Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift

Abstract

We provide an up to date summary of the theory contributions to the 2S-2P Lamb shift and the fine structure of the 2P state in the muonic helium ion $({\mu }^4\mathrm{He}{)}^{+}$. This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the ${}^3\mathrm{He}{-}^4\mathrm{He}$ isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of $n=2$ theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.

18 Pages, revised and updated manuscript, numbers are now same as in published version

References in corpus (17)

• The Proton Radius Puzzle
• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• High-precision measurement of the proton's atomic mass
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium
• Nuclear structure effects in light muonic atoms
• Higher-order recoil corrections for triplet states of the helium atom
• Zemach moments of 3He and 4He
• Nuclear recoil effect in the Lamb shift of light hydrogen-like atoms
• The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Theory of the n=2 levels in muonic helium-3 ions
• The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the Lamb shift in light muonic atoms
• Update on nuclear structure effects in light muonic atoms

Cited by in corpus (17)

• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Precision spectroscopy of helium in a magic wavelength optical dipole trap
• The proton structure in and out of muonic hydrogen
• Comprehensive theory of the Lamb shift in light muonic atoms
• Ab initio calculation of nuclear structure corrections in muonic atoms
• High-Precision Ramsey-Comb Spectroscopy Based on High-Harmonic Generation
• Zemach moments and radii of 2,3H and 3,4He
• QED theory of the nuclear recoil with finite size
• Muonic vs electronic dark forces: a complete EFT treatment for atomic spectroscopy
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Demonstration of Ramsey-Comb Precision Spectroscopy in Xenon at Vacuum Ultraviolet Wavelengths Produced with High-Harmonic Generation
• Ground state hyperfine structure of light muon-electron ions
• Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values
• A theory vade mecum for PSI experiments
• Hyperfine structure of P states in muonic ions of lithium, beryllium and boron
• Vacuum polarization corrections to the $n=2$ and $n=3$ levels in muonic ${}^4$He
• Relativistic fine structure of the (He4,mu) ion 2p-levels