Optical theorem and indefinite metric in $\lambda\phi^4$ delta-theory

TL;DR

This paper investigates the optical theorem and unitarity in delta-theory, a quantum field theory with improved ultraviolet behavior, focusing on a scalar model with quartic interaction and ghost states, revealing minor unitarity violations.

Contribution

It analyzes the optical theorem and unitarity in delta-theory with indefinite metric, demonstrating suppressed unitarity violations at one-loop order in a scalar quartic model.

Findings

Confirmed validity of cutting equations at one-loop order

Found suppressed unitarity violations proportional to delta coupling

Analyzed the impact of ghost states on unitarity

Abstract

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the $S$-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of $\xi^4$.