The fiducial cross section measured in bins of the azimuthal angle difference between the mesons for events in the fiducial region with 2 Y(1S) with absolute rapidity less than 2.0.

The expected and observed 95% CL limits on the product of the cross section and branching fraction for a tetraquark. The branching fraction is the product of the branching fraction for the decay of the resonance to a Y(1S) meson and two muons, and the Y(1S) meson dimuon branching fraction.

The expected and observed 95% CL limits on the product of the cross section and branching fraction for a scalar state. The branching fraction is the product of the branching fraction for the decay of the resonance to a Y(1S) meson and two muons, and the Y(1S) meson dimuon branching fraction.

The expected and observed 95% CL limits on the product of the cross section and branching fraction for a pseudoscalar state. The branching fraction is the product of the branching fraction for the decay of the resonance to a Y(1S) meson and two muons, and the Y(1S) meson dimuon branching fraction.

The expected and observed 95% CL limits on the product of the cross section and branching fraction for a spin-2 state. The branching fraction is the product of the branching fraction for the decay of the resonance to a Y(1S) meson and two muons, and the Y(1S) meson dimuon branching fraction.

Kinematic properties and charges of the four muons selected in data in the signal region for the measurement of the YY production cross section. MUON1 and MUON2 form the dimuon pair associated to the dimuon object required at trigger-level. The invariant mass of both muon pairs is between 8.6 and 11 GeV. All events pass the trigger requirements and have four muons with a total charge of 0 and with vertex probability above 5%. The muons have pT above 3.5 GeV if they have an absolute pseudorapidity below 0.9 and 2.5 GeV otherwise. The muons pass the medium muon identification criterion.

Exclusion regions at 95% CL in the $m_{\tilde{\chi}_1^0}$ versus $m_{\tilde{g}}$ plane for the T1tttt (upper left) and T5ttbbWW (upper right) models, with off-shell third-generation squarks, and the T5tttt (lower left) and T5ttcc (lower right) models, with on-shell third-generation squarks. For the T5ttbbWW model, $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_1^0} + 5 GeV$, for the T5tttt model, $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} = m_t$, and for the T5ttcc model, $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} = 20 GeV$ and the decay proceeds through $\tilde{t} \to c \tilde{\chi}_1^0$. The right-hand side color scale indicates the excluded cross section values for a given point in the SUSY particle mass plane. The solid black curves represent the observed exclusion limits assuming the approximate-NNLO+NNLL cross sections (thick line), or their variations of $\pm 1$ standard deviations (s.d.) (thin lines). The dashed red curves show the expected limits with the corresponding $\pm 1$ s.d. and $\pm 2$ s.d. uncertainties. Excluded regions are to the left and below the limit curves.

Exclusion regions at 95% CL in the plane of $m_{\tilde{\chi}_1^0}$ versus $m_{\tilde{g}}$ for the T5qqqqWZ model with $m_{\tilde{\chi}_1^\pm}=0.5(m_{\tilde{g}} + m_{\tilde{\chi}_1^0})$~(left) and with $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_1^0} + 20 GeV$~(right). The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m_{\tilde{\chi}_1^0}$ versus $m_{\tilde{g}}$ for the T5qqqqWZ model with $m_{\tilde{\chi}_1^\pm}=0.5(m_{\tilde{g}} + m_{\tilde{\chi}_1^0})$~(left) and with $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_1^0} + 20 GeV$~(right). The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m_{\tilde{\chi}_1^0}$ versus $m_{\tilde{g}}$ for the T5qqqqWW model with $m_{\tilde{\chi}_1^\pm}=0.5(m_{\tilde{g}} + m_{\tilde{\chi}_1^0})$~(left) and with $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_1^0} + 20 GeV$~(right). The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m_{\tilde{\chi}_1^0}$ versus $m_{\tilde{g}}$ for the T5qqqqWW model with $m_{\tilde{\chi}_1^\pm}=0.5(m_{\tilde{g}} + m_{\tilde{\chi}_1^0})$~(left) and with $m_{\tilde{\chi}_1^\pm} = m_{\tilde{\chi}_1^0} + 20 GeV$~(right). The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m_{\tilde{\chi}_1^\pm}$ versus $m_{\tilde{b}_1}$ for the T6ttWW model with $m_{\tilde{\chi}_1^0}=50 GeV$. The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m(\tilde{t}_1)$ versus $m(\tilde{t}_2)$ for the T6ttHZ model with $m(\tilde{t}_1)-m(\tilde{\chi}_1^0)=175 GeV$. The three exclusions represent $\mathcal{B}(\tilde{t}_2\to\tilde{t}_1 Z)$ of 0, 50, and 100%, respectively. The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m(\tilde{t}_1)$ versus $m(\tilde{t}_2)$ for the T6ttHZ model with $m(\tilde{t}_1)-m(\tilde{\chi}_1^0)=175 GeV$. The three exclusions represent $\mathcal{B}(\tilde{t}_2\to\tilde{t}_1 Z)$ of 0, 50, and 100%, respectively. The notations are as in Fig. 7.

Exclusion regions at 95% CL in the plane of $m(\tilde{t}_1)$ versus $m(\tilde{t}_2)$ for the T6ttHZ model with $m(\tilde{t}_1)-m(\tilde{\chi}_1^0)=175 GeV$. The three exclusions represent $\mathcal{B}(\tilde{t}_2\to\tilde{t}_1 Z)$ of 0, 50, and 100%, respectively. The notations are as in Fig. 7.

Upper limits at 95% CL on the cross section for RPV gluino pair production with each gluino decaying into four quarks and one lepton (T1qqqqL, left), and each gluino decaying into a top, bottom, and strange quarks (T1tbs, right).

Upper limits at 95% CL on the cross section for RPV gluino pair production with each gluino decaying into four quarks and one lepton (T1qqqqL, left), and each gluino decaying into a top, bottom, and strange quarks (T1tbs, right).

Upper limits at 95% CL on the product of cross section, detector acceptance, and selection efficiency, $\sigma \mathcal{A} \epsilon$, for the production of an SS lepton pair with at least two jets, as a function of the minimum $p_\mathrm{T}^\mathrm{miss}$ threshold, when $H_\mathrm{T}>300 GeV$ (left), or the minimum $H_\mathrm{T}$ threshold, when $p_\mathrm{T}^\mathrm{miss}<300 GeV$ (right).

Upper limits at 95% CL on the product of cross section, detector acceptance, and selection efficiency, $\sigma \mathcal{A} \epsilon$, for the production of an SS lepton pair with at least two jets, as a function of the minimum $p_\mathrm{T}^\mathrm{miss}$ threshold, when $H_\mathrm{T}>300 GeV$ (left), or the minimum $H_\mathrm{T}$ threshold, when $p_\mathrm{T}^\mathrm{miss}<300 GeV$ (right).

Unfolded R(b/j) cross section ratio versus Z boson transverse momentum

Unfolded R(c/b) cross section ratio versus jet transverse momentum

Unfolded R(c/b) cross section ratio versus Z boson transverse momentum

Parameters of the polynomial fit of net-proton C3/C2 and C4/C2 vs energy in 0-5$\%$ central Au+Au collisions. Polynomial of order 5 and 4 are used to fit C3/C2 and C4/C2 ratio vs energies, respectively.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in STAR Au+Au collisions for nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV for 0-5$\%$ and 70-80$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in Au+Au collisions from UrQMD for 0-5$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions from HRG GCE, HRG GEC excluded volume, HRG CE model.

Cumulants and their ratios up to fourth order in Au+Au collisions at $\sqrt{s_{NN}} = 200 GeV using conventional analytical efficiency corrections and unfolding approaches with various cases of distribution of detector response.

Rapidity dependence of cumulant ratio C4/C2 of net-proton distributions for 0-5$\%$ central Au+Au collisions at nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV.

Significance of deviations in net-proton C4/C2 (or kappa*sigma^2) for central 0-5$\%$ Au+Au collisions and those from UrQMD, HRG and peripheral 70-80$\%$ data.

Yield ratios of chi_c2 over chi_c1 mesons as a function of costh (HX) in the J/psi pT range 8-12 GeV

Yield ratios of chi_c2 over chi_c1 mesons as a function of costh (HX) in the J/psi pT range 12-18 GeV

Yield ratios of chi_c2 over chi_c1 mesons as a function of costh (HX) in the J/psi pT range 18-30 GeV

Data from Figure 32 – STEREO exclusion and exclusion sensitivity contours at 90% C.L. for 179 days reactor-on (phase-I+II). A full graphical presentation can be downloaded at "Resources" for reference.

Data from Figures 33 and 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the two-dimensional method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figures 33 and 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the two-dimensional method. A graphical presentation can be downloaded at "Resources" for reference.

$\Delta \chi^2$ map of phase-I+II data calculated by a raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to slightly modified contours. In addition, the contours were derived using a raster-scan in several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. When generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

Map of mean $\Delta \chi^2$ values derived from simulations of phase-I+II and calculated by the two-dimensional method. To be used analogously to the $\Delta \chi^2$ map of phase-I+II data in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate sensitivity contours at $x$% C.L. for phase-I+II. Additional explanations are given there.