Bounds on fifth forces from precision measurements on molecules

Highly accurate results from frequency measurements on neutral hydrogen molecules H-2, HD, and D-2 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 V-5(r) = beta exp (-r/lambda)/r, current precision measurements on hydrogenic molecules yield a constraint beta < 1.4 x 10(-8) eV. angstrom for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e., lambda approximate to 1 angstrom and beyond. This corresponds to a constraint of beta/alpha < 10(-9), where alpha represents the strength of the electromagnetic interaction, i.e., the fine-structure constant.