Precision Inclusive Higgs Physics at $e^+e^-$ Colliders With Tracking Detectors and Without Calorimetry

A primary goal of a future $e^+e^-$ collider program will be the precision measurement of Higgs boson properties. For practical reasons it is of interest to determine the minimal set of detector specifications required to reach this and other scientific goals. Such information could be useful in developing a staged approach to the full collider project with an initial lower-cost version focused on achieving some of the primary scientific objectives. Here we investigate the precision obtainable for the $e^+ e^- \rightarrow Z h \rightarrow \mu^+ \mu^- X$ inclusive cross section and the Higgs boson mass using the di-muon recoil method, considering a detector that has only an inner tracking system within a solenoidal magnetic field, surrounded by many nuclear interaction lengths of absorbing material, and an outer muon identification system. We find that the sensitivity achievable in these measurements with such a tracking detector is only marginally reduced compared to that expected for a general purpose detector with additional electromagnetic and hadronic calorimeter systems. The difference results mainly from multi-photon backgrounds that are not as easily rejected with tracking detectors. We also comment on the prospects for an analogous measurement of the inclusive cross section $\sigma( e^+ e^- \to Z h \to e^+ e^- X)$. Finally, we study searches for light scalars utilizing the di-muon recoil method, estimating the projected reach with a tracking and general purpose detector.