$e^+e^- \to ZH$ at NLO EW matched to a QED parton shower

Abstract

To prepare for the next generation particle collider, likely to be a high-energy precision-frontier electron-positron machine, theoretical predictions must improve in tandem. One aspect in which it is necessary to build on the progress made at LEP and at low-energy $e^+e^-$ colliders is in the modelling of initial-state QED radiation from leptons. In this paper we combine the MC@NLO parton shower matching method with QED resummation methods such as the electron structure function to obtain an automated, process-independent NLO-matched QED parton shower. The case of an electron-positron collider provides a particular challenge to the method due to the integrable singularity present in the lepton structure function, at variance with QCD PDFs. We develop new methods to allow a standard dipole parton shower to operate in the presence of this singularity. We validate the method by examining its dependence on infrared parameters and by verifying both the NLO-correctness, and the resummation properties, of the MC@NLO prediction. Finally, we present results for the case of Higgs production in association with an on-shell $Z$ boson at two proposed FCC-ee energies, the first such predictions at EW NLO+PS accuracy.

Figures (9)

• Figure 1: Dipole configurations of the Catani-Seymour splitting functions.
• Figure 2: The electron structure function near $x=1$, comparing different rescaling schemes. Both the $x$ and $y$ axes are logarithmic.
• Figure 3: Plots showing the effect of varying the parton shower infrared cutoff, $t_c$, for the process $e^+ e^- \to \nu_\mu \bar{\nu}_\mu$ at two different collider energies, 91.2 GeV (left) and 500 GeV (right). The observables shown are the neutrino transverse momentum (top row), the 0-to-1 jet rate (middle) and the second photon transverse momentum (bottom). The infrared cutoff is varied logarithmically between $10^{-6}\,\text{Ge V}^2$ and $10^{-1}\,\text{Ge V}^2$.
• Figure 4: Plots showing the effect of varying the structure function $\epsilon$ parameter for the process $e^+ e^- \to \nu_\mu \bar{\nu}_\mu$ at two different collider energies, 91.2 GeV (left) and 500 GeV (right). The observables shown are the neutrino-pair invariant mass (top row), the 0-to-1 jet rate (middle) and the second photon transverse momentum (bottom). $\epsilon$ is varied logarithmically between $10^{-9}$ and $10^{-5}$.
• Figure 5: Plots showing the effect of varying the structure function $\delta$ parameter for the process $e^+ e^- \to \nu_\mu \bar{\nu}_\mu$ at two different collider energies, 91.2 GeV (left) and 500 GeV (right). The observables shown are the neutrino-pair invariant mass (top row), the 0-to-1 jet rate (middle) and the second photon transverse momentum (bottom). $\delta$ is varied logarithmically between $10^{-7}$ and $10^{-3}$. For 91.2 GeV, the ratio is given with respect to $\delta=10^{-7}$ while for 500 GeV, $\delta=10^{-6}$ is used as the reference.