Solution of the Strong CP problem in the low energy effective Standard Model

Abstract

We consider the low energy effective chiral theory of QCD mesons and the electroweak Goldstone bosons. In this effective theory the pion sector contributes to the gauge boson masses and the Yukawa couplings of the fermions. Consequently the Yukawa sector of quarks and leptons can have a $SU(2)_L\times U(1)_Y\times U(1)_A$ global symmetry even with nonvanishing fermion masses. The extra chiral $U(1)_A$ symmetry can be used to rotate the CP violating $\bar \theta G\tilde G $ term away which therefore makes no contribution to low energy CP violating effects like the neutron electric dipole momment. The Goldstone mode associated with this $U(1)_A$ symmetry may be identified with the $SU(2)$ singlet meson $\eta_0$.