigate the latter possibility by studying the renormalization group equations for the Yukawa couplings of SM with one and two Higgs doublets, by evolving them from given physical values at low energies ($E \simeq 1 GeV$) to $\E_{tr}$ ($ \sim \E_{pole}$) and comparing the resulting fermion masses and CKM matrix elements at $E \simeq \E_{tr}$ for various $m_t^{phy}$ and ratios $v_u/v_d$ of vacuum expectation values. We find that the minimal SM and the closely related SM with two Higgs doublets (type I) show increasing deviation from FD when energy is increased, but that SM with two Higgs doublets (type II) clearly tends to FD with increasing energy - in both the quark and the leptonic sector (q-q and l-l FD). Furthermore, we find within the type II model that, for $\E_{pole} \ll \E_{Planck}$, $m_t^{phy}$ can be less than $200 GeV$ in most cases of chosen $v_u/v_d$. Under the assumption that also the corresponding Yukawa couplings in the quark and the leptonic sector at $E \simeq \E_{tr}$ are equal (l-q FD), we derive estimates of bounds on masses of top quark and tau-neutrino, which are compatible with experimental bounds.