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Bounds on fifth forces at the sub-Angstrom length scale

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 $\bar{p}\,^{4}$He$^{+}$ and $\bar{p}\,^{3}$He$^{+}$ 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 limits on a possible additional hadron-hadron interaction written in the form of a Yukawa potential $V_5(r)=α_5 \exp(-r/λ)/r$, with $λ$ representing the characteristic length scale associated with the mass of a hypothetical force-carrying particle via $λ=\hbar/(m_5c)$. The laser spectroscopic data of antiprotonic helium set a constraint of $α_5/α_{EM} < 10^{-8}$ for $λ< 1$ Å, while the binding energy of the muonic molecular deuterium ion delivers a constraint of $α_5/α_{EM} \sim 10^{-5}$ for $λ< 0.05$ Å, where $α_{EM}$ represents the strength of the electromagnetic interaction or the fine structure constant.