Cover your bases: asymptotic distributions of the profile likelihood ratio when constraining effective field theories in high-energy physics

We investigate the asymptotic distribution of profile likelihood ratio (PLR) when constraining effective field theories (EFTs) and show that Wilks’ theorem is often violated, meaning we should not assume PLR to follow a \chi^2 χ2 -distribution. derive correct distributions either one or two real EFT couplings modulate observable cross sections with purely linear quadratic dependence. then discover both terms contribute, does have simple form. In this case provide partly-numerical solution for one-parameter case. Using novel approach, find constants which define our may be obtained experimentally using Asimov contour. Our results immediately used obtain coverage deriving real-world constraints as test-statistic.