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.
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