Strongly Interacting Higgs Sector in the Minimal Standard Model?

TL;DR

This paper investigates the triviality Higgs mass bound in a four-dimensional O(4) scalar field theory using a higher derivative term to maintain finiteness and symmetry, revealing potential for a strongly interacting Higgs sector.

Contribution

It introduces a higher derivative regulator in the continuum, avoiding lattice artifacts, and analyzes the phase diagram and triviality bound through Monte Carlo simulations and large-N analysis.

Findings

Higher derivative regulator increases the triviality Higgs mass bound.

Ghost particles with resonance properties are associated with complex conjugate regulator masses.

The method suggests a strongly interacting Higgs sector could be consistent with the model.

Abstract

The triviality Higgs mass bound is studied {\it without} lattice regulator in the spontaneously broken phase of the four dimensional O(4) symmetric scalar field theory with quartic self-interaction. A higher derivative term is introduced in the kinetic energy of the Lagrangian to keep quantum fluctuations finite while preserving all the symmetries of the model. When viewed as a {\it finite} field theory in continuum space-time, some excitations of the Higgs field have to be quantized with indefinite metric in the Hilbert space. It is shown that the associated ghost particles, which exhibit unusual resonance properties, correspond to a complex conjugate pair of Pauli-Villars regulator masses in the euclidean path integral formulation. The phase diagram of the O(4) model is determined in a Monte Carlo simulation which interpolates between the hypercubic lattice regulator and the higher derivative regulator in continuum space-time. The same method can be used to calculate the triviality Higgs mass bound without lattice artifacts. In a large-N analysis, when compared with a hypercubic lattice, we find a relative increase in the triviality bound of the higher derivative regulator suggesting a strongly interacting Higgs