Quark and Lepton Mass and Mixing with non-universal $Z^{\prime }$ from a 5d Standard Model with gauged $SO(3)$

Abstract

We propose a theory of quark and lepton mass and mixing with non-universal $Z^{\prime }$ couplings based on a 5d Standard Model with quarks and leptons transforming as triplets under a new gauged $SO(3)$ isospin. In the 4d effective theory, the $SO(3)$ isospin is broken to $U(1{)}^{\prime }$, through a $S^1/({\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime })$ orbifold, then subsequently dynamically broken, resulting in a massive $Z^{\prime }$. Quarks and leptons in the 5d bulk appear as massless modes, with zero Yukawa couplings to the Higgs on the brane, and zero couplings to $Z^{\prime }$, at leading order, due to the $U(1{)}^{\prime }$ symmetry. However, after the $U(1{)}^{\prime }$ breaking, both Yukawa couplings and non-universal $Z^{\prime }$ couplings are generated by heavy Kaluza-Klein exchanges. Hierarchical quark and lepton masses result from a hierarchy of 5d Dirac fermion masses. Neutrino mass and mixing arises from a novel type Ib seesaw mechanism, mediated by Kaluza-Klein Dirac neutrinos. The non-universal $Z^{\prime }$ couplings may contribute to semi-leptonic $B$ decay ratios which violate $\mu -e$ universality. In this model such couplings are related to the corresponding quark and lepton effective Yukawa couplings.

Comments: 25 pages, 5 figures. v3: matches published version