TS distribution for combinations of blank fields in both the ﹩b\bar{b}﹩ and τ⁺τ⁻ channels of annihilation for the Measured (left), Benchmark (center), and Inclusive (right) samples. The blue histograms refer to the results from this work, while the yellow ones are the ones presented in A. McDaniel et al. (2024). For reference, we report the asymptotic ﹩(1/2){\chi }^{2}﹩ (two DOFs) behavior, following Chernoff’s theorem. The vertical dashed lines are the Gaussian-equivalent 3σ confidence levels (99.73% quantile) for the ﹩(1/2){\chi }^{2}﹩ (two DOFs) distribution (red), our work (blue), and A. McDaniel et al. (2024, yellow).