Theory-informed neural networks for particle physics

Abstract We present a theory-informed reinforcement-learning framework that recasts the combinatorial assignment of final-state particles in hadron collider events as a Markov decision process. A transformer-based deep Q-network, rewarded at each step by the logarithmic change in the magnitude of the tree-level matrix element, learns to map final-state particles to partons. Because the reward derives solely from first-principles theory, the resulting policy is label-free and fully interpretable, allowing every particle to be traced to a definite partonic origin. The method is validated on event reconstruction for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> <mml:mi>t</mml:mi> <mml:mrow> <mml:mover> <mml:mi>t</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:mrow> </mml:mrow> </mml:math> processes at the large hadron collider. At this stage the method is tested on parton-level data only, with tests using momentum smearing used as a proxy for a full simulation. The method maintains robust performance across all processes, demonstrating its scaling with increasing combinatorial complexity. We demonstrate how this method can be used to build a theory-informed classifier for effective discrimination of longitudinal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> pairs, and show that we can construct theory-informed anomaly-detection tools using background process matrix elements. Building on theoretical calculations, this method offers a transparent alternative to black-box classifiers. Being built on the matrix element, the classification and anomaly scores naturally respect all physical symmetries and are much less susceptible to the implicit biases common to other methods. Thus, it provides a framework for precision measurements, hypothesis testing, and anomaly searches at the high-luminosity LHC.