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 $h_2 V V$ 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 $V V \to h_2 \to Z h_1$ 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 $L=0.9~(10)~\mathrm{ab}^{-1}$. We then present the expected discovery sensitivites 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.