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 (11)

• High-precision determination of the electric and magnetic form factors of the proton
• Dispersion analysis of the nucleon form factors including meson continua
• Muonic hydrogen and MeV forces
• The RMS Charge Radius of the Proton and Zemach Moments
• New Parity-Violating Muonic Forces
• Proton size anomaly
• Spectroscopy as a test of Coulomb's law - A probe of the hidden sector
• Atomic Precision Tests and Light Scalar Couplings
• Observation of Long-Lived Muonic Hydrogen in the 2S State
• QED is not endangered by the proton's size
• Third Zemach Moment of the Proton