GeV-scale QCD Axion

Abstract

In order to solve the strong CP problem, we study the possibility that the Peccei--Quinn symmetry is broken {\it below}\/ the QCD scale. We find that a QCD axion can be above GeV, and may be among the observed $η$ resonances. It is immune to quantum gravity corrections. The only fermion that has a $U(1)$ Peccei--Quinn charge is the right-handed up quark. Flavor-changing neutral currents are surprisingly small, except for a possible but not necessary contribution to $D^0$--$\overline{D}^0$ mixing. All accelerator and astrophysical limits can be evaded. The most significant constraint is the mass splitting between $π^\pm$ and $π^0$. In a UV completed model, LHC can look for a dijet resonance in $u\bar{u}$, $u\bar{d}$, $d\bar{u}$ channels.

Figures (2)

• Figure 1: The $aF\tilde{F}$ and $\sigma F F$ couplings induced by the up-quark loop. There are also diagrams where $u_R$ is coupled to photons, and diagrams with two photons exchanged need to be added. The mass insertion can appear on any of the three up-quark propagators. When photons are on-shell and $\varphi$ on-shell, it is suppressed as $\alpha \kappa m_u / 4\pi m_\varphi^2$ instead of $\alpha/f_a$. When photons are far off-shell $q^2 \neq 0$, including the case of the on-shell $Z$ boson $q^2 = m_Z^2$, the diagram is suppressed as $\alpha \kappa m_u / 4\pi q^2$ instead of $\alpha/f_a$.
• Figure 2: The flavor-changing neutral-current processes by the scalar $\varphi$, incuding an operator Eq. \ref{['eq:FCNC']}.