Measurement of the \(\mathit{H Z\gamma}\) coupling at the future linear e+e- collider

We examine the prospects for measuring the \(H Z \gamma\) coupling of a standard model-like Higgs boson with a mass between 120 and 160 GeV at the future TESLA linear e + e - 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 \(\nu_e \bar{\nu_e}\) via the W W fusion reaction \(e^+e^- \rightarrow \nu_e \bar{\nu_e} H\), followed by the rare decay into a Z boson and a photon, \(H \rightarrow Z \gamma\). Accounting for all main background contributions, a precision of 27% can be achieved in unpolarized e + e - collisions for M H = 140 GeV. With appropriate initial state polarisations \(\Delta\)BF( \(H \rightarrow Z \gamma\))/BF( \(H \rightarrow Z \gamma\)), or the precisions on the \(H \rightarrow Z \gamma\) partial width, can be improved to 17% and provide valuable information on the \(H Z \gamma\) coupling. For M H = 120 and 160 GeV, the small significance of the signals in unpolarized collisions sets upper limits of 79% respectively 72% at 90% confidence level on the \(H \rightarrow Z \gamma\) branching fraction.