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A search for a Higgs boson decay $H\to\gamma^*\gamma\to\ell\ell\gamma$ ispresented. The analysis is performed using proton-proton collision datarecorded by the CMS detector at the CERN LHC at a centre-of-mass energy of 8TeV, corresponding to an integrated luminosity of 19.7 fb$^{-1}$. The selectedevents have an opposite-sign muon or electron pair and a high transversemomentum photon. No excess above background has been found in the three-bodyinvariant mass range $120<m_{\ell\ell\gamma}<150$ GeV, and limits have beenderived for the Higgs boson production cross section times branching fractionfor the $H\to\gamma^*\gamma\to\ell\ell\gamma$ decay, where the dileptoninvariant mass is less than 20 GeV. For a Higgs boson with $m_H=125$ GeV, a$95\%$ confidence level (CL) exclusion observed (expected) limit is 6.7($5.9^{+.2.8}_{-1.8}$) times the standard model prediction.  Additionally, a search for $H\to(J/\Psi)\gamma\to\mu\mu\gamma$ process ispresented, and an upper limit at $95\%$ CL on the branching fraction of the$H\to(J/\Psi)\gamma$ decay for the 125 GeV Higgs boson is set at$1.5\times10^{-3}$.

Search for the Higgs Boson Decays to a Photon and Two Leptons with Low Dilepton Invariant Mass