ESPRESSO scratches the surface of the small-mass planet population

The detection and characterization of the small exoplanets population (R < 2 R_⊕ and M < 10 M_⊕) is one of the main focuses of the exoplanet community. This population indeed does not miss scientific and philosophical appeals: understanding the formation, evolution and composition of rocky planets, the detection and study of secondary atmospheres, the search for an Earth-like planet and life outside of the solar system. Not completely foreign to its appeal is the challenge that represents the detection and characterization of this population. Space-based transit surveys like CoRoT, Kepler/K2, TESS and CHEOPS have been successful at detecting them, but precise measurements of the mass of small planets are one of the current challenges of exoplanetary sciences. It requires high-resolution spectrographs with extreme stability over several months mounted on the largest telescope on Earth to measure the minute reflex motion that these planets impose on their parent stars. In this talk, I will present the results obtained with one of these instruments, ESPRESSO, by the ESPRESSO consortium. Since its first light in 2018, ESPRESSO has pushed the boundaries of the radial velocity techniques. Over the past months, it has broken two times consecutively the record of the smallest planet measured with this techniques L 98-58 b (Demangeon+2021,A&A,653,A41) and Proxima Centauri d (Faria+2022,A&A,658,A115). I will give an overview of the results that we obtained for the characterisation of the small planet population of the challenges that we faced (in particular in terms of stellar activity mitigation) and of the lessons learned regarding the measurement of the mass of this tantalizing population.