"Critical Delta Chi-squared Map" of "Improved Sterile Neutrino Constraints from the STEREO Experiment with 179 Days of Reactor-On Data"

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.