Axions and the strong<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:math>problem

Abstract

Current upper bounds on the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|\overline{\ensuremath{\theta}}|\ensuremath{\lesssim}{10}^{\ensuremath{-}11}$. Since QCD explains a great deal of experimental data from the $100\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ to the TeV scale, it is desirable to explain this smallness of $|\overline{\ensuremath{\theta}}|$ in the QCD framework; this is the strong $CP$ problem. There now exist two plausible solutions to this problem, one of which leads to the existence of a very light axion. The axion decay constant window, ${10}^{9}\ensuremath{\lesssim}{F}_{a}\ensuremath{\lesssim}{10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ for an $O(1)$ initial misalignment angle ${\ensuremath{\theta}}_{1}$, has been obtained from astrophysical and cosmological data. For ${F}_{a}\ensuremath{\gtrsim}{10}^{12}\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ with ${\ensuremath{\theta}}_{1}&lt;O(1)$, axions may constitute a significant fraction of the dark matter of the universe. The supersymmetrized axion solution of the strong $CP$ problem introduces its superpartner the axino, which might have affected the evolution of the Universe significantly. The very light axion (theory, supersymmetrization, and models) using recent particle, astrophysical, and cosmological data, and present prospects for its discovery is reviewed here.