  Wide binary stars with similar components hosting planets provide a favorable
opportunity for exploring the star-planet chemical connection. We perform a
detailed characterization of the solar-type stars in the WASP-160 binary
system. No planet has been reported yet around WASP-160A while WASP-160B is
known to host a transiting Saturn-mass planet, WASP-160B b. For this planet, we
also derive updated properties from both literature and new observations.
Furthermore, using TESS photometry, we constrain the presence of transiting
planets around WASP-160A and additional ones around WASP-160B. The stellar
characterization includes, for the first time, the computation of
high-precision differential atmospheric and chemical abundances of 25 elements
based on high-quality Gemini-GRACES spectra. Our analysis reveals evidence of a
correlation between the differential abundances and the condensation
temperatures of the elements. In particular, we find both a small but
significant deficit of volatiles and an enhancement of refractory elements in
WASP-160B relative to WASP-160A. After WASP-94, this is the second stellar pair
among the shortlist of planet-hosting binaries showing this kind of peculiar
chemical pattern. Although we discuss several plausible planet formation and
evolution scenarios for WASP-160A and B that could explain the observed
chemical pattern, none of them can be conclusively accepted or rejected. Future
high-precision photometric and spectroscopic follow-up, as well as
high-contrast imaging observations, of WASP-160A and B, might provide further
constraints on the real origin of the detected chemical differences.
