Bounds on fifth forces from precision measurements on molecules

Abstract

Highly accurate results from frequency measurements on neutral hydrogen molecules ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ as well as the ${\mathrm{HD}}^{+}$ 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 ${V}_{5}(r)=\ensuremath{\beta}\mathrm{exp}(\ensuremath{-}r/\ensuremath{\lambda})/r$, current precision measurements on hydrogenic molecules yield a constraint $\ensuremath{\beta}<1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{eV}\ifmmode\cdot\else\textperiodcentered\fi{}\AA{}$ for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e., $\ensuremath{\lambda}\ensuremath{\approx}1\text{ }\text{ }\AA{}$ and beyond. This corresponds to a constraint of $\ensuremath{\beta}/\ensuremath{\alpha}<{10}^{\ensuremath{-}9}$, where $\ensuremath{\alpha}$ represents the strength of the electromagnetic interaction, i.e., the fine-structure constant.