A D_5 Model of Quarks with Explicit CP Violation

Abstract

We investigate the quark sector of a four-Higgs-doublet model with an exact D_5 symmetry. In the framework of explicit CP violation, we considered the most general real vacuum, derived the quark mass matrices, and performed a numerical fit to the quark masses and the CKM mixing matrix at the scale mu = 1 TeV using a differential evolution algorithm, based on the 2024 PDG experimental data.The results show that the model simultaneously fits the quark mass spectrum and the CKM mixing angles with an excellent overall chi^2 = 6.97, accurately reproducing the six-quark mass hierarchy and perfectly matching the nine squared moduli of the CKM matrix. The resulting Jarlskog invariant J_CP = 3.144 \times 10^{-5} agrees with the experimental value 3.12 \times 10^{-5} within 0.19σ, indicating that the new source of CP violation from the complex phases in the quark Yukawa couplings alone is sufficient to generate the observed CP violation. Moreover, the hierarchical structures of the vacuum expectation values and the quark Yukawa couplings naturally explain the observed quark mass hierarchy through their interplay.