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.

Parity-violating (PV) elastic electron-proton scattering measures Q-weak for the proton, Q p W . To extract Q p W from data, all radiative corrections must be well-known. Recently, disagreement on the γZ-box contribution to Q p W has prompted the need for further analysis of this term. Here, we support one choice of a debated factor, go beyond the previously assumed equality of electromagnetic and γZ structure functions, and find an analytic result for one of the γZ-box integrals. Our numerical evaluation of the γZ-box is in agreement within errors with previous reports, albeit somewhat larger in central value, and is within the uncertainty requirements of current experiments.

A possible explanation for the discrepancy between electronic and muonic hydrogen measurements of the proton charge radius are new, lepton-universality violating interactions. Several new couplings and particles have been suggested that account for this discrepancy. At present, these explanations are poorly constrained. Experiments such as the upcoming kaon decay experiment at JPARC may constrain or eliminate some explanations by sensitivity to the decay channel K + → µ + +ν +e − +e + . We calculate the predicted contributions of the various explanations to this channel. The predicted signals, if present, should be large enough to be resolved in the experiment.