NNLO QCD predictions for jet observables in ZH production at electron-positron colliders

TL;DR

This work delivers NNLO QCD predictions for jet observables in $e^+e^- \to ZH$ production at $\sqrt{s}=240$ GeV, with $Z$ decaying leptonically and the Higgs hadronically via $H\to b\bar{b}$ or $H\to gg$ in the infinite top-mass limit. The authors implement a fully-differential, factorised calculation using antenna subtraction within the NNLOJET framework, treating the two hadronic Higgs decay channels independently due to massless-quark kinematics and including off-shell $Z$ and $H$ effects in the lab frame. They analyze jet rates, jet energies, and angular observables, exploring the Durham jet parameter $y_{\text{cut}}$ and highlighting mode-dependent differences: the gluonic channel shows larger higher-order corrections and perturbative uncertainties, while the $H\to b\bar{b}$ channel exhibits better convergence. The results provide crucial inputs for precision Higgs coupling measurements at future $e^+e^-$ colliders and guide the interpretation of hadronic Higgs decays in boosted $ZH$ events.

Abstract

We present precise predictions for a variety of jet observables in $ZH$ production at electron-positron colliders, with the $Z$ boson decaying leptonically and the Higgs boson decaying into two hadronic jets, up to NNLO in perturbative QCD. We consider a Higgs boson decaying into bottom (charm) quark pairs via Yukawa interaction and into gluons via an effective vertex in the limit of infinite top quark mass. We present results for the two decay modes separately, highlighting relevant differences in the differential distributions, and for the sum of all decay channels, including a comparison between different choices of the Durham (or $k_T$) jet resolution parameter.

Figures (6)

• Figure 1: Feynman diagrams for the production of a $Z$ and a Higgs boson at electron-positron colliders, with leading order hadronic decays of the Higgs boson to bottom quarks via Yukawa interaction and gluons via an effective vertex denoted as a crossed dot.
• Figure 2: Top row: jet rates in the $H\rightarrow b\bar{b}$ (left) and $H\rightarrow gg$ (right) channels in $ZH$ production at lepton colliders. Bottom row: two-jet (left) and three-jet rate (right) for individual decay channel and the total sum, with the ratio to total shown in the lower frame.
• Figure 3: Energy distribution of the leading Durham-algorithm jets. In the top row: results for $y_{\text{cut}} = 0.03$ in the $H\to b\bar{b}$ (left) and the $H\to gg$ (right) channels at LO (green), NLO (blue), and NNLO (red), with the ratio to NLO shown in the lower frame. Bottom left panel: comparison between the total sum of all decay channels (teal), $H\to b\bar{b}$ (yellow), $H\to gg$ (purple), and $H\to c\bar{c}$ (light blue) at NNLO, with the ratio to the total shown in the lower frame. Bottom right panel: comparison between predictions for the sum over all decay channels at NNLO at $y_{\text{cut}} = 0.01$, $y_{\text{cut}} = 0.03$ and $y_{\text{cut}} = 0.1$, with the ratio to the $y_{\text{cut}} = 0.03$ results shown in the lower frame.
• Figure 4: Energy distribution of the subleading Durham-algorithm jet. In the top row: results for $y_{\text{cut}} = 0.03$ in the $H\to b\bar{b}$ (left) and the $H\to gg$ (right) channels at LO (green), NLO (blue), and NNLO (red), with the ratio to NLO shown in the lower frame. Bottom left panel: comparison between the total sum of all decay channels (teal), $H\to b\bar{b}$ (yellow), $H\to gg$ (purple), and $H\to c\bar{c}$ (light blue) at NNLO, with the ratio to the total shown in the lower frame. Bottom right panel: comparison between predictions for the sum over all decay channels at NNLO at $y_{\text{cut}} = 0.01$, $y_{\text{cut}} = 0.03$ and $y_{\text{cut}} = 0.1$, with the ratio to the $y_{\text{cut}} = 0.03$ results shown in the lower frame.
• Figure 5: Distribution of the angle between leading and subleading Durham-algorithm jet. In the top row: results for $y_{\text{cut}} = 0.03$ in the $H\to b\bar{b}$ (left) and the $H\to gg$ (right) channels at LO (green), NLO (blue), and NNLO (red), with the ratio to NLO shown in the lower frame. Bottom left panel: comparison between the total sum of all decay channels (teal), $H\to b\bar{b}$ (yellow), $H\to gg$ (purple), and $H\to c\bar{c}$ (light blue) at NNLO, with the ratio to the total shown in the lower frame. Bottom right panel: comparison between predictions for the sum over all decay channels at NNLO at $y_{\text{cut}} = 0.01$, $y_{\text{cut}} = 0.03$ and $y_{\text{cut}} = 0.1$, with the ratio to the $y_{\text{cut}} = 0.03$ results shown in the lower frame.