Unitarity Bound of the Wave Function Renormalization Constant

Details Unitarity Bound of the Wave Function Renormalization Constant Unitarity Bound of the Wave Function Renormalization Constant

2003-04-06

arxiv.org/abs/hep-th/0304047v2

Prog.Theor.Phys. 110 (2003) 107-114

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 2 figures, comments added

Scientific paper

10.1143/PTP.110.107

The wave function renormalization constant $Z$, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound $0 \leq Z \leq 1$ in field theories without negative metric states. This unitarity bound implies the positivity of the anomalous dimension of the field in the one-loop approximation. In nonlinear sigma models, however, this bound is apparently broken because of the field dependence of the canonical momentum. The contribution of the bubble diagrams to the anomalous dimension can be negative, while the contributions from more than two particle states satisfies the positivity of the anomalous dimension as expected. We derive the genuine unitarity bound of the wave function renormalization constant.

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