arXiv2023
Extracting electroweak observables from experiments on atomic parity violation (APV) using the Stark interference technique requires accurate knowledge of transition polarizabilities. In cesium, the focus of our paper, the $6S_{1/2}\rightarrow{7S_{1/2}}$ APV amplitude is deduced from the measured ratio of the APV amplitude to the vector transition polarizability, $β$. This ratio was measured with a $0.35\%$ uncertainty by the Boulder group [Science 275, 1759 (1997)]. Currently, there is a sizable discrepancy in different determinations of $β$ critically limiting the interpretation of the APV measurement. The most recent value [Phys. Rev. Lett. 123, 073002 (2019)] of $β=27.139(42)\, \mathrm{a.u.}$ was deduced from a semi-empirical sum-over-state determination of the scalar transition polarizability $α$ and the measured $α/β$ ratio [Phys. Rev. A 55, 1007 (1997)]. This value of $β$, however, differs by $\sim 0.7\%$ or $2.8σ$ from the previous determination of $β=26.957(51)$ by [Phys. Rev. A 62, 052101 (2000)] based on the measured ratio $M1/β$ of the magnetic-dipole $6S_{1/2}\rightarrow{7S_{1/2}}$ matrix element to $β$. Here, we revise the determination of $β$ by [Phys. Rev. Lett. 123, 073002 (2019)], using a more consistent and more theoretically complete treatment of contributions from the excited intermediate states in the sum-over-state $α/β$ method. Our result of $β=26.887(38)\, \mathrm{a.u.}$ resolves the tension between the $α/β$ and $M1/β$ approaches. We recommend the value of $β=26.912(30)$ obtained by averaging our result and that of [Phys. Rev. A 62, 052101 (2000)].