Axions And Other Very Light Bosons

L ` = CITATION: K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002) (URL: http://pdg.lbl.gov) -- 2-- ` eff is so small (` eff . 10 ) as required by the current limits on the neutron electric dipole moment, even though ` eff O(1) is perfectly allowed by the QCD gauge invariance. Here, ` eff is the effective ` parameter after the diagonalization of the quark masses, and F is the gluon field strength and = 2 ffl aeoe F aeoea . An axion is a pseudoNG boson of a spontaneously broken Peccei--Quinn symmetry, which is an exact symmetry at the classical level, but is broken quantum mechanically due to the triangle anomaly with the gluons. The definition of the Peccei--Quinn symmetry is model dependent. As a result of the triangle anomaly, the axion acquires an effective coupling to gluons ` ` eff \Gamma OE A f A ' ; (2) where OE A is the axion field. It is often convenient to define the axion decay constant f A with this Lagrangian [6]