ILD Benchmark: Search for Extra Scalars Produced in Association with a $Z$ boson at $\sqrt{s}=500$ GeV

We study the prospects for discovering an extra scalar boson $S^0$ at the International Linear Collider (ILC) based on a full simulation of the International Large Detector (ILD). In order to provide results in an as model-independent way as possible, the analysis uses the recoil of the scalar against a $Z$ boson decaying into a pair of muons, $e^+e^- \to \mu\mu S^{0}$. This process serves as a physics benchmark for the ILD detector performance at $\sqrt{s}=500$ GeV, specifically for the muon ID and momentum resolution, as well as for the identification of initial state radiation photons and their energy measurement. As final results, the sensitivities for discovering the extra scalars at 2 $\sigma$ level are evaluated in terms of a scale factor $\sin^2{\theta}$ with respect to the Standard Model value of the cross section for the Higgs--strahlung process. Two detector models, IDR-L and IDR-S, are considered in the analysis, which differ in radius of the tracking volume, aspect ratio and strength of the magnetic field. While the two detector models show a visible difference in the precision of the reconstructed invariant di-muon mass, no difference is found at the level of the final results.