We report the discovery of a super-Earth candidate orbiting the nearby mid-M dwarf Gl\,725A using the radial velocity (RV) method. The planetary signal has been independently identified using high-precision RVs from the SOPHIE and SPIRou spectrographs, in the optical and near-infrared (NIR) domains, respectively. We modelled the stellar activity signal jointly with the planet using two Gaussian processes, one for each instrument to account for the chromaticity of the stellar activity and instrumental systematics, along with a Keplerian model. The signal was significantly detected with a RV semi-amplitude of $1.67 m/s. The planet Gl\,725A b is found to be in an orbit compatible with circular with a period of $11.2201 days. We analysed 27 sectors of TESS photometry, for which no transit event was found. We determined a minimum mass of p i oplus oplus $. The proximity of Gl\,725A (at only 3.5\,pc) makes this new exoplanet one of the closest to Earth and joins the group of S-type low-mass planets in short orbits ($P<15$ days) around close M dwarfs.
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