Carl E. Carlson, Benjamin C. Rislow
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 a new particle that couples only to muons and hadrons, but none satisfy the additional constraints laid out by measurements of the muon's anomalous moment and kaon decay rates. 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.
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http://arxiv.org/abs/1206.3587
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