High-Precision Muonic X-Ray Measurement of the rms Charge Radius ofC12with a Crystal Spectrometer

A precision measurement with the SIN bent-crystal spectrometer of the wavelength of the $2p_{\frac{3}{2}}-1\mathrm{}{s}_{\frac{1}{2}}$ transition in muonic ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ yields $\lambda =16.473\mathrm{}766\left(89\right)\mathrm{}$ pm, the accuracy being an order of magnitude higher than that of earlier investigations. The rms charge radius of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ is deduced as ${〈{\mathcal{r}}^2〉}^{\frac{1}{2}}=2.4832\mathrm{}\left(18\right)\mathrm{}$ fm, differing by 2.4 standard deviations from the most accurate electron-scattering results. Consequences of attributing this discrepancy to a $\mu -N$ interaction beyond QED are discussed.