A direct search for the Standard Model Higgs boson decaying to a pair of charm quarks is presented. Associated production of the Higgs and $Z$ bosons, in the decay mode $ZH\rightarrow \ell^+ \ell^- c \bar{c}$ is studied. A dataset with an integrated luminosity of 36.1 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13$ TeV recorded by the ATLAS experiment at the LHC is used. The $H\rightarrow c\bar{c}$ signature is identified using charm-tagging algorithms. The observed (expected) upper limit on $\sigma(pp \rightarrow ZH) \times \mathcal{B}(H \rightarrow c\bar{c})$ is 2.7 ($3.9^{+2.1}_{-1.1}$) pb at the 95% confidence level for a Higgs boson mass of 125 GeV, while the Standard Model value is 26 fb.

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