Dynamical relaxation of the CP phases in next–to–minimal supersymmetry

After promoting the phases of the soft masses to dynamical fields corresponding to Goldstone bosons of spontaneously broken global symmetries in the supersymmetry breaking sector, the next–to–minimal supersymmetric model is found to solve the μ problem and the strong CP problem simultaneously with an invisible axion. The domain wall problem persists in the form of axionic domain formation. Relaxation dynamics of the physical CP–violating phases is determined only by the short–distance physics and their relaxation values are not necessarily close to the CP–conserving points. Consequently, the solution of the supersymmetric CP problem may require heavy enough superpartners and nonminimal flavor structures, where the latter may be also relevant for avoiding the formation of axionic domain walls. PACS: 12.60.Jv, 11.30.Er, 12.60.Fr, 14.80.Mz