Axionic Extensions of the Standard Model

After a brief review of the axion solution of the strong CP problem, its supersymmetric extension and the superstring axion are discussed. I also present one interesting cosmological scenario, the axino-gravitino cosmology, for the large scale structure of the universe. The standard model describes the low energy phenomena very successfully with 19 free parameters given by Quarks : 6 masses + 4 angles Vacuum angle : θ QCD with two constraints, M 2 H = λ(2/π)(M 2 W /α 2), M 2 W = M 2 Z cos 2 θ W. It is known that the fundamental problem of the standard model is to understand the origin of these parameters. In fact, the progresses of particle physics during the last two decades are along this line as shown below: Parameters Extensions gauge couplings GUTs 1) θQCD axions 2) Higgs boson mass technicolor, 3) SUSY 4) fermion masses, etc. U (1) horizontal , 5) etc. In this talk, I will concentrate on the parameter problem on θ QCD , the so-called the strong CP problem. 6) The strong interactions are described by quantum chromo dynamics (QCD), in which quarks and gluons interact based on the SU (3) c gauge symmetry. From gluon fields, we expect the following gauge invariant terms