Direct measurement of the Higgs self-coupling in $e^+e^- \to ZH$

Abstract: A new method to measure the trilinear Higgs self-coupling $\lambda_3<sup>{}$ in a single Higgs production process is proposed. Time-reversal-odd (T-odd) asymmetries in the process $e^{+<em>{}e^-</em>{}} \to ZH$, $Z \to f\bar{f}$ 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 $\lambda_3<sup>{}$. The proposed method is quite challenging; a relatively large statistics and polarized $e<sup>+<em>{}e^-</em>{}$ beams are demanded. However, this is probably the only approach to directly measure $\lambda_3<sup>{}$ in $e<sup>+<em>{}e^-</em>{}$ collisions, when a beam energy above the $ZHH$ production threshold is not available.