Inferring Interpretable Models of Fragmentation Functions using Symbolic Regression

Fragmentation functions represent a key ingredient in the description of hadron production cross sections in various high-energy physics (HEP) processes, i.e., lepton-nucleon, nucleon-nucleon, and nuclei-nuclei collisions. They provide a quantitative description of the hadronization mechanism [1], which is intrinsically non-perturbative in the Quantum Chromodynamics (QCD) theory. FFs are not calculable in perturbative QCD, and their determination fully relies on physical observables measured in high-energy physics experiments, e.g., the large hadron collider at CERN [2-5], among others. The current methodology relies on global QCD fits [6, 7], commonly referred to as "FFs parameterizations", where a pre-assumed functional form of FFs is fit to a wide range of physical observables to learn its parameters by involving the DGLAP evolution equations [8] which considers the different energy scales of the experimental measurements. FFs represent a key ingredient to describe hadron production in all HEP processes at the running experiments at the large hadron collider (LHC) at CERN, and to make predictions for the next generation of experiments such as the future Electron Ion Collider (EIC) at the Berkeley National Laboratory (BNL) and the future Circular Colider (FCC) at CERN which will run at significantly higher energies (with center-of-mass energy of 100 TeV versus 14 TeV at LHC) thus covering new regions of the kinematic phase space. It is mandatory to question, in the fast-evolving AI era, whether ML could assist in inferring a functional form of FFs directly from data rather than pre-assuming a function, and, most importantly, if the function learned using AI tools is interpretable, human-understandable, and how it compares to designated functions.