The Higgs Model with a Complex Ghost Pair

TL;DR

This paper introduces a higher derivative modification to the Higgs model, resulting in a finite, consistent quantum field theory with complex ghost pairs that alter triviality and unitarity properties, while remaining physically undetectable.

Contribution

It presents a novel Higgs model with higher derivatives and complex ghost pairs, providing a finite, consistent quantum theory that addresses triviality and unitarity issues.

Findings

Replaces Landau ghost with complex ghost pair at finite mass

Ghost states show unusual resonance behavior

Maintains unitarity in the observable sector

Abstract

A higher derivative term is introduced in the kinetic energy of the Higgs Lagrangian in the minimal Standard Model. A logically consistent and {\it finite} field theory is obtained when some excitations of the Higgs field are quantized with indefinite metric in the Hilbert space. The Landau ghost phenomenon of the conventional triviality problem is replaced by the state vectors of a complex ghost pair at a finite mass scale with observable physical consequences. It is shown that the ghost states exhibit unusual resonance properties and correspond to a complex conjugate pair of Pauli-Villars regulator masses in the euclidean path integral formulation of the theory. An argument is given that microscopic acausality effects associated with the ghost pair remain undetectable in scattering processes with realistic wave packects, and the S-matrix should exhibit unitarity in the observable sector of the Hilbert space. Part One of Extended UCSD-PTH 92-40