We present sensitive observations carried out with the Atacama Large Millimeter/Submillimeter Array (ALMA) of the dusty debris disk HD 95086. These observations were made in bands 6 (223 GHz) and 7 (338 GHz) with an angular resolution of about 1$$ which allowed us to resolve well the debris disk with a deconvolved size of 7.0$$ $times$ 6.0$$ and with an inner depression of about 2$$. We do not detect emission from the star itself and the possible inner dusty belt. We also do not detect CO (J=2-1) and (J=3-2) emission, excluding the possibility of an evolved gaseous primordial disk as noted in previous studies of HD95086. We estimated a lower limit for the gas mass of $leq$0.01 M$_oplus$ for the debris disk of HD95086. From the mm. emission, we computed a dust mass for the debris disk HD95086 of 0.5$pm$0.2 M$_oplus$, resulting in a dust-to-gas ratio of $geq$50. Finally, we confirm the detection of a strong submillimeter source to the northwest of the disk (ALMA-SMM1) revealed by recent ALMA observations. This new source might be interpreted as a planet in formation on the periphery of the debris disk HD 95086 or as a strong impact between dwarf planets. However, given the absence of the proper motions of ALMA-SMM1 similar to those reported in the debris disk (estimated from these new ALMA observations) and for the optical star, this is more likely to be a submillimeter background galaxy.
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