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A compact representation of the ggg → 0 amplitude

A compact representation of the loop amplitude γγggg → 0 is presented. The result has been obtained by using helicity methods and sorting with respect to an irreducible function basis. We show how to convert spinor representations into a field strength representation of the amplitude. The amplitude defines a background contribution for Higgs boson searches at the LHC in the channel H → γγ + jet which was earlier extracted indirectly from the one-loop representation of the 5-gluon amplitude.