Aims. Galaxy clusters are key targets in the search for ultra high energy particle accelerators. The Coma cluster represents one of the best candidates for such a search owing to its high mass, proximity, and the established non-thermal radio emission centred on the cluster core. Methods. The HESS (High Energy Stereoscopic System) telescopes observed Coma for 8h in a search for -ray emission at energies >1TeV. The large 3.5FWHM field of view of HESS is ideal for viewing a range of targets at various sizes including the Coma cluster core, the radio-relic (1253+275) and merger/infall (NGC4839) regions to the southwest, and features greater than away. Results. No evidence for point-like nor extended TeV-ray emission was found and upper limits to the TeV flux F(E) for E>1, >5, and >10TeV were set for the Coma core and other regions. Converting these limits to an energy flux E2F(E) the lowest or most constraining is the E>5TeV upper limit for the Coma core (0.2radius) at 8% Crab flux units or phcm-2s-1. Conclusions. The upper limits for the Coma core were compared with a prediction for the -ray emission from proton-proton interactions, the level of which ultimately scales with the mass of the Coma cluster. A direct constraint using our most stringent limit for E>5TeV, on the total energy content in non-thermal protons with injection energy spectrum and spatial distribution following the thermal gas in the cluster, is found to be 0.2times the thermal energy, or erg. The E>5TeV-ray threshold in this case corresponds to cosmic-ray proton energies 50TeV. Our upper limits rule out the most optimistic theoretical models for gamma ray emission from clusters and complement radio observations which constrain the cosmic ray content in clusters at significantly lower proton energies, subject to assumptions on the magnetic field strength. Key words: gamma rays: observations - galaxies: clusters: individual: Coma (ACO1656)
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