This note presents a search for the Standard Model Higgs boson in the decay channel $H \rightarrow Z\gamma$, $Z \rightarrow ℓℓ$, where $ℓ=e$ or $\mu$, using 20.7 $fb^{−1}$ of proton-proton collisions at $\sqrt{s} =$ 8 TeV and 4.6 $fb^{−1}$ of proton-proton collisions at $\sqrt{s}=7$ TeV recorded with the ATLAS detector at the LHC. The distribution of the difference $\Delta m$ between the final state three-body invariant mass $m_{ℓℓ\gamma}$ and the di-lepton invariant mass $m_{ℓℓ}$ is compared to Standard Model background expectations. No significant deviation from the SM prediction is observed and upper limits on the cross section of a Higgs boson with a mass between 120 and 150 GeV are derived. The expected exclusion limits at 95% confidence level range between 7.3 and 22 times the predicted Standard Model cross section. The observed exclusion limits range between 5.4 and 37 times the Standard Model cross section. For a Higgs boson mass of 125 GeV, the expected and observed limits are 13.5 and 18.2 times the Standard Model, respectively.

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