$M_{\tau}$ distribution in signal region, (OS$\mu$, Belle II)

$M_{\tau}$ distribution in signal region, (SS$e$, Belle)

$M_{\tau}$ distribution in signal region, (SS$e$, Belle II)

$M_{\tau}$ distribution in signal region, (SS$\mu$, Belle)

$M_{\tau}$ distribution in signal region, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$ and $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$e$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$e$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$e$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$e$, Belle II)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle)

Efficiency as function the helicity angle of the kaon $\cos\theta_{K}$, and the helicity angle of the lepton $\cos\theta_{\ell}$ in bin e the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$e$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$e$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$\mu$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (OS$\mu$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$e$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$e$, Belle II)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$\mu$, Belle)

Efficiency as function of the helicity angle of the kaon $\cos\theta_{K}$, (SS$\mu$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$e$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$e$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$\mu$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (OS$\mu$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$e$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$e$, Belle II)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$\mu$, Belle)

Efficiency as function of the helicity angle of the lepton $\cos\theta_{\ell}$, (SS$\mu$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (OS$e$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (OS$e$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (OS$\mu$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (OS$\mu$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (SS$e$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (SS$e$, Belle II)

Efficiency as function of the acoplanarity angle $\phi$, (SS$\mu$, Belle)

Efficiency as function of the acoplanarity angle $\phi$, (SS$\mu$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$e$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$e$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (OS$\mu$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$e$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$e$, Belle II)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle)

Efficiency as function of the four-momentum-transfer $q^{2}$, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}\ell)$, (SS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (OS$\mu$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$e$, Belle II)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle)

Efficiency as function of the invariant mass squared $m^2(K^{*0}t_{\tau})$, where $t_{\tau}$ is the track from the $\tau$, (SS$\mu$, Belle II)

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of $|y_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Fiducial differential cross-sections as a function of $m_{e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Fiducial differential cross-sections as a function of $|\Delta\phi_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Fiducial differential cross-sections as a function of $\cos(\theta^{*})$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Fiducial differential cross-sections as a function of $E_{\mathrm{T}}^{\mathrm{miss}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Fiducial differential cross-sections as a function of $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Fiducial differential cross-sections as a function of $m_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of the number of jets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Fiducial differential cross-sections as a function of $S_{\mathrm{T}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Measured value of the charge asymmetry, $A_{C}$.

Charge asymmetry $A_C$ measured as a function of the absolute difference of the absolute lepton rapidities $||\eta_{l+}|-|\eta_{l-}||$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Charge asymmetry $A_C$ measured as a function of the invariant mass of the dilepton system $m_{e\mu}$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Measured value of the asymmetry in the CP-odd observable $O_{z}$, $A_{CP}$.

$\xi$ distributions for different jet $p_T$ bins.

$\xi$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

$r$ distributions for different jet $p_T$ bins.

Unfolded $R(\rho_{s})$ observable in the 2-to-3 measurement (normalized and divided by bin width). The parton level is defined with two stable top-quarks and a jet with $p_{T}>50$ GeV and $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Impact of systematic uncertainties on the 2-to-3 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-3 unfolded observable.

Unfolded number of events in the 2-to-7measurement (not normalized). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Covariance matrix for statistical and systematic effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Unfolded $R(\rho_{s})$ observable in the 2-to-7 measurement (normalized and divided by bin width). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Impact of systematic uncertainties on the 2-to-7 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-7 unfolded observable.

Observed profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Observed profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. 3he lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

The expected number of events (estimated by using simulation) from the SM HH signals and single Higgs boson production, and the expected number of events from the continuum background, evaluated in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window in Run 3 for the different low-mass (LM) and high-mass (HM) categories. For comparison, the number of data events is also shown. The uncertainties in the HH signals and single Higgs boson backgrounds include the systematic uncertainties discussed in Section 6. Asymmetric uncertainties arise primarily from the theory calculation of the SM ggF HH cross section and the large uncertainty in the yield of single Higgs bosons produced in ggF events in association with heavy-flavour jets. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious signal uncertainty.

The invariant yields of $\phi$ and $\omega+\rho$ mesons as a function of $\langle N_{\rm part}\rangle$ in Au+Au collisions. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

$R_{AA}$ of $\phi$ meson as a function of $p_T$ for in Au+Au collisions at $\sqrt{s_{_{NN}}}=200$~GeV, compared with Cu+Au collisions at $1.2<|y|<2.2$. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

$R_{AA}$ of $\phi$ meson as a function of $\langle N_{\rm part}\rangle$ for $1.2<|y|<2.2$ in Au+Au collisions at $\sqrt{s_{_{NN}}}=200$~GeV. The systematic uncertainties of type-A (uncorrelated) are combined with statistical uncertainties in quadrature and are labeled as stat. Type-B (correlated) systematic uncertainties are listed as sys.

Observed 95% $\text{CL}_\text{S}$ upper limits on the production cross-section times acceptance times branching ratio to jets, $\sigma \cdot A \cdot \text{BR}$, of Gaussian-shaped signals of 5%, 10%, and 15% width relative to their peak mass, $m_G$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J50 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Acceptance of simulated $Z^\prime$ signal events given the analysis event selection as a function of $m_{Z^\prime}$. The solid black line corresponds to the acceptance without a lower $m_{jj}$ requirement applied, the solid blue line includes the $m_{jj} > 344$ GeV requirement of the J50 signal region, and the solid red line includes the $m_{jj} > 481$ GeV requirement of the J100 signal region.

Numbers of events in each of the two considered datasets after consecutively applying the analysis selections.

Target asymmetry T, recoil asymmetry P, and polarization observable H for $\gamma n \to \eta n$ as a function of the polar center-of-mass angle for bins at the given centroid c.m. energies.