Symbolic Regression for Beyond the Standard Model Physics

Abstract

We propose symbolic regression as a powerful tool for studying Beyond the Standard Model physics. As a benchmark model, we consider the so-called Constrained Minimal Supersymmetric Standard Model, which has a four-dimensional parameter space defined at the GUT scale. We provide a set of analytical expressions that reproduce three low-energy observables of interest in terms of the parameters of the theory: the Higgs mass, the contribution to the anomalous magnetic moment of the muon, and the cold dark matter relic density. To demonstrate the power of the approach, we employ the symbolic expressions in a global fits analysis to derive the posterior probability densities of the parameters, which are obtained extremely rapidly in comparison with conventional methods.

Figures (4)

• Figure 1: Symbolic regressors' performance on the test set. Upper panels: "true vs. prediction" scatter plots, the solid lines marking the boundary of the physically viable values of the observables. Lower panels: distribution of relative errors, the vertical lines offering a visual guide for relative errors of order 1%, 10%, and 100%.
• Figure 2: Performance of the classifier symbolic regressor on the test set. Left panel shows the output of the classifier where class 0 (in blue) are physically disallowed points and class 1 (in green) are allowed points. The right panel shows the ROC curve which makes clear the excellent performance of the classifier.
• Figure 3: The posterior distributions obtained by MultiNest for global fits of the CMSSM parameters to $m_{H^0}$, $\delta (g-2)_\mu$, and $\Omega_{\rm DM} h^2$, using solely package-based (2-dimensional scatter plots on the off-diagonal entries, and black lines on the 1-dimensional plots) versus solely expression-based (the red lines) approaches. Mass dimensionful parameters are in GeV.
• Figure 4: The posterior distributions obtained by Dynesty for global fits of the CMSSM parameters to $m_{H^0}$, $\delta (g-2)_\mu$, and $\Omega_{\rm DM} h^2$, using solely package-based (2-dimensional scatter plots on the off-diagonal entries, and black lines on the 1-dimensional plots) versus solely expression-based (the red lines) approaches. Mass dimensionful parameters are in GeV.