Testable Likelihoods for Beyond-the-Standard Model Fits

TL;DR

This paper introduces a novel approach using normalising flows to construct likelihood functions for Beyond-the-Standard Model (BSM) fits, enabling accurate information transfer from low-energy data to high-energy models and facilitating goodness-of-fit testing.

Contribution

It proposes a new method employing normalising flows to build likelihood functions for BSM analyses, improving transfer accuracy and testing capabilities.

Findings

Normalising flows can accurately model complex likelihoods.

The method enables effective goodness-of-fit testing.

Application to non-Gaussian, multi-modal examples demonstrates robustness.

Abstract

Studying potential BSM effects at the precision frontier requires accurate transfer of information from low-energy measurements to high-energy BSM models. We propose to use normalising flows to construct likelihood functions that achieve this transfer. Likelihood functions constructed in this way provide the means to generate additional samples and admit a ``trivial'' goodness-of-fit test in form of a $\chi^2$ test statistic. Here, we study a particular form of normalising flow, apply it to a multi-modal and non-Gaussian example, and quantify the accuracy of the likelihood function and its test statistic.