  Debris disks or belts are important signposts for the presence of colliding
planetesimals and, therefore, for ongoing planet formation and evolution
processes in young planetary systems. Imaging of debris material at small
separations from the star is very challenging but provides valuable insights
into the spatial distribution of so-called hot dust produced by solid bodies
located in or near the habitable zone. We report the first detection of
scattered light from the hot dust around the nearby (d = 28.33 pc) A star HD
172555. We want to constrain the geometric structure of the detected debris
disk using polarimetric differential Imaging (PDI) with a spatial resolution of
25 mas and an inner working angle of about 0.1$''$. We measured the polarized
light of HD 172555, with SPHERE-ZIMPOL, in the very broad band (VBB;
$\lambda=735$ nm) filter for the projected separations between 0.08$''$ (2.3
au) and 0.77$''$ (22 au). We constrained the disk parameters by fitting models
for scattering of an optically thin dust disk taking the limited spatial
resolution and coronagraphic attenuation of our data into account. The
geometric structure of the disk in polarized light shows roughly the same
orientation and outer extent as obtained from thermal emission at 18 $\mu$m.
Our image indicates the presence of a strongly inclined ($i\sim 103.5^\circ$),
roughly axisymmetric dust belt with an outer radius in the range between
0.3$''$ (8.5 au) and 0.4$''$ (11.3 au). We derive a lower limit for the
polarized flux contrast ratio for the disk of $(F_{\rm pol})_{\rm disk}/F_{\rm
\ast}> (6.2 \pm 0.6)\cdot 10^{-5}$ in the VBB filter. This ratio is small, only
9 %, when compared to the fractional infrared flux excess ($\approx 7.2\cdot
10^{-4}$). The model simulations show that more polarized light could be
produced by the dust located inside 2 au, which cannot be detected with the
instrument configuration used.
