Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

TL;DR

This paper introduces a novel non-linear moment morphing method for interpolating between multi-dimensional histograms, enabling efficient modeling of complex parameter dependencies in particle physics analyses.

Contribution

The method provides a scalable approach to interpolate multi-dimensional templates with non-linear dependencies, improving modeling of systematic uncertainties in particle physics.

Findings

Efficient interpolation of multi-dimensional histograms.

Handles non-linear dependencies between model parameters.

Scales well with the number of templates.

Abstract

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates is often required to model the impact of systematic uncertainties.