Measuring the Higgs Self-Coupling Constant at a Multi-TeV Muon Collider

A lepton collider in the multi-TeV range has the potential to measure the trilinear Higgs self-coupling constant ${\lambda }_{hhh}$ via the W-fusion mode ${\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\to {\nu }_{\mathrm{\ell }}{\bar{\nu }}_{\mathrm{\ell }}hh$. In this paper we do a generator-level study to explore how center-of-mass energy spread, cone size, tracking resolution, and collision energy range affect how precisely a muon collider can measure ${\lambda }_{hhh}$ in comparison to an $e^{+}{e}^{-}$ collider. The smaller spread in center-of-mass energy and higher energy range of a muon collider improve cross section while the larger cone required to reduce beam-induced background hinders detection of double-Higgs events. Our results motivate a more detailed study of a multi-TeV muon collider and innovative detector and analysis technologies required for background rejection and precision measurement.