Proton Size Anomaly

A measurement of the Lamb shift in muonic hydrogen yields a charge radius of the proton that is smaller than the CODATA value by about 5 standard deviations. We explore the possibility that new scalar, pseudoscalar, vector, and tensor flavor-conserving nonuniversal interactions may be responsible for the discrepancy. We consider exotic particles that, among leptons, couple preferentially to muons and mediate an attractive nucleon-muon interaction. We find that the many constraints from low energy data disfavor new spin-0, spin-1, and spin-2 particles as an explanation.

Figure 1

The 95% C.L. range of ${\alpha }_{\chi }/\alpha$ required to reproduce the muonic Lamb shift is indicated by the green shaded region. The black solid, red dashed, and blue dot-dashed lines are the upper limits for vector, scalar, and spin-2 particles, respectively, from a combination of $n-{}^{208}\mathrm{Pb}$ scattering data and the anomalous magnetic moment of the muon. The black dotted curve is the upper bound obtained from atomic x-ray transitions. All bounds are at the 95% C.L.

Figure 2

The curves are 95% C.L. upper bounds on the muonic couplings $C_{\mu }^S$, $C_{\mu }^V$, and $C_{\mu }^T$ from $\Delta a_{\mu }$. The green shading marks the values of the nucleon coupling $C_n^{S,V,T}$ excluded by $n-{}^{208}\mathrm{Pb}$ scattering at the 95% C.L.