Elementary excitations of a Higgs-Yukawa system

TL;DR

This paper analyzes the elementary excitations in the Higgs-Yukawa system using RPA, revealing bound states, decay constraints, and implications for Higgs boson mass and coupling constants based on LHC data.

Contribution

It introduces a linearized RPA approach to study excitations in the Higgs-Yukawa model and connects theoretical predictions with experimental Higgs boson observations.

Findings

Identification of one-boson and two-fermion excitation modes.

Existence of bound states in certain phase diagram regions.

Constraints on Higgs boson decay channels and mass limits.

Abstract

This work investigates the physics of elementary excitations for the so-called relativistic quantum scalar plasma system, also known as the Higgs-Yukawa system. Following the Nemes-Piza-Kerman-Lin many-body procedure, the Random-Phase Approximation (RPA) equations were obtained for this model by linearizing the Time-Dependent Hartree-Fock-Bogoliubov equations of motion around equilibrium. The resulting equations have a closed solution, from which the spectrum of excitation modes are studied. We show that the RPA oscillatory modes give the one-boson and two-fermion states of the theory. The results indicate the existence of bound states in certain regions in the phase diagram. Applying these results to recent LHC observations concerning the mass of the Higgs boson, we determine limits for the intensity of the coupling constant g of the Higgs-Yukawa model, in the RPA mean-field approximation, for three decay channels of the Higgs boson. Finally, we verify that, within our approximations, only Higgs bosons with masses larger than 190 GeV/c^2 can decay into top quarks.