Infrared fixed points in asymptotically free field theories: What do they tell us?

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Abstract
The meaning of infrared fixed points in asymptotically free field theories is discussed in connection with a recent paper of Kubo, Sakakibara, and Stevenson. It is argued that our understanding of the infrared behavior of perturbation theory depends crucially on our ability to cope with the divergences of perturbation expansions for physical quantities. As at any finite order the presence or absence of the infrared fixed point of an associated β function is a matter of choice of the appropriate renormalization scheme (RS), the resulting infrared behavior of truncated perturbation expansions of physical quantities is RS dependent. It is shown that under certain circumstances the principle of minimal sensitivity fails already at finite values of external momenta and cannot therefore in this case be used in investigation of the infrared behavior of physical quantities. It is furthermore explained why contrary to popular belief ‘‘critical’’ exponents associated with infrared fixed points, present in some renormalization conventions, have no direct physical meaning.