  We carried out a systematic analysis of time lags between X-ray energy bands
in a large sample (32 sources) of unabsorbed, radio quiet active galactic
nuclei (AGN), observed by XMM-Newton. The analysis of X-ray lags (up to the
highest/shortest frequencies/time-scales), is performed in the
Fourier-frequency domain, between energy bands where the soft excess (soft
band) and the primary power law (hard band) dominate the emission. We report a
total of 15 out of 32 sources displaying a high frequency soft lag in their
light curves. All 15 are at a significance level exceeding 97 per cent and 11
are at a level exceeding 99 per cent. Of these soft lags, 7 have not been
previously reported in the literature, thus this work significantly increases
the number of known sources with a soft/negative lag. The characteristic
time-scales of the soft/negative lag are relatively short (with typical
frequencies and amplitudes of \nu\sim 0.07-4 \times 10^{-3} Hz and \tau\sim
10-600 s, respectively), and show a highly significant (\gsim 4\sigma)
correlation with the black hole mass. The measured correlations indicate that
soft lags are systematically shifted to lower frequencies and higher absolute
amplitudes as the mass of the source increases. To first approximation, all the
sources in the sample are consistent with having similar mass-scaled lag
properties. These results strongly suggest the existence of a mass-scaling law
for the soft/negative lag, that holds for AGN spanning a large range of masses
(about 2.5 orders of magnitude), thus supporting the idea that soft lags
originate in the innermost regions of AGN and are powerful tools for testing
their physics and geometry.

High Energy Astrophysical Phenomena