Probing Extended Scalar Sectors with Precision $e^+e^-\to Zh$ and Higgs Diphoton Studies.

We compute the one-loop corrections to $\sigma(e^+ e^- \to Z h)$ arising from representative extended Standard Model scalar sector scenarios. According to the new scalar $\mathrm{SU(2)_L}$ representations, we consider the inert doublet, real and complex triplet, quintuplet, and septuplet models. With the sub-percent level precision expected for prospective future $e+e-$ collider measurements of $\sigma(e^+ e^- \to Z h)$, studies of the Higgsstrahlung process will probe extended scalar sector particle spectrum and interactions in a manner complementary to direct searches at the Large Hadron Collider and possible future $pp$ colliders. We also compare with the sensitivity of future Higgs diphoton decay rate measurements. We find that the $\sigma(e^+ e^- \to Z h)$ and $\Gamma(h\to\gamma\gamma)$ complementarity is particularly pronounced for the complex triplet model