The Higgs precision program at future lepton colliders aims at (sub) percent level precision measurement of the Higgs properties, shedding light on new physics through the Higgs lamppost. Among the many exclusive Higgs channels that can be measured precisely, the $WW$ fusion to Higgs with subsequent decays into the $b\overline{b}$ final state is of particular importance. This channel provides leading constraints on the Higgs total width in the $\kappa$ framework and greatly improves the constraints in the EFT framework in conjunction with the Higgsstrahlung process. We argue in this paper that there are two effects involving the interplay between the $WW$-fusion and Higgsstrahlung processes which affect the physical information one can extract from the precision measurements. One is the interference between the two amplitudes that amounts to a $-10\%$ correction to the $WW$-fusion signal strength and results in a $4–5\sigma$ discrepancy between theory and measurement if not taken into account. The other takes place in the global fitting procedure where the $ZH$ process is the dominant background with a cross section around 7 times larger than the $WW$-fusion signal. Although the $ZH$ process can be measured to great precision at future lepton colliders, failing to take this interplay into consideration in the coupling extraction will result in constraints on ${\kappa }_W$, the Higgs coupling to $W$-boson pairs, that are 100% too aggressive.

• Received 12 December 2018

DOI:https://doi.org/10.1103/PhysRevD.99.033011

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Published by the American Physical Society