A measurement of the Standard Model Higgs boson produced in association with a or boson and decaying into a pair of -leptons is presented. This search is based on proton-proton collision data collected at TeV by the ATLAS experiment at the LHC corresponding to an integrated luminosity of 140 fb. For the Higgs boson candidate, only final states with at least one -lepton decaying hadronically () are considered. For the vector bosons, only leptonic decay channels are considered: and , with . An excess of events over the expected background is found with an observed (expected) significance of 4.2 (3.6) standard deviations, providing evidence of the Higgs boson produced in association with a vector boson and decaying into a pair of -leptons. The ratio of the measured cross-section to the Standard Model prediction is . This result represents the most accurate measurement of the \vh process achieved to date.

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