The heavy Higgs searches at LHC are carried out in gg→H→WW→lνlν, gg→H→ZZ→llll, llνν, llqq channels. 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 Monte Carlo 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 M H above 600GeV. 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 the equivalence theorem for (off-shell) virtual vector-bosons. Analytic continuation in a theory with unstable particles is thoroughly discussed. © 2012 Elsevier B.V.
Goria, S., Passarino, G., & Rosco, D. (2012). The Higgs-boson lineshape. Nuclear Physics B, 864(3), 530–579. https://doi.org/10.1016/j.nuclphysb.2012.07.006