Data-driven discovery of Tsallis-like distribution using symbolic regression in high-energy physics.

The application of atificial intelligence (AI) in fundamental physics has faced limitations due to its inherently uninterpretable nature, which is less conducive to solving physical problems where natural phenomena are expressed in human-understandable language, i.e. mathematical equations. Fortunately, there exists a form of interpretable AI that aligns seamlessly with this requirement, namely, symbolic regression (SR), which learns mathematical equations directly from data. We introduce a groundbreaking application of SR on actual experimental data with an unknown underlying model, representing a significant departure from previous applications, which are primarily limited to simulated data. This application aims to evaluate the reliability of SR as a bona fide scientific discovery tool. SR is applied on transverse-momentum-dependent distributions of charged hadrons measured in high-energy-physics experiments. The outcome underscores the capability of SR to derive an analytical expression closely resembling the Tsallis distribution. The latter is a well-established and widely employed functional form for fitting measured distributions across a broad spectrum of hadron transverse momentum. This achievement is among the first instances where SR demonstrates its potential as a scientific discovery tool. It holds promise for advancing and refining SR methods, paving the way for future applications on experimental data.