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The self-couplings of the electroweak gauge bosons are probed at hadroncolliders through the production of a massive gauge boson and a photon. Toextend the theoretical description of this type of final states towardsnext-to-next-to-leading order (NNLO) in QCD, we derive the two-loop QCDcorrections to the helicity amplitudes describing the production of a massivegauge boson in association with a real photon. Our results are obtained byapplying projectors to the general parton-level tensor structure. The leptonicdecay of the vector boson is included, thus allowing for a fully exclusivedescription of the final state. The infrared poles of the amplitudes aredescribed by an infrared factorization formula. We provide an analyticexpression for the finite remainder of the amplitude in terms of one- andtwo-dimensional harmonic polylogarithms. The amplitudes are expressed in thephysical kinematics relevant to gauge-boson-plus-photon production at hadroncolliders. As a by-product, we also derive the two-loop QCD amplitudes forvector-boson-plus-jet production at hadron colliders.

Two-loop QCD helicity amplitudes for $q\bar q \to W^\pm \gamma$ and $q\bar q \to Z^0 \gamma$