Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment

Abstract

Currently, both the g factor measurement of the muon as well as the Lamb shift 2S-2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both "muonic" discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification. PACS numbers 31.30.jf, 12.20.Ds

Nucleon andΔ(1232)form factors at low momentum transfer and small pion masses

“…Much effort since then have been focused on finding a "missing" correction in the muonic-hydrogen result, e.g. [5][6][7][8]. We, on the other hand, will attempt to provide here some grounds for an improvement of the electron-scattering analysis.…”

The proton radius puzzle

“…See [63][64][65][66][67][68][69][70][71][72]. Some of the references discuss new physics possibilities, some discuss problems that ensue, some discuss both, and some suggest possible further experiments.…”

Coordinate-space approach to vacuum polarization

“…In view of this discrepancy, a thorough review of the theory is warranted, and a number of such investigations have been carried out, with recent reviews given in Refs. [5][6][7][8][9][10][11][12].…”