Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression

TL;DR

This paper showcases how symbolic regression can derive analytical formulas for complex particle kinematic variables, including those defined algorithmically and from simulated data, advancing collider phenomenology analysis methods.

Contribution

It introduces the application of symbolic regression to derive analytical formulas for particle kinematics, including cases without known formulas and after detector simulation.

Findings

Successfully derived formulas for $M_{T2}$ in known cases

Reproduced NLO distribution formulas from simulated data

Generated new analytical approximations post-detector simulation

Abstract

We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the stransverse mass, $M_{T2}$, which are defined algorithmically through an optimization procedure and not in terms of an analytical formula. We then train a symbolic regression and obtain the correct analytical expressions for all known special cases of $M_{T2}$ in the literature. As a second application, we reproduce the correct analytical expression for a next-to-leading order (NLO) kinematic distribution from data, which is simulated with a NLO event generator. Finally, we derive analytical approximations for the NLO kinematic distributions after detector simulation, for which no known analytical formulas currently exist.