The challenge of monochromatization: Direct s-Channel Higgs Production: $e^+e^- \to H

The FCC-ee could measure the electron Yukawa coupling in a dedicated run at $\sim $125 GeV collision energy, provided that the center-of-mass (CM) energy spread can be reduced by means of monochromatization, e.g., through introducing nonzero horizontal dispersion of opposite sign at the interaction point (IP), for the two colliding beams. If the IP dispersion is nonzero, beamstrahlung blows up the horizontal emittance, and self-consistent IP parameters need to be determined. Two configurations are being studied. The first uses crab cavities to establish effective head-on collisions. The second configuration maintains the standard FCC-ee crossing angle, which, together with the IP dispersion, introduces a correlation between the local collision energy and the longitudinal location inside the detector, thereby allowing for an integrated scan of the Higgs resonance curve. We compare both approaches.