Measuring the Higgs Branching Fraction into two Photons at Future Linear \ee Colliders

We examine the prospects for measuring the \gaga branching fraction of a Standard Model-like Higgs boson with a mass of 120 GeV at the future TESLA linear \ee collider, assuming an integrated luminosity of 1 ab$^{-1}$ and center-of-mass energies of 350 GeV and 500 GeV. The Higgs boson is produced in association with a fermion pair via the Higgsstrahlung process \ee $\to ZH$, with $Z \to$ \qq or \nn, or the WW fusion reaction $e^+e^- \to \nu_e \bar{\nu_e} H$. A relative uncertainty on BF(\hgg) of~16% can be achieved in unpolarized \ee collisions at $\sqrt{s}$=~500 GeV, while for $\sqrt{s}$=~350 GeV the expected precision is slightly poorer. With appropriate initial state polarizations $\Delta$BF(\hgg)/BF(\hgg) can be improved to 10%. If this measurement is combined with the expected error for the total Higgs width, a precision of 10% on the \gaga Higgs boson partial width appears feasible.