An Elementary (Pseudo)Scalar at all scales

Abstract

We consider an extended linear $\sigma $ model in which the fermions are quarks and are coupled to gluons. Equivalently, this is QCD extended by coupling the quarks to a colour singlet chiral multiplet of ($ \sigma, \vec \pi $) fields. This theory has a phase governed by a UV fixed point where all couplings are AF (asymptotically free). This implies that the scalars are elementary at high energies (UV) and, as they are colour singlets, they are not confined at low energy (IR). Thus, the scalar particles are elementary at all scales.