Chirally Extended QCD or An Asymptotically Free Chiral Linear Sigma Model With Quarks Coupled to Gluons

We show that the quark (not nucleon) based chiral linear $\sigma$ model which receives strong support as a mean field theory for the strong interactions can actually be made asymptotically free by coupling to gluons. It has the further bonus of providing confinement.Alternatively, this theory is QCD that is chirally extended by the addition of a $(\sigma,\pi)$ chiral multiplet. It could therefore be a candidate theory for the strong interactions which is somewhat different from QCD.Comment: 14 pages, LaTe