Fifth Force and Hyperfine Splitting in Bound Systems

Abstract

Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^{+}$ to $0^{+}$ and $0^{-}$ to $0^{+}$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. The effect of virtual annihilation and its contribution to the hyperfine splitting also is considered. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for $S$ states, are given by modifications of short-range (Dirac-delta) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, muonium, true muonium (${\mu }^{+}{\mu }^{-}$ bound system), and positronium.

14 pages; RevTeX

References in corpus (16)

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• Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb${}^{+}$ and Cs atomic clocks
• Particle Physics Models for the 17 MeV Anomaly in Beryllium Nuclear Decays
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• Direct high-precision measurement of the magnetic moment of the proton
• Glashow resonance as a window into cosmic neutrino sources
• Nuclear structure effects in light muonic atoms
• New evidence supporting the existence of the hypothetic X17 particle
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Quantum electrodynamic corrections to the hyperfine structure of excited S states
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
• Positronium energy levels at order $m{\alpha }^7$: light-by-light scattering in the two-photon-annihilation channel
• One More Hard Three-Loop Correction to Parapositronium Energy Levels
• Hadronic Vacuum Polarization in True Muonium
• X17: A new force, or evidence for a hard $\gamma +\gamma$ process?

Cited by in corpus (3)

• Anomalies in ${}^8$Be nuclear transitions and $(g-2{)}_{e,\mu }$: towards a minimal combined explanation
• Atomki anomaly in gauged $U(1{)}_R$ symmetric model
• CFNS Ad-Hoc meeting on Radiative Corrections Whitepaper