Reduced Theoretical Error for QED Tests with 4He+ Spectroscopy

Abstract

We apply point-particle effective field theory (PPEFT) to electronic and muonic 4He+ ions, and use it to identify linear combinations of spectroscopic measurements for which the theoretical uncertainties are much smaller than for any particular energy levels. The error is reduced because these combinations are independent of all short-range physics effects up to a given order in the expansion in the small parameters R/a_B and(Z alpha) (where R and a_B are the ion's nuclear and Bohr radii). In particular, the theory error is not limited by the precision with which nuclear matrix elements can be computed, or compromised by the existence of any novel short-range interactions, should these exist. These combinations of 4He+ measurements therefore provide particularly precise tests of QED. The restriction to 4He+ arises because our analysis assumes a spherically symmetric nucleus, but the argument used is more general and extendable to both nuclei with spin, and to higher orders in R/a_B and (Z alpha).

21 pages, 4 plots; This version greatly expands the mathematical background and detailed derivations of our results. Application of our results to available experimental data is also included

References in corpus (13)

• The Proton Radius Puzzle
• Model independent extraction of the proton charge radius from electron scattering
• Muonic hydrogen and MeV forces
• The RMS Charge Radius of the Proton and Zemach Moments
• New Parity-Violating Muonic Forces
• Proton size anomaly
• Three-photon exchange nuclear structure correction in hydrogenic systems
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential
• Explaining the Proton Radius Puzzle with Disformal Scalars
• Point-Particle Effective Field Theory II: Relativistic Effects and Coulomb/Inverse-Square Competition
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation

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• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Nuclear Predictions for $H$ Spectroscopy without Nuclear Errors
• Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors
• On the EFT of Dyon-Monopole Catalysis
• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour