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The non-detection of zero-metallicity stars in ultra-faint dwarf galaxies(UFDs) can be used to constrain the Initial Mass Function (IMF) of the first(PopIII) stars by means of a statistical comparison between available data andpredictions from chemical evolution models. To this end we develop a model thatfollows the formation of isolated UFDs, calibrated to best reproduce theavailable data for the best studied system: Bo\"otes I. Our statisticalapproach shows that UFDs are the best suitable systems to study theimplications of the persisting non-detection of zero-metallicity stars on thePopIII IMF, i.e. its shape, the minimum mass ($m_{min}$), and thecharacteristic mass ($m_{ch}$). We show that accounting for the incompletesampling of the IMF is essential to compute the expected number of long-livedPopIII stars in inefficiently star-forming UFDs. By simulating the ColorMagnitude Diagram of Bo\"otes I, and thus take into account the mass-range ofthe observed stars, we can obtain even tighter constrains on $m_{min}$. Byexploiting the 96 stars with measured metallicities ($\rm i < 19$) in the UFDsrepresented by our model, we demonstrate that: $m_{ch} > 1 \rm M_{\odot}$ or$m_{min} > 0.8 \rm M_{\odot}$ at $99\%$ confidence level. This means that apresent day IMF for PopIII stars is excluded by our model, and a top-heavyPopIII IMF is strongly favoured. We can limit $m_{min} > 0.8 \rm M_{\odot}$independent of the PopIII IMF shape by targeting the four UFDs Bo\"otes I,Hercules, Leo IV and Eridanus II with future generation instruments, such asELT/MOSAIC ($\rm i < 25$), which can provide samples of >10\,000 stars.

Ultra-faint dwarf galaxies: unveiling the minimum mass of the first stars