Abstract

The stability of tree-level relations among the parameters of a quantum field theory with respect to renormalization group (RG) running is typically explained by the existence of a symmetry. A simple model of two real scalar fields is presented in which a tree-level relation among the squared-mass parameters of the scalar potential is RG-stable without the presence of a conventional underlying symmetry. Some authors have attempted to explain this result by introducing a so-called GOO Fy symmetry. In this talk, the stability of this parameter relation with respect to RG running is explained by complexifying the original scalar field theory. It is then possible to exhibit a conventional symmetry that guarantees the relations of relevant beta functions of squared-mass parameters of the complexified theory. We can then show that the RG-stability of the parameter relations of the original real scalar field theory is inherited from the conventional symmetry of the corresponding complexified theory.