Abstract : We studied X-ray reverberation lags in the BHXRB GX 339–4 at the end of the 2014-2015 outburst. We analysed data from a $XMM-Newton$ campaign covering the end of the transition from the soft to the hard state, and the decrease of luminosity in the hard state. During all the observations we detected, at high frequencies, significant disc variability, responding to variations of the power law emission with an average time delay of ∼ 0.009 ± 0.002 s. These new detections of disc thermal reverberation add to those previously obtained and suggest the lag to be always present in hard and hard-intermediate states. Our study reveals a net decrease of lag amplitude as a function of luminosity. We ascribe this trend to variations of the inner flow geometry. A possible scenario implies a $decrease$ of the inner disc truncation radius as the lumi-nosity increases at the beginning of the outburst, followed by an increase of the inner disc truncation radius as the luminosity decreases at the end of the outburst. Finally, we found hints of FeK reverberation (∼ 3σ significance) during the best quality observation of the XMM monitoring. The lag at the FeK energy has similar amplitude as that of the thermally reprocessed component, as expected if the same irradiated region of the disc is responsible for producing both the thermalized and reflected component. This finding suggests FeK reverberation in BHXRBs to be at the reach of current detectors provided observations of sufficiently long exposure are available.
