The Higgs Boson Lineshape

TL;DR

This paper examines the limitations of the narrow Higgs-width approximation for heavy Higgs bosons, providing a comprehensive analysis of the lineshape, gauge invariance, and theoretical uncertainties in the Standard Model.

Contribution

It introduces a general framework for describing the Higgs boson lineshape in the heavy mass region, addressing gauge invariance and perturbative limitations.

Findings

Numerical results for gluon-fusion Higgs production

Discussion of gauge invariance issues

Analysis of perturbative breakdown and off-shell effects

Abstract

The current searches for a heavy Higgs boson assume on-shell (stable) Higgs-boson production. The Higgs-boson production cross section is then sampled with a Breit-Wigner distribution (with fixed-width or running-width) and implemented in MonteCarlo simulations. Therefore the question remains of what is the limitation of the narrow Higgs-width approximation. The main focus of this work is on the description of the Standard Model Higgs--boson-lineshape in the heavy Higgs region, typically $\MH$ above $600\UGeV$. The framework discussed in this paper is general enough and can be used for all processes and for all kinematical regions. Numerical results are shown for the gluon-fusion process. Issues of gauge invariance and residual theoretical uncertainties are also discussed. Limitations due to a breakdown of the perturbative expansion are comprehensively discussed, including a discussion of th equivalence theorem for (off-shell) virtual vector-bosons. Analytic continuation in a theory with unstable particles is thoroughly discussed.