Higgs Interference Effects in $\Pg \Pg \to \PZ\PZ$ and their Uncertainty

TL;DR

This paper investigates the interference between the Standard Model Higgs signal and the gluon-fusion continuum in gg→ZZ for a heavy Higgs. It discusses how to coherently combine LO background/interference with NNLO Higgs production cross-sections and proposes a conservative method to estimate the theoretical uncertainty using additive, multiplicative, and intermediate prescriptions. Numerical studies with the HTO framework show that interference has a small impact on inclusive cross-sections but can substantially distort ZZ invariant-mass distributions, necessitating a robust central value (intermediate) plus an uncertainty band (A–M). The work emphasizes careful treatment of interference in experimental analyses and outlines directions for improved higher-order calculations and uncertainty modeling.

Abstract

Interference between the Standard Model Higgs boson and continuum contributions is considered in the heavy-mass scenario. Results are available at leading order for the background. It is discussed how to combine the result with the next-to-next-to-leading order Higgs production cross-section and a proposal for estimating the associated theoretical uncertainty is presented.

Figures (10)

• Figure 1: The ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ invariant mass distribution in the OFFP-scheme of Ref. Goria:2011wa with running QCD scales for $\mu{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$μ_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$= 600~\text{GeV}$. $B = 4.36\,\cdot 10^{-3}$ represents the BR for both ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ bosons to decay into ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{e}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ or ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{\upmu}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$. The black line gives the full ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ process at LO; the cyan line gives signal plus background (LO) neglecting interference while the blue line includes both ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ and ${} {} { {} { {} { { {{\bm{ { {\mathsf{ {} {} {{\overline{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{q}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}}_{ {\!\mspace{1mu}\mspace{1mu}} }^{\mspace{1mu} { {\raisebox{-0.55ex}{${{\bm{ {\mathsf{{ { {{\bm{ { {\mathsf{}} } }}} } }}} }}}$}} } }} \mspace{-0.6mu} }} } }}} } } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{q}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ components (LO). The red line gives the LO signal.
• Figure 2: The ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ invariant mass distribution in the OFFP-scheme of Ref. Goria:2011wa with running QCD scales for $\mu{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$μ_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$= 600~\text{GeV}$. $B = 4.36\,\cdot 10^{-3}$ represents the BR for both ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ bosons to decay into ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{e}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ or ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{\upmu}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$. The black line is the full LO ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ result, the brown line gives the multiplicative option of Eq.(\ref{['Mopt']}), the red line is the additive option of Eq.(\ref{['Aopt']}) while the blue line is the intermediate option of Eq.(\ref{['Iopt']}). The cyan line gives signal plus background (LO) neglecting interference.
• Figure 3: The ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ invariant mass distribution in the OFFP-scheme of Ref. Goria:2011wa with running QCD scales for $\mu{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$μ_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$= 700~\text{GeV}$. $B = 4.36\,\cdot 10^{-3}$ represents the BR for both ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ bosons to decay into ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{e}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ or ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{\upmu}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$. The black line is the full LO ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{g}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace \to {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ result, the brown line gives the multiplicative option of Eq.(\ref{['Mopt']}), the red line is the additive option of Eq.(\ref{['Aopt']}) while the blue line is the intermediate option of Eq.(\ref{['Iopt']}). The cyan line gives signal plus background (LO) neglecting interference.
• Figure 4: Interference effects (see Eq.(\ref{['percp']})) in the ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ distribution for $\mu{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$μ_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$= 700~\text{GeV}$. The black line is the central value, the blue lines give the estimated theoretical uncertainty.
• Figure 5: Interference effects (see Eq.(\ref{['percp']})) in the ${} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace {} { {} { { {{\bm{ { {\mathsf{ {} {} {{Z}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace$ distribution for $\mu{ {} { {} { { {{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}} } } } \xspace}$μ_ ${{\bm{ { {\mathsf{ {} {} {{H}_{ {\!\mspace{1mu}} }^{}} \mspace{-0.6mu} }} } }}}$$= 800~\text{GeV}$. The black line is the central value, the blue lines give the estimated theoretical uncertainty.