HD95086 (A8V, 17Myr) hosts a rare planetary system for which a multi-belt debris disk and a giant planet of 4-5MJup have been directly imaged. Our study aims to characterize the physical and orbital properties of HD95086b, search for additional planets at short and wide orbits and image the cold outer debris belt in scattered light. We used HARPS at the ESO 3.6m telescope to monitor the radial velocity of HD95086 over 2 years and investigate the existence of giant planets at less than 3au orbital distance. With the IRDIS dual-band imager and the IFS integral field spectrograph of SPHERE at VLT, we imaged the faint circumstellar environment beyond 10au at six epochs between 2015 and 2017. We do not detect additional giant planets around HD95086. We identified the nature (bound companion or background contaminant) of all point-like sources detected in the IRDIS field of view. None of them correspond to the ones recently discovered near the edge of the cold outer belt by ALMA. HD95086b is resolved for the first time in J-band with IFS. Its near-infrared spectral energy distribution is well fitted by a few dusty and/or young L7-L9 dwarf spectral templates. The extremely red 1-4um spectral distribution is typical of low-gravity objects at the L/T spectral type transition. The planets orbital motion is resolved between January 2015 and May 2017. Together with past NaCo measurements properly re-calibrated, our orbital fitting solutions favor a retrograde low to moderate-eccentricity orbit e=0.2 (0.0 to 0.5), with a semi-major axis 52au corresponding to orbital periods of 288$ yrs and an inclination that peaks at i = 141deg, which is compatible with a planet-disk coplanar configuration. Finally, we report the detection in polarimetric differential imaging of the cold outer debris belt between 100 and 300au, consistent in radial extent with recent ALMA 1.3mm resolved observations.
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