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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)=βexp(-r/λ)/r current precision measurements on hydrogenic molecules yield a constraint β< 1 \times 10^{-7} eVÅfor long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. λ~1 Åand beyond.