Reevaluation of Stark-induced transition polarizabilities in cesium

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, $\beta$. 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 $\beta$ critically limiting the interpretation of the APV measurement. The most recent value [Phys. Rev. Lett. 123, 073002 (2019)] of $\beta=27.139(42)\, \mathrm{a.u.}$ was deduced from a semi-empirical sum-over-state determination of the scalar transition polarizability $\alpha$ and the measured $\alpha/\beta$ ratio [Phys. Rev. A 55, 2 (1997)]. This value of $\beta$, however, differs by $\sim 0.7\%$ or $2.8\sigma$ from the previous determination of $\beta=26.957(51)$ by [Phys. Rev. A 62, 052101 (2000)] based on the measured ratio $M1/\beta$ of the magnetic-dipole $6S_{1/2}\rightarrow{7S_{1/2}}$ matrix element to $\beta$. Here, we revise the determination of $\beta$ 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 $\alpha/\beta$ method. Our result of $\beta=26.887(38)\, \mathrm{a.u.}$ resolves the tension between the $\alpha/\beta$ and $M1/\beta$ approaches. We recommend the value of $\beta=26.912(30)$ obtained by averaging our result and that of [Phys. Rev. A 62, 052101 (2000)].