# The leptonic future of the Higgs

## TL;DR

This paper evaluates the potential of future lepton colliders to precisely measure Higgs and electroweak processes, using a global effective-field-theory approach to compare different collider designs.

## Contribution

It introduces a global determinant parameter (GDP) to quantify the overall constraint improvements and assesses the reach of various proposed collider projects.

## Key findings

- Future colliders can significantly improve Higgs and electroweak measurements.
- Differential measurements at different energies enhance constraint precision.
- The GDP provides a basis-independent measure of constraint strength.

## Abstract

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.