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The second and third channels target LLPs respectively produced in association with a $W$ or $Z$ boson that decays leptonically. In each channel, different search regions target different kinematic regimes, to cover a broad range of LLP mass hypotheses and models. No excesses of events relative to the background predictions are observed. Higgs boson branching fractions to pairs of hadronically decaying neutral LLPs larger than 1% are excluded at 95% confidence level for proper decay lengths in the range of 30~cm to 4.5~m depending on the LLP mass, a factor of three improvement on previous searches in the hadronic calorimeter. The production of long-lived dark photons in association with a $Z$ boson with cross-sections above 0.1~pb is excluded for dark photon mean proper decay lengths in the range of 20~cm to 50~m, improving previous ATLAS results by an order of magnitude. Finally, long-lived photo-phobic axion-like particle models are probed for the first time by ATLAS, with production cross-sections above 0.1~pb excluded in the 0.1~mm to 10~m range.","hasPart":[{"@id":"https://doi.org/10.17182/hepdata.153520.v1/t1","@type":"Dataset","description":"Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as...","name":"Figure 8a"},{"@id":"https://doi.org/10.17182/hepdata.153520.v1/t2","@type":"Dataset","description":"Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as...","name":"Figure 8b"},{"@id":"https://doi.org/10.17182/hepdata.153520.v1/t3","@type":"Dataset","description":"Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as...","name":"Figure 8c"},{"@id":"https://doi.org/10.17182/hepdata.153520.v1/t4","@type":"Dataset","description":"Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; 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