The leptonic future of the Higgs

Precision study of electroweak symmetry breaking strongly motivates the construction of a lepton collider with center-of-mass energy of at least 240 GeV. Besides Higgsstrahlung ($e^+e^- \to hZ$), such a collider would measure weak boson pair production ($e^+e^- \to WW$) with an astonishing precision. The weak-boson-fusion production process ($e^+e^- \to \nu \bar{\nu} h$) provides an increasingly powerful handle at higher center-of-mass energies. High energies also benefit the associated top-Higgs production ($e^+e^-\to t\bar th$) that is crucial to constrain directly the top Yukawa coupling. The impact and complementarity of differential measurements, at different center-of-mass energies and for several beam polarization configurations, are studied in a global effective-field-theory framework. We define a "global determinant parameter" (GDP) which characterizes the overall strengthening of constraints independently of the choice of operator basis. The reach of the CEPC, CLIC, FCC-ee, and ILC designs is assessed.