Asymptotic freedom and the Lee model

Abstract

Using dimensional regularization we renormalize the Lee model in arbitrary space-time dimension $D$. We compute $\ensuremath{\beta}(g)$ and $\ensuremath{\gamma}(g)$, 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 $\ensuremath{\beta}(g)$ and the presence of a ghost state: There is no ghost when $\ensuremath{\beta}(g)<0$. 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.