Measurement of the $HZ\gamma$ Coupling at the Future Linear \ee Collider

We examine the prospects for measuring the $HZ\gamma$ coupling of a Standard Model-like Higgs boson with a mass between 120 and 160 GeV at the future TESLA linear \ee collider, assuming an integrated luminosity of 1 ab${}^{-1}$ and a center-of-mass energy of 500 GeV. We consider the Higgs boson produced in association with ${\nu }_e\overline{{\nu }_e}$ via the $WW$ fusion reaction $e^{+}{e}^{-}\to {\nu }_e\overline{{\nu }_e}H$, followed by the rare decay into a $Z$ boson and a photon, $H\to Z\gamma$. Accounting for all main background contributions, different selection procedures are discussed. Uncertainties on the \hZg branching fraction of approximately 48% (27%, 44%) can be achieved in unpolarised \ee collisions for $M_H$ = 120 (140, 160) GeV. With appropriate initial state polarisations $\mathrm{\Delta }$BF(\hZg)/BF(\hZg), or the precisions on the \hZg partial width, can be improved to 29% (17%, 27%) and provide valuable information on the $HZ\gamma$ coupling. We regard our results as a convincing confirmation of the great potential of a linear collider to access and reliably measure important parameters of the Higgs boson despite initially overwhelming background with final state signature similar to the signal events.