Flavor democracy in standard models at high energies

It is possible that the standard model (SM) is replaced around some transition energy Λ by a new, possibly Higgsless, “flavor gauge theory” such that the Yukawa (running) parameters of SM at E ∼ Λ 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 ⋍ 1 GeV) to Λ (∼Λpole) and comparing the resulting fermion masses and CKM matrix elements at E ⋍ Λ for various mtphy and ratios νu/νd 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 Λpole ⪡ ΛPlack, mtphy can be less than 200 GeV in most cases of chosen νu/νd. Under the assumption that also the corresponding Yukawa couplings in the quark and the leptonic sector at E ⋍ Λ are equal (l-q FD), we derive estimates of bounds on masses of top quark and tau-neutrino, which are compatible with experimental bounds.