CP violation in 5D Split Fermions Scenario

Abstract

We give a new configuration of split fermion positions in one extra dimension with two different Yukawa coupling strengths for up-type, $h_u$, and down-type, $h_d$, quarks at $\frac{h_u}{h_d}=36.0$. The new configurations can give enough CP violating (CPV) phase for accommodating all currently observed CPV processes. Therefore, a 5D standard model with split fermions is viable. In addition to the standard CKM phase, new CPV sources involving Kaluza-Klein(KK) gauge bosons coupling which arise from the fact that unitary rotation which transforms weak eigenstates into their mass eigenstates only holds for the zero modes which are the SM fields and not for the KK excitations. We have examined the physics of kaon, neutron, and $B/D$ mesons and found the most stringent bound on the size $R$ of the extra dimension comes from $|\epsilon_K|$. Moreover, it depends sensitively on the width, $\sigma$, of the Gaussian wavefunction in the extra dimension used to describe of the fermions. When $\sigma/R \ll 1$, the constraint will be lifted due to GIM suppression on the flavor changing neutral current(FCNC) and CPV couplings.