Constraining anomalous<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi><mml:mi>V</mml:mi><mml:mi>V</mml:mi></mml:math>interactions at proton and lepton colliders

In this paper, we study the extent to which $CP$ parity of a Higgs boson, and more generally its anomalous couplings to gauge bosons, can be measured at the LHC and a future electron-positron collider. We consider several processes, including Higgs boson production in gluon and weak boson fusion and production of a Higgs boson in association with an electroweak gauge boson. We consider decays of a Higgs boson including $ZZ,WW,\ensuremath{\gamma}\ensuremath{\gamma}$, and $Z\ensuremath{\gamma}$. A matrix element approach to three production and decay topologies is developed and applied in the analysis. A complete Monte Carlo simulation of the above processes at proton and ${e}^{+}{e}^{\ensuremath{-}}$ colliders is performed and verified by comparing it to an analytic calculation. Prospects for measuring various tensor couplings at existing and proposed facilities are compared.