We will present upper limits on the production of heavy neutral leptons (HNLs) decaying to muon-pion pairs using data collected with the MicroBooNE liquid-argon time projection chamber (TPC) operating at Fermilab. This search is the first of its kind performed in a liquid-argon TPC and the first beyond the Standard Model result obtained with the MicroBooNE detector. We use data collected in 2017 and 2018 corresponding to an exposure of 2 x 1020 protons on target from the Fermilab Booster Neutrino Beam, which produces mainly muon neutrinos with an average energy of about 800 MeV. HNLs with higher mass are expected to have a longer time-of-flight to the liquid-argon TPC than Standard Model neutrinos. The data are therefore recorded with a dedicated trigger configured to detect HNL decays that occur after the neutrino spill reaches the detector. We set upper limits at the 90\% confidence level on the element U_mu2 of the extended PMNS mixing matrix in the range for Dirac HNLs and Majorana HNLs, assuming HNL masses between 260 and 385 MeV.
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