Context : The recent development of brand new observational techniques and theoretical models have greatly advanced the exoplanet research field .
Despite significant achievements , which have allowed the detection of thousands extrasolar systems , a comprehensive understanding of planetary formation and evolution mechanisms is still desired .
One relevant limitation is given by the accuracy in the measurements of planet-host star ages .
The star GJ 504 has been found to host a substellar companion whose nature is strongly debated .
There has been a recent difference of opinion in the literature owing to the uncertainty on the age of the system : a young age of \sim 160 Myr would imply a giant planet as a companion , but a recent revision pointing to a solar age ( \sim 4 Gyr ) instead suggests a brown dwarf .

Aims : With the aim of shedding light on this debated topic , we have carried out a high-resolution spectroscopic study of GJ 504 to derive stellar parameters , metallicity , and abundances of both light and heavy elements , providing a full chemical characterisation .
The main objective is to infer clues on the evolutionary stage ( hence the age ) of this system .

Methods : We performed a strictly differential ( line-by-line ) analysis of GJ 504 with respect to two reference stars , that is the planet-host dwarf \iota Hor and the subgiant HIP 84827 .
The former is crucial in this context because its stellar parameters ( hence the evolutionary stage ) is well constrained from asteroseismic observations .
Regardless of the zero point offsets , our differential approach allows us to put tight constraints on the age of GJ 504 with respect to \iota Hor , thereby minimising the internal uncertainties .

Results : We found that the surface gravity of GJ 504 is 0.2 \pm 0.07 dex lower than that of the main-sequence star \iota Hor , suggesting a past turn-off evolution for our target .
The isochrone comparison provides us with an age range between 1.8 and 3.5 Gyr , with a most probable age of \approx 2.5 Gyr .
Thus , our findings support an old age for the system ; further evidence comes from the barium abundance , which is compatible with a solar pattern and not enhanced as observed in young stars .

Conclusions : We envisaged a possible engulfment scenario to reconcile all the age indicators ( spectroscopy , isochrones , rotation , and activity ) ; this engulfment could have occurred very recently and could be responsible for the enhanced levels of rotation and chromospheric activity , as previously suggested .
We tested this hypothesis , exploiting a tidal evolution code and finding that the engulfment of a hot Jupiter , with mass not larger than \approx 3 M _ { j } and initially located at \approx 0.03 AU , seems to be a very likely scenario .