Taming systematic uncertainties at the LHC with the central limit theorem

TL;DR

This paper demonstrates that in LHC likelihood analyses with many small systematic uncertainties, the central limit theorem allows for analytical marginalization, simplifying the treatment of uncertainties and aiding in reporting detector effects.

Contribution

It introduces a novel analytical approach using the central limit theorem to simplify the handling of numerous small systematic uncertainties in LHC likelihood functions.

Findings

Systematic uncertainties can be marginalized analytically.

The approach simplifies the reporting of detector effects.

Likelihood functions become more manageable with many small uncertainties.

Abstract

We study the simplifications occurring in any likelihood function in the presence of a large number of small systematic uncertainties. We find that the marginalisation of these uncertainties can be done analytically by means of second-order error propagation, error combination, the Lyapunov central limit theorem, and under mild approximations which are typically satisfied for LHC likelihoods. The outcomes of this analysis are i) a very light treatment of systematic uncertainties ii) a convenient way of reporting the main effects of systematic uncertainties such as the detector effects occuring in LHC measurements.