Evidence for narrow resonant structures at W approximate to 1.68 GeV and W approximate to 1.72 GeV in real Compton scattering off the proton

First measurement of the beam asymmetry Sigma for Compton scattering off the proton in the energy range E-gamma = 0.85-1.25 GeV is presented. The data reveal two narrow structures at E-gamma = 1.036 and E-gamma = 1.119 GeV. They may signal narrow resonances with masses near 1.68 and 1.72 GeV, or they may be generated by the subthreshold K Lambda and omega p production. Their decisive identification requires additional theoretical and experimental efforts.