Characterising New Physics Models by Effective Dimensionality of Parameter Space

TL;DR

This paper introduces a geometric approach using effective dimensionality to characterize and compare different new physics models based on the distribution of their valid parameter points.

Contribution

It presents a simple algorithm to calculate the box-counting dimension of parameter spaces, providing a quantitative measure for model comparison.

Findings

Effective dimensionality distinguishes different physics models.

The method quantifies the distribution of phenomenologically valid points.

Illustrations demonstrate the approach with models related to flavor observables.

Abstract

We show that the dimension of the geometric shape formed by the phenomenologically valid points inside a multi-dimensional parameter space can be used to characterise different new physics models and to define a quantitative measure for the distribution of the points. We explain a simple algorithm to determine the box-counting dimension from a given set of parameter points, and illustrate our method with examples from different models that have recently been studied with respect to precision flavour observables.