The study of high-energy gamma rays from passive Giant Molecular Clouds (GMCs) in our Galaxy is an indirect way to characterize and probe the paradigm of the sea of cosmic rays in distant parts of the Galaxy. By using data from the High Altitude Water Cherenkov (HAWC) observatory, we measure the gamma-ray flux above 1 TeV of a set of these clouds to test the paradigm. We selected high-galactic latitude clouds that are in HAWCs field-of-view and which are within 1~kpc distance from the Sun. We find no significant excess emission in the cloud regions, nor when we perform a stacked log-likelihood analysis of GMCs. Using a Bayesian approach, we calculate 95% credible intervals upper limits of the gamma-ray flux and estimate limits on the cosmic-ray energy density of these regions. These are the first limits to constrain gamma-ray emission in the multi-TeV energy range ($>$1 TeV) using passive high-galactic latitude GMCs. Assuming that the main gamma-ray production mechanism is due to proton-proton interaction, the upper limits are consistent with a cosmic-ray flux and energy density similar to that measured at Earth.
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