Improved calculation of the muonic-helium Lamb shift

Abstract

Several small, previously uncalculated contributions to the $2{s}_{\frac{1}{2}}\ensuremath{-}2{p}_{\frac{3}{2}}$ splitting ${S}_{1}$ in muonic $^{4}\mathrm{He}$ are calculated, and previously calculated contributions are verified. The improved theoretical result is $1817.5\ifmmode\pm\else\textpm\fi{}0.6+0.4{〈{r}^{2}〉}^{\frac{1}{2}}\ensuremath{-}106.2〈{r}^{2}〉+1.4{〈{r}^{2}〉}^{\frac{3}{2}}\ensuremath{\simeq}1527.3\ensuremath{-}102.6(〈{r}^{2}〉=2.80)$ meV, where $〈{r}^{2}〉$ is the mean-square charge radius of $^{4}\mathrm{He}$ in ${\mathrm{fm}}^{2}$. Using the most recent value of the rms charge radius we get ${S}_{1\mathrm{th}}=1527.1\ifmmode\pm\else\textpm\fi{}4.2$ meV, in excellent agreement with the experimental result ${S}_{1\mathrm{exp}}=1527.5\ifmmode\pm\else\textpm\fi{}0.3$ meV.