Strong CP from a Hidden Chiral Condensate

Abstract

Models which solve the strong CP problem by employing discrete spacetime symmetries generically suffer fine-tuning and quality problems. We demonstrate that these issues are greatly ameliorated when the only source of spontaneous CP breaking is from the chiral condensate of a strongly coupled hidden sector. This is shown explicitly in a model with the SM extended by a vector-like quark family and a complex scalar portal to QCD-like dark sector with $N_f$ families of dark fermions that confines at a high scale. The dark pions of the hidden sector are natural dark matter candidates, with the correct relic abundance obtained via freeze-in. These "confining" Nelson-Barr solutions connect phenomenological questions regarding the strong CP problem to recent developments in the understanding of confining gauge theories, and present ample room for further model building.

Figures (3)

• Figure 1: One-loop diagrams showing the schematic corrections to $\mathcal{M}_{Q\bar{d}}$ (top row), $\mathcal{M}_{Q\bar{D}}$ (bottom-left) and $\mathcal{M}_{D\bar{D}}$ (bottom-right), leading to corrections to $\overline{\theta}$.
• Figure 2: Region plots showing the scales in the model for which the strong CP and dark matter problems are successfully solved via coupling to a strongly-coupled ${\mathrm{SU}}(N)$ sector with $N_f = 2$ dark quarks. In these panels we fix $\mu_D = 2\,\textrm{TeV}$ and show the constraints as a function of $\Lambda_{\textsc{CP}}$ and $M$, with the correct freeze-out abundance indicated by the dashed black line. We also show contours of constant tuning for the dark quark Yukawa couplings, $\delta \lambda / \lambda$ assuming ${\mathrm{SU}}(10)$. In the blue region, the CKM phase is too small to reproduce the SM while in the green region the corrections to $\overline{\theta}$ from non-renormalizable operators are too large. The grey region indicates where $M$ is larger than the Planck scale. We assume $T_{\textrm{rh}} = 10\, m_{\tilde{\pi}}$.
• Figure 3: Similar to Fig. \ref{['fig:region_plots_1']}, except that we show the constraints as a function of $\Lambda_{\textsc{CP}}$ and $\mu_D$, with $M$ fixed to reproduce the correct relic abundance via freeze-out. The red region shows the direct LHC constraints on vector-like quarks, while the other regions are the same as in Fig. \ref{['fig:region_plots_1']}.