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Invariant-mass distribution at LO (magenta) and NLO (green) for the OS scheme (a) and the $\MSbar$ scheme with the choice $\mu_t = M_{ZH}/2$ (b). The scale uncertainties are depicted as shaded bands. The lower panels show the $K$-factor.

Invariant-mass distribution at LO (magenta) and NLO (green) for the OS scheme (a) and the $\MSbar$ scheme with the choice $\mu_t = M_{ZH}/2$ (b). The scale uncertainties are depicted as shaded bands. The lower panels show the $K$-factor.

Invariant-mass distribution at LO (magenta) and NLO (green) for the OS scheme (a) and the $\MSbar$ scheme (b) for a wide $M_{ZH}$ range. The NLO results in which the $Z$-radiated diagrams are excluded are shown in blue. The lower panels show the $K$-factor.

Invariant-mass distribution at LO (magenta) and NLO (green) for the OS scheme (a) and the $\MSbar$ scheme (b) for a wide $M_{ZH}$ range. The NLO results in which the $Z$-radiated diagrams are excluded are shown in blue. The lower panels show the $K$-factor.

(a) Various contributions to $ZH$ production at $\mathcal{O}(\as^3)$: the real-emission contributions from the $qg$ and $q\bar{q}$ channel that include all the diagrams considered in this paper are shown as orange and red lines, respectively. The contributions to the same channels including only the $Z$-radiated diagrams are shown as green ($qg$) and yellow ($q \bar{q}$) lines. The Drell-Yan-like contribution at NNLO is shown as a black line. (b) Comparison of the invariant-mass distribution for $gg\to ZH$ at LO and NLO with the Drell-Yan-like contribution at NNLO. For $gg\to ZH$ at NLO, the results with (blue) and without (orange) the contribution from the $Z$-radiated diagrams are shown.

(a) Various contributions to $ZH$ production at $\mathcal{O}(\as^3)$: the real-emission contributions from the $qg$ and $q\bar{q}$ channel that include all the diagrams considered in this paper are shown as orange and red lines, respectively. The contributions to the same channels including only the $Z$-radiated diagrams are shown as green ($qg$) and yellow ($q \bar{q}$) lines. The Drell-Yan-like contribution at NNLO is shown as a black line. (b) Comparison of the invariant-mass distribution for $gg\to ZH$ at LO and NLO with the Drell-Yan-like contribution at NNLO. For $gg\to ZH$ at NLO, the results with (blue) and without (orange) the contribution from the $Z$-radiated diagrams are shown.

Invariant-mass distribution at LO (a) and NLO (b) for different choices of the top-mass renormalization scheme. The lower panels show the ratio of the $\MSbar$ results using various scales over the OS results.

Invariant-mass distribution at LO (a) and NLO (b) for different choices of the top-mass renormalization scheme. The lower panels show the ratio of the $\MSbar$ results using various scales over the OS results.