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$^-$ → hZ), such a collider would measure weak boson pair production (e$^+$e$^-$ → WW) with an astonishing precision. The weak-boson-fusion production process (e$^+$e$^-$→ $\nu\bar{\nu}$h) provides an increasingly powerful handle at higher center-of-mass energies. High energies also benefit the associated top-Higgs production (e$^+$e$^-$ → $t\bar{t}$h) 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