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

## TL;DR

This paper proposes a novel method to directly measure the Higgs self-coupling in electron-positron collisions using T-odd asymmetries, providing a unique approach when other methods are infeasible.

## Contribution

It introduces a new technique utilizing T-odd asymmetries in $e^+e^- o ZH$ to directly probe the Higgs self-coupling, especially when high-energy $ZHH$ production is not accessible.

## Key findings

- T-odd asymmetries relate to the Higgs self-coupling.
- Method requires large data and polarized beams.
- Potentially the only direct measurement approach in certain conditions.

## Abstract

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.