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

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".