Why three-body physics do not solve the proton radius puzzle

Abstract

The possible involvement of weakly bound three-body systems in the muonic hydrogen spectroscopy experiment [1], which could resolve the current discrepancy between determinations of the proton radius, is investigated. Using variational calculations with complex coordinate rotation, it is shown that the $p\mu e$ ion, which was recently proposed as a possible candidate [2], has no resonant states in the energy region of interest. QED level shifts are included phenomenologically by including a Yukawa potential in the three-body Coulomb Hamiltonian before diagonalization. It is also shown that the $pp\mu$ molecular ion cannot play any role in the observed line.

References in corpus (28)

• High-precision determination of the electric and magnetic form factors of the proton
• New Limits to the Drift of Fundamental Constants from Laboratory Measurements
• Improved Measurement of the Hydrogen 1S - 2S Transition Frequency
• Dispersion analysis of the nucleon form factors including meson continua
• High Precision Measurement of the Proton Elastic Form Factor Ratio ${\mu }_p{G}_E/G_M$ at low $Q^2$
• Muonic hydrogen and MeV forces
• The RMS Charge Radius of the Proton and Zemach Moments
• New Parity-Violating Muonic Forces
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Lamb Shift in Light Muonic Atoms - Revisited
• Proton size anomaly
• Spectroscopy as a test of Coulomb's law - A probe of the hidden sector
• Model independent analysis of proton structure for hydrogenic bound states
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Atomic Precision Tests and Light Scalar Couplings
• Constraint on parity-violating muonic forces
• Proton structure corrections to hyperfine splitting in muonic hydrogen
• Collisional deexcitation of exotic hydrogen atoms in highly excited states. II. Cascade calculations
• High accuracy results for the energy levels of the molecular ions H2+, D2+ and HD+, up to J=2
• Observation of Long-Lived Muonic Hydrogen in the 2S State
• The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses
• Natural Resolution of the Proton Size Puzzle
• QED is not endangered by the proton's size
• Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions
• Non-relativistic contributions in order ${\alpha }^5{m}_{\mu }{c}^2$ to the Lamb shift in muonic hydrogen, deuterium and helium ion
• Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms
• Third Zemach Moment of the Proton
• Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

Cited by in corpus (8)

• Muonic hydrogen and the proton radius puzzle
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Model independent extraction of the proton magnetic radius from electron scattering
• Experiments towards resolving the proton charge radius puzzle
• Muonic bound systems, virtual particles and proton radius
• Antihydrogen $(\bar{\mathrm{H}})$ and muonic antihydrogen $({\bar{\mathrm{H}}}_{\mu })$ formation in low energy three-charge-particle collisions
• Effects of Non-Commutativity on Light-Hydrogen-Like Atoms and Proton Radius
• Analytical matrix elements of the Uehling potential in three-body systems, and applications to exotic molecules