Title: The environmental low-frequency background for macro-calorimeters at the millikelvin scale

Abstract: Many of the most sensitive physics experiments searching for rare events, like neutrinoless double beta ($0\nu\beta\beta$) decay and dark matter interactions, rely on cryogenic macro-calorimeters operating at the mK-scale. Located underground at the Gran Sasso National Laboratory (LNGS), in central Italy, CUORE (Cryogenic Underground Observatory for Rare Events) is one of the leading experiments for the search of $0\nu\beta\beta$ decay, implementing the low-temperature calorimetric technology. We present a novel multi-detector analysis to correlate environmental phenomena with the low-frequency noise of low-temperature calorimeters. Indeed, the correlation of marine and seismic data with data from a pair of CUORE detectors indicates that cryogenic detectors are sensitive not only to intense vibrations generated by earthquakes, but also to the much fainter vibrations induced by marine microseisms in the Mediterranean Sea due to the motion of sea waves. Proving that cryogenic macro-calorimeters are sensitive to such environmental sources of noise opens the possibility of studying their impact on the detectors physics-case sensitivity. Moreover, this study could pave the road for technology developments dedicated to the mitigation of the noise induced by marine microseisms, from which the entire community of cryogenic calorimeters can benefit.