Correlations (stat.+syst.) between the $d\Gamma_i/d w$ bins for the individual $B \rightarrow D \ell \nu$ modes (40x40). Element indices 0-39 are organized as: - Indices 0-9: $B^+ \to D^0 e^+ \nu_e$ in $w$ bins 0-9 - Indices 10-19: $B^+ \to D^0 \mu^+ \nu_\mu$ in $w$ bins 0-9 - Indices 20-29: $B^0 \to D^- e^+ \nu_e$ in $w$ bins 0-9 - Indices 30-39: $B^0 \to D^- \mu^+ \nu_\mu$ in $w$ bins 0-9 where $w$ bins 0-9 correspond to: 0: [1.00, 1.06], 1: [1.06, 1.12], 2: [1.12, 1.18], 3: [1.18, 1.24], 4: [1.24, 1.30], 5: [1.30, 1.36], 6: [1.36, 1.42], 7: [1.42, 1.48], 8: [1.48, 1.54], 9: [1.54, 1.59]

$M_{\tau}$ 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 $1/f_{\mathrm{a}}=2~\mathrm{TeV}^{-1}$

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|y_{e u}|$, versus $S_{e u}$ mass for scalar LQs coupled to electrons.

Observed and Expected UL exclusions on the $BR(H\to S)$ of generic signals with $m_{A'} = 1.0\;GeV$ and $BR(A' \rightarrow \pi\pi) = 1.0$.

The observed data in the dielectron channel and the fitted signal-plus-background templates, shown for the $S_{e d}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Observed and Expected UL exclusions on the number of 'signal' yields in sideband A from the model agnostic fit, assuming no 'SUEP-like' signal contamination in the CRs.

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|y_{e d}|$, versus $S_{e d}$ mass for scalar LQs coupled to electrons.

Postfit values for SR in the B-Only CR+SR and CR-Only fits with the prefit signal overlayed for reference

The observed data in the dimuon channel and the fitted signal-plus-background templates, shown for the $S_{\mu u}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Postfit values for PR in the B-Only CR+SR and CR-Only fits with the prefit signal overlayed for reference

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|y_{\mu u}|$, versus $S_{\mu u}$ mass for scalar LQs coupled to muons.

Postfit values for CRDY in the B-Only CR+SR and CR-Only fits with the prefit signal overlayed for reference

The observed data in the dimuon channel and the fitted signal-plus-background templates, shown for the $S_{\mu d}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Postfit values for CRTT in the B-Only CR+SR and CR-Only fits with the prefit signal overlayed for reference

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|y_{\mu d}|$, versus $S_{\mu d}$ mass for scalar LQs coupled to muons.

Per-selection efficiencies on Generic - $m_{A'} = 1.0\;GeV$ $BR(A' \rightarrow \pi\pi) = 1.0$ Hadronic - $m_{A'} = 0.7\;GeV$ and $BR(A' \rightarrow ee) = BR(A' \rightarrow \mu\mu) = 0.15$ $BR(A' \rightarrow \pi\pi) = 0.7$ Leptonic - $m_{A'} = 0.5\;GeV$ and $BR(A' \rightarrow ee) = BR(A' \rightarrow \mu\mu) = 0.2$ and $BR(A' \rightarrow \pi\pi) = 0.6$ samples. Selections: 2 OSSF leptons, one SUEP cluster, $60\leq Z_{m}\leq 120$ GeV, $p_{T}^Z\geq 25$ GeV, veto events with b-tagged jets, $p_{T}^{SUEP} > 60\;GeV$, and $dR^{Ak4}_{Ak15} < 1.5$. Efficiencies are the ratio of the histogram size at the selection step to the previous step (except twoLepton vs. initial). The final column is the total cumulative efficiency (dR vs. initial). Note that these selection numbers were all calculated using samples generated with 600,000 events for each signal point considered.

The observed data in the dielectron channel and the fitted signal-plus-background templates, shown for the $V_{e u}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Interpolated observed and expected UL exclusions on $BR(H\to S) = 1$ for generic signals with $m_{A'} = 1.0\;GeV$ and $BR(A' \rightarrow \pi\pi) = 1.0$. The discreate heatmap points can be found in the UL Generic (Observed & Expected) figure in this sandbox

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|g_{e u}|$, versus $V_{e u}$ mass for vector LQs coupled to electrons.

The observed data in the dielectron channel and the fitted signal-plus-background templates, shown for the $V_{e d}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|g_{e d}|$, versus $V_{e d}$ mass for vector LQs coupled to electrons.

The observed data in the dimuon channel and the fitted signal-plus-background templates, shown for the $V_{\mu u}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|g_{\mu u}|$, versus $V_{\mu u}$ mass for vector LQs coupled to muons.

The observed data in the dimuon channel and the fitted signal-plus-background templates, shown for the $V_{\mu d}$ scenario with a candidate LQ mass of 2.5 TeV. Distributions of events are binned in the reconstructed dilepton mass, rapidity, and cosine theta.

Upper limits at $95\%$ CL on the LQ-fermion couplings, $|g_{\mu d}|$, versus $V_{\mu d}$ mass for vector LQs coupled to muons.

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.

Measured values of $R(\tau/e)$ in the different $p_T$ bins. The first row gives the main inclusive measurement of $R(\tau/e)$.

Breakdown of systematic uncertainties in the fit to data. Different individual components used in the fit are combined into categories. The size of the impact each group of uncertainties has on $R(\tau/e)$, which is shown in the second column, is assessed by subtracting in quadrature the uncertainty from the nominal fit and the fit with the relevant nuisance parameters fixed to their post-fit values. The group 'Other sources' includes the uncertainties due to trigger, JVT, luminosity, and pile-up.

Distributions of $|d_0|$ for the $\mu e$ channel of the nominal sample in $7 < p_T < 10$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

Distributions of $|d_0|$ for the $\mu e$ channel of the nominal sample in $10 < p_T < 20$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

Distributions of $|d_0|$ for the $\mu e$ channel of the nominal sample in $20 < p_T < 250$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

Distributions of $|d_0|$ for the $e e$ channel of the nominal sample in $5 < p_T < 10$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

Distributions of $|d_0|$ for the $e e$ channel of the nominal sample in $10 < p_T < 20$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

Distributions of $|d_0|$ for the $e e$ channel of the nominal sample in $20 < p_T < 250$ GeV bin. The data are represented by black markers. The different contributions to the nominal sample, taken from simulation after the fit (`Post-Fit'), are shown by stacked histograms. The bottom panels show the ratio of the data to the simulation prediction after the fit. The systematic uncertainties in the prediction with the constraints from the fit and the correlation between the nuisance parameters applied are represented by the blue hatched bands.

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.