Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC

Pair production of helicity-polarized weak bosons $(V_\lambda=W^\pm_\lambda, Z_\lambda)$ from gluon fusion $(gg\to V_\lambda V'_{\lambda'})$ and weak boson fusion $(V_1V_2\to V_\lambda V'_{\lambda'})$ are powerful probes of the Standard Model, new physics, and properties of quantum systems. Measuring cross sections of polarized processes is a chief objective of the Large Hadron Collider's (LHC) Run 3 and high luminosity programs, but progress is limited by the simulation tools that are presently available. We propose a method for computing polarized cross sections that works by directly modifying Feynman rules instead of (squared) amplitudes. The method is applicable to loop-induced processes, and can capture the interference between arbitrary polarization configurations, interference with non-resonant diagrams, as well as off-shell/finite-width effects. By construction, previous results that work at the (squared) amplitude level are recoverable. As a demonstration, we report the prospect of observing and studying polarized $Z_\lambda Z_{\lambda'}$ pairs when produced via gluon fusion and electroweak processes in final-states with four charged leptons at the LHC, using the new method to simulate the gluon fusion process. Our Feynman rules are publicly available as a set of \textit{Universal FeynRules Object} libraries called \texttt{SM\_Loop\_VPolar}.