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Axions and the Strong CP Problem

Current upper bounds of the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|\barθ| \lesssim 10^{-11}$. Since QCD explains vast experimental data from the 100 MeV scale to the TeV scale, it is better to explain this smallness of $|\barθ|$ in the QCD framework, which is the strong \Ca\Pa problem. Now, there exist two plausible solutions to this problem, one of which leads to the existence of the very light axion. The axion decay constant window, $10^9\ {\gev}\lesssim F_a\lesssim 10^{12} \gev$ for a ${\cal O}(1)$ initial misalignment angle $θ_1$, has been obtained by astrophysical and cosmological data. For $F_a\gtrsim 10^{12}$ GeV with $θ_1<{\cal O}(1)$, axions may constitute a significant fraction of dark matter of the universe. The supersymmetrized axion solution of the strong \Ca\Pa problem introduces its superpartner the axino which might have affected the universe evolution significantly. Here, we review the very light axion (theory, supersymmetrization, and models) with the most recent particle, astrophysical and cosmological data, and present prospects for its discovery.