论文标题
覆盖您的基础：在限制高能量物理学的有效领域理论时，概况可能比率的渐近分布
Cover Your Bases: Asymptotic Distributions of the Profile Likelihood Ratio When Constraining Effective Field Theories in High-Energy Physics
论文作者
论文摘要
当限制有效的场理论（EFT）时，我们研究了概况似然比（PLR）的渐近分布，并表明Wilks的定理经常受到侵犯，这意味着我们不应该假设PLR遵循$χ^2 $ distibution。当一个或两个真实的EFT耦合以纯粹的线性或二次依赖性调节可观察到的横截面时，我们会得出正确的渐近分布。然后，我们发现，当线性和二次术语贡献时，PLR分布没有简单的形式。在这种情况下，我们为单参数案例提供了部分数字解决方案。使用一种新颖的方法，我们发现可以使用Asimov可能性轮廓的轮廓实验获得定义我们渐近分布的常数。我们的结果可以立即用于获得正确的覆盖范围，当使用PLR作为测试统计量来得出现实世界EFT约束。
We investigate the asymptotic distribution of the profile likelihood ratio (PLR) when constraining effective field theories (EFTs) and show that Wilks' theorem is often violated, meaning that we should not assume the PLR to follow a $χ^2$-distribution. We derive the correct asymptotic distributions when either one or two real EFT couplings modulate observable cross sections with a purely linear or quadratic dependence. We then discover that when both the linear and quadratic terms contribute, the PLR distribution does not have a simple form. In this case we provide a partly-numerical solution for the one-parameter case. Using a novel approach, we find that the constants which define our asymptotic distributions may be obtained experimentally using a profile of the Asimov likelihood contour. Our results may be immediately used to obtain the correct coverage when deriving real-world EFT constraints using the PLR as a test-statistic.
