The Method of Moments is a powerful framework to disentangle the relative contributions of amplitudes of a specific process to its various phase space regions. We apply this method to carry out a fully differential analysis of the Higgs decay channel h → 4ℓ and constrain gauge-Higgs coupling modifications parametrised by dimension-six effective operators. We find that this analysis approach provides very good constraints and minimises degeneracies in the parameter space of the effective theory. By combining the decay h → 4ℓ with Higgs-associated production processes, Wh and Zh, we obtain the strongest reported bounds on anomalous gauge-Higgs couplings.

We study standard electroweak/Higgs processes at the high-energy lepton colliders ILC and CLIC. We identify a subset of three operators in the SMEFT that give leading contributions to these processes at high energies. We then perform a ‘high-energy fit’ including these operators. Our final bounds surpass existing LEP bounds and HL-LHC projections by orders of magnitude. Furthermore, we find that these colliders can probe scales up to tens of TeV, corresponding to the highest scales explored in electroweak/Higgs physics.