Uncertainties in the determination of the trilinear Higgs coupling from single-Higgs observables

Circular $${\text{e}}^{+} {\text{e}}^{-}$$ e + e - colliders operating at energies below the di-Higgs production threshold can provide information on the trilinear Higgs self-coupling $$\lambda _{\text {hhh}}$$ λ hhh via its loop contributions to single-Higgs production processes and electroweak precision observables. We investigate how well a non-SM value of $$\lambda _{\text {hhh}}$$ λ hhh can be determined indirectly via its loop contributions within a global EFT fit. Using an inert doublet extension of the SM Higgs sector as an example for a scenario of physics beyond the SM that could be realised in nature, we find that theoretical uncertainties related to the treatment of loop contributions and the truncation of the EFT expansion, which are usually neglected, play an important role in determining the sensitivity to $$\lambda _{\text {hhh}}$$ λ hhh in a global fit. The results obtained from such an indirect determination of $$\lambda _{\text {hhh}}$$ λ hhh without taking these additional uncertainties into account should be considered to be too optimistic, leading to an artificially high precision in the determination of $$\lambda _{\text {hhh}}$$ λ hhh . Such results could therefore be misleading in the quest to precisely identify the underlying physics of electroweak symmetry breaking.