Next-to-next-to-leading order event generation for $t\bar{t}H$ production with approximate two-loop amplitude

Abstract

We study Higgs-boson production in association with a top-quark pair ($t\bar{t}H$) at hadron colliders and present the first matching of next-to-next-to-leading order (NNLO) QCD corrections to parton showers using the MiNNLOPS method. For the two-loop amplitude, we employ two established approximations, based on the soft Higgs-boson and high-energy limits, respectively. For the first time, we also construct the latter in full colour and propose a pointwise combination of the two approximations across phase space. By assigning a conservative uncertainty estimate, which remains well below the perturbative uncertainties, we ensure robust and reliable differential predictions, explicitly validated at the one-loop level. Apart from the two-loop amplitude, all remaining ingredients of the MiNNLOPS calculation are included exactly. After thorough validation, we present a series of phenomenological results illustrating the impact of NNLO corrections and parton-shower effects. We consider fiducial predictions for the Higgs-boson decay into photons and include off-shell top-quark decays with tree-level spin correlations in both the dilepton and semileptonic channels. Our $t\bar{t}H$ MiNNLOPS generator is publicly available within the POWHEG framework.

Figures (10)

• Figure 1: Sample of Feynman diagrams for the process $pp\to t\bar{t}H$ at LO.
• Figure 2: Sketch of the behaviour of the weight function $\omega$, which ensures a smooth transition between the two kinematic regimes.
• Figure 3: Predictions for the Higgs-boson transverse momentum ${p_{\text{\scalefont{0.77}T,$H$}}}$ (left column), the invariant mass $m_{t\bar{t}}$ of the top-quark pair (central column), and the invariant mass $m_{t\bar{t} H}$ of the $t \bar{t} H$ final state (right column). The upper plots show the comparison between the exact (solid brown curve), SA (dot-dashed green curve), MA (dotted blue curve), and CA (dashed violet curve) results for the integrated one-loop hard-virtual coefficient, as defined in Eq.\ref{['eq:dsigma_H1']}. The lower plots compare NLO+PS predictions based on the exact (brown solid curve) and CA (dashed violet curve) one-loop amplitude, respectively. The lighter bands display the scale uncertainties, while the darker ones represent the systematic uncertainty assigned to the CA result.
• Figure 4: Predictions for the pseudorapidity $\eta_{\bar{t}}$ of the anti-top quark (left column), the separation $\Delta R^{\eta}_{H,t}$ in the $(\eta-\phi)$ plane between the Higgs boson and the top quark (central column), and the azimuthal angle separation $\Delta \phi_{t,\bar{t}}$ between the top and anti-top quarks (right column). The layout is explained in the caption of figure \ref{['fig:one-loop_validation_fig1']}.
• Figure 5: Comparison of MiNNLO$_{\rm PS}$, MiNLO$^{\prime}$ and NNLO QCD predictions. See text for details.