Asymptotic freedom and the Lee model

Using dimensional regularization we renormalize the Lee model in arbitrary space-time dimension D. We compute β(g) and γ(g), the coefficient functions of the Callan-Symanzik equation, in closed form and show that the model is asymptotically free when $D<4$. In addition, we demonstrate a strict correlation between the sign of β(g) and the presence of a ghost state: There is no ghost when β(g)<0. Finally, we study an extended Lee model with two coupling constants and study the behavior of the effective coupling constants in the deep-Euclidean region.