S-matrix unitarity and renormalizability in higher-derivative theories. (23rd August 2019) - Abe, Yugo; Inami, Takeo; Izumi, Keisuke; Kitamura, Tomotaka; Noumi, Toshifumi
Abstract: We investigate the relation between S -matrix unitarity (SS^=1 ) 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 S -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 S -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 S -matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.