We report the discovery of a super-Earth mass planet in the microlensing event MOA-2012-BLG-505. This event has the second shortest event timescale of $t_{rm E}=10 pm 1$ days where the observed data show evidence of planetary companion. Our 15 minute high cadence survey observation schedule revealed the short subtle planetary signature. The system shows the well known close/wide degeneracy. The planet/host-star mass ratio is $q =2.1 times 10^{-4}$ and the projected separation normalized by the Einstein radius is s = 1.1 or 0.9 for the wide and close solutions, respectively. We estimate the physical parameters of the system by using a Bayesian analysis and find that the lens consists of a super-Earth with a mass of $6.7^{+10.7}_{-3.6}M_{oplus}$ orbiting around a brown-dwarf or late M-dwarf host with a mass of $0.10^{+0.16}_{-0.05}M_{odot}$ with a projected star-planet separation of $0.9^{+0.3}_{-0.2}$AU. The system is at a distance of $7.2 pm 1.1$ kpc, i.e., it is likely to be in the Galactic bulge. The small angular Einstein radius ($theta_{rm E}=0.12 pm 0.02$ mas) and short event timescale are typical for a low-mass lens in the Galactic bulge. Such low-mass planetary systems in the Bulge are rare because the detection efficiency of planets in short microlensing events is relatively low. This discovery may suggest that such low mass planetary systems are abundant in the Bulge and currently on-going high cadence survey programs will detect more such events and may reveal an abundance of such planetary systems.
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