Bounds on fifth forces at the sub-Å length scale

Abstract

Constraints on a possible fifth-force interaction between hadrons are derived based on an analysis of results from laser precision frequency measurements of antiprotonic helium atoms, both p¯4He+ and p¯3He+ species, and from experiments on resonant formation rates of ddμ+-ions in muon-catalyzed fusion processes. A comparison is made between accurate experimental data and first-principles theoretical descriptions of the exotic systems within a quantum electrodynamical framework. The agreement between theory and experiment sets general limits on a possible additional hadron–hadron interaction, written in the form of a Yukawa potential V5(r)=α5exp(-r/λ)/r, with λ representing the characteristic length scale associated with the mass of a hypothetical force-carrying particle via λ=ℏ/(m5c). The laser spectroscopic data of antiprotonic helium set a constraint of α5/αEM<10-8 for λ<1Å, while the binding energy of the muonic molecular deuterium ion delivers a constraint of α5/αEM∼10-5 for λ<0.05Å, where αEM represents the strength of the electromagnetic interaction or the fine structure constant.