-matrix Unitarity and Renormalizability in Higher-derivative Theories
Yugo Abe (National Institute of Technology, Miyakonojo College, Miyakonojo 885-8567, Japan); Takeo Inami (Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan); Keisuke Izumi (Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan); Tomotaka Kitamura (Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan); Toshifumi Noumi (Department of Physics, Kobe University, Kobe 657-8501, Japan)
Abstract We investigate the relation between -matrix unitarity () and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the -matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the -matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for -matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.
