The Higgs Boson Lineshape

TL;DR

The paper argues that a gauge-invariant description of the Higgs lineshape in the heavy-mass regime requires moving beyond the on-shell, zero-width approximation and adopting a complex-pole formalism. It advocates the CPP-scheme as the theoretically consistent method for defining a Higgs signal, though it notes practical use of OFFP for current calculations, and it highlights the necessity of including background and interference effects. Numerical studies with the HTO framework illustrate substantial differences between schemes, emphasize the role of off-shell decay, and quantify QCD-scale uncertainties and higher-order corrections, particularly as the Higgs mass rises beyond ~1 TeV. The work also discusses analytic continuation, Nielsen identities, and the limitations of perturbation theory at very high masses, offering guidance for interpreting heavy-Higgs searches and extracting pseudo-observables from data.

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.

Figures (11)

• Figure 1: In the left figure we show a comparison of production cross-section as computed with the OFFP-scheme of Eq.(\ref{['offp']}) or with the OFFBW-scheme of Eq.(\ref{['offbw']}). The red curve gives Breit--Wigner parameters in the OS-scheme and the blue one in the Bar-scheme of Eq.(\ref{['Bars']}). In the right figure we show the effect of using dynamical QCD scales for the production cross-section of Eqs.(\ref{['PDFprod_1']})--(\ref{['PDFprod_3']}).
• Figure 2: In the left figure the blue curve gives the off-shell production cross-section sampled over the (complex) Higgs propagator while the red curves is sampled over a Breit--Wigner distribution The black curve gives the on-shell production cross-section. The right figure shows differential $K\,$factor for the process ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{p}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{p}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to ( {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to 4\, {} { {} { { {{\bm{ { {\mathsf{ {} {} {{e}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace) + {} { {} { { {{\bm{ { {\mathsf{ {} {} {{X}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$, comparing the fixed scale option, $\mu{{\mathrm{R}}}$μ_R$= \mu{{\mathrm{F}}}$μ_F$= M{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$M_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$/2$, and the running scale option, $\mu{{\mathrm{R}}}$μ_R$= \mu{{\mathrm{F}}}$μ_F$= M(4\, {} { {} { { {{\bm{ { {\mathsf{ {} {} {{e}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace)/2$.
• Figure 3: The normalized invariant mass distribution in the OFFP-scheme with running QCD scales (left) for $600~\text{GeV}$ (black), $700~\text{GeV}$ (blue), $800~\text{GeV}$ (red) in the windows $M_{{\hbox{\scriptsize peak}}} \pm 2\,\Gamma{\mathrm{OS}}$Γ_OS$$. The normalized invariant mass distribution in the OFFP-scheme (blue) and OFFBW-scheme (red) with running QCD scales (right) at $800~\text{GeV}$ in the window $M_{{\hbox{\scriptsize peak}}} \pm 2\,\Gamma{\mathrm{OS}}$Γ_OS$$.
• Figure 4: The normalized invariant mass distribution in the OFFP-scheme with running QCD scales for $600~\text{GeV}$ (left), $800~\text{GeV}$ (right) in the windows $M_{{\hbox{\scriptsize peak}}} \pm 2\,\Gamma{\mathrm{OS}}$Γ_OS$$. The blue line refers to $8~\text{TeV}$, the red one to $7~\text{TeV}$.
• Figure 5: The invariant mass distribution in the OFFP-scheme with running QCD scales for $800~\text{GeV}$ in the window $M_{{\hbox{\scriptsize peak}}} \pm 2\,\Gamma{\mathrm{OS}}$Γ_OS$$. The blue line refers to $8~\text{TeV}$, the red one to $7~\text{TeV}$.