A significant fraction of nearby young moving group members harbor circumstellar debris dust disks. Due to their proximity and youth, these disks are attractive targets for studying the early evolution of debris dust and planetesimal belts. Here we present 70 and 160$mu$m observations of 31 systems in the $beta$ Pic moving group, and in the Tucana-Horologium, Columba, Carina and Argus associations, using the Herschel Space Observatory. None of these stars were observed at far-infrared wavelengths before. Our Herschel measurements were complemented by photometry from the WISE satellite for the whole sample, and by submillimeter/millimeter continuum data for one source, HD 48370. We identified six stars with infrared excess, four of them are new discoveries. By combining our new findings with results from the literature, we examined the incidence and general characteristics of debris disks around Sun-like members of the selected groups. With their dust temperatures of <45 K the newly identified disks around HD 38397, HD 48370, HD 160305, and BD-20 951 represent the coldest population within this sample. For HD 38397 and HD 48370, the emission is resolved in the 70$mu$m PACS images, the estimated radius of these disks is ~90 au. Together with the well-known disk around HD 61005, these three systems represent the highest mass end of the known debris disk population around young G-type members of the selected groups. In terms of dust content, they resemble the hypothesized debris disk of the ancient Solar System.
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