Muonic vs electronic dark forces: a complete EFT treatment for atomic spectroscopy

Abstract

Precision atomic spectroscopy provides a solid model independent bound on the existence of new dark forces among the atomic constituents. We focus on the keV-GeV region investigating the sensitivity to such dark sectors of the recent measurements on muonic atoms at PSI. To this end we develop for the first time, the effective field theory that describes the leading effect of a new (pseudo-)vector or a (pseudo-)scalar particle of any mass at atomic energies. We identify in the Lamb Shift measurement in muonic deuterium (μD) and the 2s Hyperfine Splitting (HFS) in muonic hydrogen (μH) the most promising measurements to probe respectively spin-independent and spin-dependent new forces. Furthermore, we evaluate the expression of the vector force HFS finding that a future measurement of the 2s HFS in regular hydrogen could provide the strongest atomic bound for such a force for masses above 100 MeV.

The Proton Structure in and out of Muonic Hydrogen

“…A recent study (139) highlighted the peculiar sensitivity of μH, μD, and H(1S-2S) to a dark sector with masses in the keV-GeV range. The sensitivity presented in this study is greatly enhanced when accounting for the upcoming measurement of the 1S HFS in μH and improved determinations of r p .…”

Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory

“…Such combination would allow to test BSQED for three-body systems at higher Z. Conversely, one could benchmark nuclear polarizability calculations in systems heavier than He. At the level in which these calculations are reliable, one could search for new physics affecting the muonic and/or electronic observables [41][42][43].…”

Towards Precision Muonic X-ray Measurements of Charge Radii of Light Nuclei

“…Due to the heavy mass of muons (m µ ∼ 200 m e , with m e the electron mass), the Bohr radius of muonic atoms is approximately 200 times smaller than that of electronic atoms, and thus, for low angular momentum states, the muon wavefunction has a 200 3 ≈ 10 6 times larger overlap with that of the nucleus. The nuclear properties thus lead to measurable shifts in the atomic transition energies, making muonic atom spectroscopy an effective probe of phenomena such as finite nuclear size effects [1][2][3][4][5][6][7], relativistic QED (quantum electrodynamics) contributions [4,[7][8][9], and possible short-range interactions carried by new mediators [10][11][12][13][14][15][16]. These systems are particularly well-suited to accurately determining the RMS (root mean squre) nuclear charge radius (the slope of the Sachs form factor at small momentum transfer, henceforth called 'radius' for brevity), which can be obtained using the spectroscopy of low-lying radiative transitions (mostly 2P − 1S) [1,17,18].…”