Use of $Z$ polarization in $e^{+}{e}^{-}\to ZH$ to measure the triple-Higgs coupling

It is shown that a certain angular asymmetry of charged leptons produced in the decay of $Z$ in the process $e^{+}{e}^{-}\to ZH$, related to a tensor polarization component of the $Z$, can be used to constrain the anomalous triple-Higgs coupling, independent of the other anomalous couplings like the $ZZH$ coupling which dominate at tree level. This is because the angular asymmetry is odd under na" ive time reversal, and hence dependent on loop-level contributions. At a future $e^{+}{e}^{-}$ collider like the International Linear Collider (ILC), for example, a limit of about $3.4$ might be placed on the ratio of the actual triple Higgs coupling to that predicted in the standard model for a centre-of-mass energy of 500 GeV and an integrated luminosity of 30 fb${}^{-1}$ with electron and positron beams having longitudinal polarization of $-80\mathrm{\%}$ and $+30\mathrm{\%}$, respectively.