The CARMENES search for exoplanets around M dwarfs. Two planets on opposite sides of the radius gap transiting the nearby M dwarf LTT 3780

We present the discovery and characterisation of two transiting planets observed by the Transiting Exoplanet Survey Satellite (TESS) orbiting the nearby (d<SUB>⋆</SUB> ≈ 22 pc), bright (J ≈ 9 mag) M3.5 dwarf LTT 3780 (TOI-732). We confirm both planets and their association with LTT 3780 via ground-based photometry and determine their masses using precise radial velocities measured with the CARMENES spectrograph. Precise stellar parameters determined from CARMENES high-resolution spectra confirm that LTT 3780 is a mid-M dwarf with an effective temperature of T<SUB>eff</SUB> = 3360 ± 51 K, a surface gravity of log g<SUB>⋆</SUB> = 4.81 ± 0.04 (cgs), and an iron abundance of [Fe/H] = 0.09 ± 0.16 dex, with an inferred mass of M<SUB>⋆</SUB> = 0.379 ± 0.016M<SUB>☉</SUB> and a radius of R<SUB>⋆</SUB> = 0.382 ± 0.012R<SUB>☉</SUB>. The ultra-short-period planet LTT 3780 b (P<SUB>b</SUB> = 0.77 d) with a radius of 1.35<SUB>-0.06</SUB><SUP>+0.06</SUP> R<SUB>⊕</SUB>, a mass of 2.34<SUP>-0.23</SUP><SUB>+0.24</SUB> M<SUB>⊕</SUB>, and a bulk density of 5.24<SUB>-0.81</SUB><SUP>+0.94</SUP> g cm<SUP>-3</SUP> joins the population of Earth-size planets with rocky, terrestrial composition. The outer planet, LTT 3780 c, with an orbital period of 12.25 d, radius of 2.42<SUB>-0.10</SUB><SUP>+0.10</SUP> R<SUB>⊕</SUB>, mass of 6.29<SUB>-0.61</SUB><SUP>+0.63</SUP> M<SUB>⊕</SUB>, and mean density of 2.45<SUB>-0.37</SUB><SUP>+0.44</SUP> g cm<SUP>-3</SUP> belongs to the population of dense sub-Neptunes. With the two planets located on opposite sides of the radius gap, this planetary system is anexcellent target for testing planetary formation, evolution, and atmospheric models. In particular, LTT 3780 c is an ideal object for atmospheric studies with the James Webb Space Telescope (JWST).