Estimating Large Global Significances with a New Monte Carlo Extrapolation Method

TL;DR

This paper introduces a new Monte Carlo extrapolation method to efficiently estimate large global significances in particle physics, overcoming limitations of traditional counting approaches especially with small sample sizes.

Contribution

The paper presents a novel extrapolation technique for global significance estimation, improving efficiency and applicability over conventional counting methods in Monte Carlo simulations.

Findings

The new method accurately estimates large global significances.

It is effective even with limited Monte Carlo samples.

The approach is validated against traditional methods.

Abstract

In particle physics, it is needed to evaluate the possibility that excesses of events in mass spectra are due to statistical fluctuations as quantified by the standards of local and global significances. Without prior knowledge of a particle's mass, it is especially critical to estimate its global significance. The usual approach is to count the number of times a significance limit is exceeded in a collection of simulated Monte Carlo (MC) 'toy experiments.' To demonstrate this conventional method for global significance, we performed simulation studies according to a recent Compact Muon Solenoid (CMS) result to show its effectiveness. However, this counting method is not practical for computing large global significances. To address this problem, we developed a new 'extrapolation' method to evaluate the global significance. We compared the global significance estimated by our new method with that of the conventional approach, and verified its feasibility and effectiveness. This method is also applicable for cases where only small toy MC samples are available. In this approach, the significance is calculated based on p-values, assuming symmetrical Gaussian distributions.