Three-body QED test and fifth-force constraint from vibrations and rotations of HD$^+$

International audienceWe present a parts-per-million test of quantum electrodynamics (QED) in the HD+ molecular hydrogen ion, improving on previous tests based on vibrational and rotational transitions by factors of 76 and 1.4, respectively. The test is performed following a unified statistical approach that also produces improved constraints on physics beyond the standard model. We furthermore show how individual constraints derived from the various degrees of freedom in HD+ and antiprotonic helium can be combined to enhance the sensitivity, thus ruling out “fifth forces” on the Ångstrom scale that are 1011 times weaker than the electromagnetic interaction