The Higgs Model with a Complex Ghost Pair

TL;DR

The paper addresses the Higgs sector’s finiteness by adding a higher-derivative term and quantizing a subset of Higgs modes with an indefinite metric, yielding a finite theory that replaces the Landau ghost with a complex ghost pair at finite mass. It develops a non-perturbative framework: a Hamiltonian with six canonical variables and an euclidean path integral in which the complex ghost poles act as Pauli-Villars regulators, while the real-time theory remains well-defined in the physical subspace. The complex ghost pair has masses ${\cal M}=M e^{i\Theta}$ (with ${\cal M}=M_G+i\gamma/2$), producing resonant structures at $s={\cal M}^2$ and ${\cal M}^{*2}$ without detectable acausal effects in realistic scattering, and contributing to RG running in a controlled way. The approach yields a consistent, potentially TeV-scale, strongly interacting Higgs sector with calculable non-perturbative signatures and a clear separation between observable physics and unobservable ghost states.

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