Mathematical Properties of Numerical Inversion for Jet Calibrations

TL;DR

This paper formalizes the statistical properties of numerical inversion for jet calibration at the LHC, highlighting its biases and proposing extensions to improve accuracy, especially at low energies.

Contribution

It provides a formal statistical framework for numerical inversion, analyzes its biases, and introduces extensions to reduce these biases in jet calibration.

Findings

Numerical inversion is inherently biased.

Common approximations over-estimate resolution.

Extensions can reduce calibration biases.

Abstract

Numerical inversion is a general detector calibration technique that is independent of the underlying spectrum. This procedure is formalized and important statistical properties are presented, using high energy jets at the Large Hadron Collider as an example setting. In particular, numerical inversion is inherently biased and common approximations to the calibrated jet energy tend to over-estimate the resolution. Analytic approximations to the closure and calibrated resolutions are demonstrated to effectively predict the full forms under realistic conditions. Finally, extensions of numerical inversion are presented which can reduce the inherent biases. These methods will be increasingly important to consider with degraded resolution at low jet energies due to a much higher instantaneous luminosity in the near future.