  Binary stars hosting exoplanets are a unique laboratory where chemical
tagging can be performed to measure with high accuracy the elemental abundances
of both stellar components, with the aim to investigate the formation of
planets and their subsequent evolution. Here, we present a high-precision
differential abundance analysis of the XO-2 wide stellar binary based on high
resolution HARPS-N@TNG spectra. Both components are very similar K-dwarfs and
host planets. Since they formed presumably within the same molecular cloud, we
expect they should possess the same initial elemental abundances. We
investigate if the presence of planets can cause some chemical imprints in the
stellar atmospheric abundances. We measure abundances of 25 elements for both
stars with a range of condensation temperature $T_{\rm C}=40-1741$ K, achieving
typical precisions of $\sim 0.07$ dex. The North component shows abundances in
all elements higher by $+0.067 \pm 0.032$ dex on average, with a mean
difference of +0.078 dex for elements with $T_{\rm C} > 800$ K. The
significance of the XO-2N abundance difference relative to XO-2S is at the
$2\sigma$ level for almost all elements. We discuss the possibility that this
result could be interpreted as the signature of the ingestion of material by
XO-2N or depletion in XO-2S due to locking of heavy elements by the planetary
companions. We estimate a mass of several tens of $M_{\oplus}$ in heavy
elements. The difference in abundances between XO-2N and XO-2S shows a positive
correlation with the condensation temperatures of the elements, with a slope of
$(4.7 \pm 0.9) \times 10^{-5}$ dex K$^{-1}$, which could mean that both
components have not formed terrestrial planets, but that first experienced the
accretion of rocky core interior to the subsequent giant planets.
