A new method to measure the trilinear Higgs self-coupling $\lambda_3^{}$ in a single Higgs production process is proposed. Time-reversal-odd (T-odd) asymmetries in the process $e^+_{}e^-_{} \to ZH$, $Z \to f\bar{f}$ are computed from the absorptive part of the electroweak one-loop amplitude. Since the T-odd asymmetries measure the tree-level $t$-channel $ZH \to ZH$ scattering, they can be direct probes of $\lambda_3^{}$. The proposed method is quite challenging; a relatively large statistics and polarized $e^+_{}e^-_{}$ beams are demanded. However, this is probably the only approach to directly measure $\lambda_3^{}$ in $e^+_{}e^-_{}$ collisions, when a beam energy above the $ZHH$ production threshold is not available.
Nakamura, J., & Shivaji, A. (2019). Direct measurement of the Higgs self-coupling in $e^+e^- \to ZH$. Physics Letters. Section B: Nuclear, Elementary Particle and High-Energy Physics, B797, 134821. https://doi.org/10.1016/j.physletb.2019.134821 (Original work published 2019)