Model-independent probes of CP violation in the heavy scalar sector at muon colliders

We propose a model-independent test of CP violation in the scalar sector. We consider a heavy neutral scalar $h_2$ with tree-level couplings at the $h_{2}VV$ and $h_2{h}_{1}Z$ vertices (with $V=W^{\pm },Z$), alongside the 125~GeV SM-like Higgs boson $h_1$. At future muon colliders (MuC), we exploit vector-boson-fusion (VBF) production of $h_2$ followed by the decay $h_2\to Z{h}_1$. In our framework, observing the single process $VV\to h_2\to Z{h}_1$ implies both relevant couplings are nonzero, which is sufficient to establish CP violation in the scalar sector. We simulate signal and backgrounds at $\sqrt{s}=3(10)$~TeV with integrated luminosity $L=0.9(10){\mathrm{a}\mathrm{b}}^{-1}$. We then present the expected discovery sensitivities across the $(c_2,c_{12})$ parameter space (with the coupling parameters $c_2$ and $c_{12}$ defined in the text) for multiple $m_{h_2}$ hypotheses.