Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics

TL;DR

This paper demonstrates that symbolic regression can efficiently derive accurate analytical expressions for key observables in BSM physics models, enabling faster and more robust parameter inference compared to traditional methods and neural networks.

Contribution

The study shows that symbolic regression can produce accurate, differentiable expressions for BSM observables, improving the speed and robustness of parameter fitting in particle physics models.

Findings

SR yields highly accurate expressions for observables.

SR-based fits agree well with conventional methods.

SR offers advantages in differentiability and global robustness.

Abstract

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.