Nelson-Barr Models with Vector-Like Quark Doublets

Abstract

We investigate Nelson--Barr solutions to the strong CP problem in which spontaneous CP violation is transmitted to the Standard Model through mixing with a vector-like partner of the SM quark doublet. We show that these constructions constitute compelling and phenomenologically viable alternatives to the more widely studied singlet-based NB models. A key result of our analysis is that an accidental symmetry of the renormalizable theory delays the leading contributions to \barθ until three loops, naturally suppressing hadronic CP violation. We outline the main phenomenological constraints, including future EDM experiments, as well as the main differences between these scenarios and generic models with doublet vector-like quarks.

Figures (9)

• Figure 1: Distribution of $\sqrt{x_i}/y_3$ against $1-\mu$ for up (left) and down (right) sectors with $i=3,2,1$ corresponding to green, orange and blue points. Points shown in a lighter shade only reproduce the eigenvalues of the SM Yukawas while the points in a darker shade also reproduce the CKM angles and phase. The horizontal lines show $y_i/y_3$ while the vertical line refers to $(1-\mu)_{\rm min}$ in \ref{['doublet:mu-constraint']}.
• Figure 2: $|\tilde{w}|$ as a function of $1-\mu$ for physical points that reproduce the SM. The dashed lines obey $|\tilde{w}|=\sqrt{\frac{2}{1-\mu}}$ and $|\tilde{w}|=\sqrt{\frac{556}{1-\mu}}$, corresponding to $\sin\theta=1$ and $0.03$ in \ref{['deltamu:w-tide:approx']} approximately.
• Figure 3: Ratios $|\tilde{w}_i|/|\tilde{w}_3|$, $i=1,2$ against the norm $|\tilde{w}|$. All points reproduce the SM.
• Figure 4: $|Y^{Qu}_i|$ (left) and $|Y^{Qd}_i|$ (right) as a function of $|\tilde{w}|$ for $i=3,2,1,$ respectively in green, orange and blue. The lighter green points are excluded by the perturbativity limit \ref{['cYu<3']}. The dashed lines with the same color as the points show the approximate functions in \ref{['estimate:YQ']}. The horizontal continuous (dashed) red line indicate the constraint coming from electroweak precision observables for $M_Q=2\,\unit{TeV}$ ($M_Q=8\,\unit{TeV}$); see Sec. \ref{['sec:S.T']}.
• Figure 5: Eigenvalues $\hat{\mathscr{Y}}^u_i$ (left) and $\hat{\mathscr{Y}}^d_i$ (right) of the CP conserving Yukawa couplings as functions of $|\tilde{w}|$. The dashed lines correspond to the values of the SM Yukawas at 1 TeV. The color coding is the same as in Fig. \ref{['fig:YQ.wtilde']}.