Polarization measurement for the dileptonic channel of $W^+ W^-$ scattering using generative adversarial network

Measuring the polarization fractions of the $W^+W^-$ scattering reveals the interactions of the Higgs boson as well as new neutral states that are related to the standard model electroweak symmetry breaking. The dileptonic channel has a relatively lower background rate, but the kinematics of its final states can not be fully reconstructed due to the presence of two neutrinos. We propose neural networks to establish maps between the distributions of measurable quantities and the distributions of the lepton angles in $W$ boson rest frames. New physics contributions and collision energy can largely affect the kinematic properties of the $W^+W^-$ scattering beside the lepton angles. To make the network in ignorance of that information, the loss function is modified in two different ways. We show that the networks are promising in reproducing the lepton angle distributions, and the precision of the fitted polarization fractions obtained from network predictions is comparable to that obtained with the truth lepton angle. Although the best-fit values of polarization fractions do not change much after including the background uncertainty, the precisions is substantially reduced. Our trained models are available at GitHub.