Relativistic recoil as a key to the fine-structure puzzle in muonic ${}^{90}\text{Zr}$

Abstract

The long-standing fine-structure anomaly in muonic ${}^{90}$Zr is resolved through a rigorous treatment of the relativistic-recoil effect. From a fit of ab initio QED calculations of the muonic ${}^{90}$Zr spectrum to precision measurements performed four decades ago, we extract a significantly more precise root-mean-square (rms) charge radius with 6-fold improvement in quality of the fit. A 2-parameter Fermi (2pF) distribution is assumed to model the nuclear charge density and yields a best-fit value of rms charge radius of $r_{\text{rms}}{[}^{90}\text{Zr}]=4.2732(7)$ fm (${\chi }^2/\text{DoF}=0.995$), in agreement with the previous muonic spectroscopy value, but a factor $6$ more precise, and 3$\sigma$ larger than the accepted literature value. Additionally, the same analysis has been performed for ${}^{120}$Sn, where the extracted value of $r_{\text{rms}}{[}^{120}\text{Sn}]=4.6518(34)$ fm (${\chi }^2/\text{DoF}=0.88$) is consistent with the accepted value. These results confirm our assumption that the muonic fine-structure puzzle arose from an incomplete treatment of QED effects and their uncertainties.

Comments: 8 pages, 4 figures