Background: The recent disagreement between the proton charge radius
extracted from Lamb shift measurements of muonic and electronic hydrogen
invites speculation that new physics may be to blame. Several proposals have
been made for new particles that account for both the Lamb shift and the muon
anomalous moment discrepancies. Purpose: We explore the possibility that new
particles' couplings to the muon can be fine-tuned to account for all
experimental constraints. Method: We consider two fine-tuned models, the first
involving new particles with scalar and pseudoscalar couplings, and the second
involving new particles with vector and axial couplings. The couplings are
constrained by the Lamb shift and muon magnetic moments measurements while mass
constraints are obtained by kaon decay rate data. Results: For the
scalar-pseudoscalar model, masses between 100 to 200 MeV are not allowed. For
the vector model, masses below about 200 MeV are not allowed. The strength of
the couplings for both models approach that of electrodynamics for particle
masses of about 2 GeV. Conclusions: New physics with fine tuned couplings may
be entertained as a possible explanation for the Lamb shift discrepancy.Comment: 6 pages, 6 figures, v2 contains revised comment on competing model of
Lamb Shift discrepanc
