$S$-matrix unitarity and renormalizability in higher-derivative theories. (23rd August 2019)

• Record Type: Journal Article
• Authors: Abe, Yugo; Inami, Takeo; Izumi, Keisuke; Kitamura, Tomotaka; Noumi, Toshifumi
• Is Part Of: Progress of theoretical and experimental physics. Volume 2019:Number 8(2019)
• Publication Date: 2019-08-23
• Subjects: B32 -- E03 -- E05; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptz084
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: We investigate the relation between $S$ -matrix unitarity ($SS^\dagger=1$ ) 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.