Bounds on fifth forces from precision measurements on molecules

Highly accurate results from frequency measurements on neutral hydrogen molecules H₂, HD, and D₂ as well as the HD⁺ ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V₅(r)=βexp(-r/λ)/r, current precision measurements on hydrogenic molecules yield a constraint β<1.4×10^-8 eV· for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e., λ≈1 and beyond. This corresponds to a constraint of β/α<10^-9, where α represents the strength of the electromagnetic interaction, i.e., the fine-structure constant.