From the unification scale to the weak scale: A self consistent supersymmetric Dine-Fischler-Srednicki-Zhitnitsky axion model

The distinguishing feature of the Dine–Fischler–Srednicki–Zhitnitsky (DFSZ) axion is that it couples to the electroweak Higgs fields. There is thus an immediate connection between the Peccei–Quinn (PQ) scale and the weak scale. We wish to incorporate the DFSZ axion in a complete supersymmetric model, valid at all scales, and then to implement it in a numerical code connecting the high scale and the low scale physics on a quantitative level. We find that the simplest supersymmetric DFSZ model, as proposed by Rajagopal et al. in 1990, is inconsistent when we consider the minimization of the scalar potential. The problem is that we obtain a negative squared mass for the saxion, the scalar partner of the axion, at the minimum. We then consider the minimal extension in order to get a consistent model for all scales: one has to include an additional explicit sector to spontaneously break the PQ symmetry. In the complete model we can determine the mass of the axino, the fermionic partner of the axion. It is useful to distinguish two cases: 1) the supersymmetry (SUSY)-breaking scale is lower than the PQ-breaking scale, and 2) the scales are comparable. We find that the axino is very light in case 1, while its mass is generically of the order of the other soft SUSY-breaking masses in case 2. We have implemented SUSY breaking via generic soft-breaking terms, and thus make no explicit statement about the form and mediation of SUSY breaking. This complete model can then be incorporated in a numerical code connecting the two scales. We briefly discuss the renormalization group equations and the couplings of the axion to gluons and photons.

Figure 1

The mass of the axino as a function of $\tan {\beta }^{\prime }=\sqrt{v_{\overline{a}}/v_a}$. We fixed $f_a=10^{12}\mathrm{GeV}$, $\lambda =10^{-2}$, $T_{\lambda }=-1\mathrm{TeV}$ and used $v_{\chi }=10^4\mathrm{GeV}$ (dotted line), $v_{\chi }=10^3\mathrm{GeV}$ (dashed line) and $v_{\chi }=10^2\mathrm{GeV}$ (plain line).

Figure 2

Diagrams contributing to the axino mass when integrating out the heavy fields ${\varphi }_{b,c}$.