Equivariant neural networks for robust <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> observables

We introduce the usage of equivariant neural networks in the search for violations of the charge-parity (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math>) symmetry in particle interactions at the CERN Large Hadron Collider. We design neural networks that take as inputs kinematic information of recorded events and that transform equivariantly under a symmetry group related to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mi>P</c:mi></c:math> transformation. We show that this algorithm allows one to define observables reflecting the properties of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>C</e:mi><e:mi>P</e:mi></e:math> symmetry, showcasing its performance in several reference processes in top quark and electroweak physics. Imposing equivariance as an inductive bias in the algorithm improves the numerical convergence properties with respect to other methods that do not rely on equivariance and allows one to construct optimal observables that significantly improve the state-of-the-art methodology in the searches considered. Published by the American Physical Society 2024