Search for $\gamma\gamma$ decays of a Higgs boson in $e^+e^-$ collisions at $\sqrt{s}$ up to 209 GeV

A search for events with a photon pair arising from the decay of a Higgs boson produced in association with a fermion pair, is performed in 893pb^-1 of data recorded by the ALEPH detector at LEP at centre-of-mass energies up to 209GeV. No excess of such events is found over the expected background. An upper limit is derived on the product of the e^+e^- -> HZ cross section and the H -> gamma gamma branching fraction as a function of the Higgs boson mass. A fermiophobic Higgs boson produced with the Standard Model cross section is excluded at 95\% confidence level for all masses below 105.4GeV/c2