Axionless strong CP problem solution: the spontaneous CP violation case

TL;DR

The paper investigates an axionless approach to the strong CP problem by enforcing CP as a symmetry of the Lagrangian that is spontaneously broken, using a $\mathbb{Z}_2$-assisted Yukawa texture in a three-family Georgi-type setup. It shows that at tree level $\mathrm{Arg Det}(M_u M_d)=0$, while one-loop corrections induce a small $\bar{\theta}$, with estimates $\mathrm{Arg Det}(M_u M_d)\sim \lambda_5 f_Y\,10^{-5}$ subject to $m_A^2=2\lambda_5(v_1^2+v_2^2)$ and $\lambda_5\gtrsim 0.02$. A global $\chi^2$ fit to quark masses, CKM data, FCNC constraints, and a neutron EDM bound with a benchmark point demonstrates compatibility with current experimental limits, though the solution relies on moderate fine-tuning typical of two-Higgs-doublet models. The work provides a concrete, testable axionless framework that preserves CP at the Lagrangian level and yields suppressed but nonzero strong-CP effects, motivating further global analyses including the scalar sector.

Abstract

We propose an alternative to the axion mechanism for addressing the charge parity (CP) problem in quantum chromodynamics (QCD). Our approach involves imposing CP as an inherent symmetry of the Lagrangian, which is then spontaneously broken. To generate the correct texture for the Yukawa matrices, we introduce a discrete $\mathbb{Z}_2$ symmetry that is softly broken by the scalar potential. By identifying a benchmark point for the Yukawa couplings that aligns with the measured quark masses, the CKM matrix, and low-energy flavor-changing constraints, our findings suggest that this model offers a viable solution to the CP problem.

Figures (1)

• Figure 1: One-loop diagrams correcting $\bar{\theta}$.