$M_{\tau}$ 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)

An example of the measured energy distribution in a single OHCal tower, showing the MIP distribution from a GEANT-4 simulation of cosmic-ray muons from EcoMug.

$\frac{dE_T}{d\eta}$ measurements in Au+Au collisions at $\sqrt{s_\mathrm{_{NN}}} = 200$ GeV over the pseudorapidity range $\left|\eta\right| < 1.1$.

Measurement of $\frac{dE_T}{d\eta}$ in 0-5% central Au+Au events as a function of $\eta$ over the range $\left|\eta\right| < 1.1$.

Measured $\frac{dE_T}{d\eta}$ normalized by the estimated number of participant pairs ($0.5$$N_{part}$), as a function of $N_{part}$, using the full calorimeter system.

Measured $\frac{dE_T}{d\eta}$ normalized by the estimated number of participant pairs ($0.5$$N_{part}$), as a function of $N_{part}$, predictions from AMPT.

Measured $\frac{dE_T}{d\eta}$ normalized by the estimated number of participant pairs ($0.5$$N_{part}$), as a function of $N_{part}$, predictions from EPOS.

Measured $\frac{dE_T}{d\eta}$ normalized by the estimated number of participant pairs ($0.5$$N_{part}$), as a function of $N_{part}$, predictions from HIJING.

The distributions of the variables used in the simultaneous fit for the SR. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the predicted uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.

Expected and observed 95% upper limits on the product of the cross section and branching fraction$\sigma(\mathrm{pp} \ ightarrow W\mathrm{a})\mathcal{B}(W ightarrow \ell^{+} v_{\ell})\mathcal{B}(\mathrm{a} \rightarrow Z\gamma)\mathcal{B}(Z \rightarrow \ell^{+} \ell^{-})$ s a function of the ALP mass from 110 to 400 GeV

Expected and observed 95% upper limits on the photophobic ALP model parameter $1/f_{\mathrm{a}}$ as a function of ALP mass reinterpreted from $1/f_{\mathrm{a}}=2~\mathrm{TeV}^{-1}$

Pre-fit MC statistical uncertainties per bin. These values are used to quantify the MC statistical uncertainty contributions to the total uncertainty in $m_t$ based on elements from the covariance matrix obtained in the profile likelihood fit. Each MC statistical contribution is estimated by dividing the relevant covariance matrix entry (see Table 2) by the corresponding pre-fit MC statistical uncertainty for that bin.

The contribution of each source of systematic uncertainty to the total uncertainty in $m_t$ is provided. Each source's contribution is taken directly from the relevant element of the covariance matrix for the profile likelihood fit to $\overline{m_J}$, $m_{jj}$, and $m_{tj}$ using data. The sign of the effect of each uncertainty is included.

The fitted $m_t$ is provided for each replica generated using bootstrapping. Each replica is a 3D histogram of $m_{J}$, $m_{jj}$, and $m_{tj}$, where $m_{J}$ has 50 bins between 145.0 GeV and 205.0 GeV. This method uses the BootstrapGenerator class in ROOT to initialise a pseudo-random number generator for each event, which is seeded by the value of the eventNumber and runNumber variables for a given event in the input dataset. The pseudo-random numbers are drawn from a Poisson distribution with rate parameter equal to 1. These are used to fluctuate the amount by which each replica histogram is filled. There are 1000 replicas, numbered from 0 to 999.

The systematic covariance matrix for the $e^+e^- \to \pi^+ \pi^- \pi^0$ cross section measurement at the Belle II. The 212 x 212 matrix of the energy ranges from 0.62 to 3.50 GeV. This covariance matrix includes all systematic uncertainty given in Table I. The total covariance matrix for the measured cross section can be obtained by adding statistical and systematic covariance matrices.

This table provides the ``inverse'' of the total (stat.+ sys.) covariance matrix. This matrix can be used for a chi-square fit of the mass spectrum. We provide this inverse matrix since special care is needed to take the inverse of the given covariance matrix.

Observed yields and fit results in bins of $\eta(\rm{BDTh})$ as obtained by the HTA fit, corresponding to an integrated luminosity of 362 fb$^{-1}$. The yields are shown for the $B^+ \rightarrow K^{+}\nu\bar\nu$ signal and the three background categories ($B\bar{B}$ decays, $c\bar{c}$ continuum, and light-quark continuum).

Distributions of $\eta(\rm{BDT}_{2})$ in data (points with error bars) and simulation (filled histograms) shown individually for the $B^+ \to K^+ \nu \bar \nu$ signal, neutral and charged $B$-meson decays, and the sum of the five continuum categories in the ITA. Events in the full signal region, with $\eta(\rm{BDT_{2}}) > 0.92$, are shown.

Distributions of $q^2_{\textrm{rec}}$ in data (points with error bars) and simulation (filled histograms) shown individually for the $B^+ \to K^+ \nu \bar \nu$ signal, neutral and charged $B$-meson decays, and the sum of the five continuum categories in the ITA. Events in the full signal region, with $\eta(\rm{BDT_{2}}) > 0.92$, are shown.

Distributions of $\eta(\rm{BDT}_{2})$ in data (points with error bars) and simulation (filled histograms) shown individually for the $B^+ \to K^+ \nu \bar \nu$ signal, neutral and charged $B$-meson decays, and the sum of the five continuum categories in the ITA. Events in the most signal-rich region, with $\eta(\rm{BDT_{2}}) > 0.98$, are shown.

Distributions of $q^2_{\textrm{rec}}$ in data (points with error bars) and simulation (filled histograms) shown individually for the $B^+ \to K^+ \nu \bar \nu$ signal, neutral and charged $B$-meson decays, and the sum of the five continuum categories in the ITA. Events in the most signal-rich region, with $\eta(\rm{BDT_{2}}) > 0.98$, are shown.

Distribution of $q^2$, computed using $B_{tag}$ kinematics for events in the signal region of the HTA. These distributions are obtained for $B^+ \to K^+ \nu \bar \nu$ candidates reconstructed in data (points with error bars), simulation (filled histograms) of $B^+ \rightarrow K^{+}\nu\bar\nu$ signal, $B\bar{B}$ decays, $c\bar{c}$ continuum, and light-quark continuum backgrounds, normalized according to the fit yields in the HTA.

Signal-selection efficiency as a function of the dineutrino invariant mass squared $q^2$ for simulated events in the SR for the ITA. The error bars indicate the statistical uncertainty.

Signal-selection efficiency as a function of the dineutrino invariant mass squared $q^2$ for simulated events in the SR for the HTA. The error bars indicate the statistical uncertainty.

Twice the negative profile log-likelihood ratio as a function of the signal strength $\mu$ for the HTA result. The value for each scan point is determined by fitting the data, where all parameters but $\mu$ are varied.

Twice the negative profile log-likelihood ratio as a function of the signal strength $\mu$ for the ITA result. The value for each scan point is determined by fitting the data, where all parameters but $\mu$ are varied.

Twice the negative profile log-likelihood ratio as a function of the signal strength $\mu$ for the combined result. The value for each scan point is determined by fitting the data, where all parameters but $\mu$ are varied.

Branching-fraction values measured by Belle II, measured by previous experiments, and predicted by the SM.

Data of the decay $\bar{B}^+ \to D^* \mu \nu_\mu$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B0 -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 48 - 95: B0 -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 96 - 143: B+ -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 144 - 191: B+ -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ...

Data of the B+/B0 average $B \to D^* e \nu_e$.

Data of the B+/B0 average $B \to D^* \mu \nu_\mu$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B -> D* e nu_e: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ... Entry 48 - 95: B -> D* mu nu_mu: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], .....

Data of the B+/B0 and e/mu average $B \to D^* \ell \nu_\ell$.

The full experimental (statistical and systematical) correlations of the angular coefficients are shown. The elements are ordered as: Entry 0 - 47: B -> D* l nu_l: DJ1s/Dw [w_bin0, w_bin1, w_bin2, w_bin3], DJ1c/Dw [w_bin0, w_bin1, w_bin2, w_bin3], ...