Mathematical Properties of Numerical Inversion for Jet Calibrations

Understand

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.