Planck-Scale Physics and the Peccei-Quinn Mechanism

Global-symmetry violating higher-dimension operators, expected to be induced by Planck-scale physics, in general drastically alter the properties of the axion field associated with the Peccei-Quinn solution to the strong-CP problem, and render this solution unnatural. The particle physics and cosmology associated with other global symmetries can also be significantly changed. ⋆ Research supported by an SSC Fellowship from the Texas National Research Laboratory Commission. e-mail: [email protected] † Research supported by NSF grant NSF-PHY-90-21984. e-mail: [email protected], [email protected] After almost twenty years of experimental verification, there is little room to doubt that quantum chromodynamics (QCD) is the true theory of the strong interactions [1]. Perhaps the only outstanding flaw in the the theory arises from non-perturbative effects which, unless suppressed, lead to a neutron electric-dipole moment orders of magnitude larger than that observed. This is the infamous strong-CP problem. Essentially, the problem is that the QCD Lagrangian contains a term θ̄ g 32π2 GG̃aμν , (1) where Gaμν is the gluon field and θ̄ is an undetermined parameter. This term leads to an electric-dipole moment of order dn ≃ 5 × 10θ̄ e cm. The current experimental limit is dn < ∼ 10 e cm which constrains θ̄ to be less than 10. Here we have performed an anomalous chiral rotation to move the phase of the determinant of the fermion mass-matrix into the theta-term, resulting in a net theta-angle θ̄. To date, the most elegant and intriguing solution to the strong-CP problem has been that proposed by Peccei and Quinn [2] where θ̄ becomes a dynamical field with a potential minimized at θ̄ = 0. Their solution involves introducing a new global chiral symmetry U(1)PQ spontaneously broken at a scale fPQ which leads to a Nambu-Goldstone boson, the axion [3]. Due to the anomalous nature of the U(1)PQ symmetry, QCD-instanton (and other, more general, non-perturbative) effects result in the axion acquiring a periodic potential VQCD(θ̄) = (m i a) fPQ (1− cos θ̄), (2) minimized at θ̄ = 0 (where, for simplicity, we consider the case where no axion domain walls occur). Here ma ≃ 0.4 fπmπ fPQ . (3) is the mass of the axion induced by QCD non-perturbative effects.