Reexamination of transition polarizabilities in experiments on atomic parity violation

Stark interference is a ubiquitous technique in experiments on atomic parity-violation (APV). In $^{133}{\rm Cs}$, the central quantity of interest, the $6S\rightarrow{7S}$ APV transition amplitude, $E_{\mathrm{APV}}$, is deduced from the measured ratio of $E_{\mathrm{APV}}$ to the vector transition polarizability $\beta$, $E_{\mathrm{APV}}/\beta$. Ideally, the uncertainty in $\beta$ should be much smaller than that of the above ratio. The $E_{\mathrm{APV}}/\beta$ ratio was measured with a $0.35\%$ uncertainty by the Boulder group [Science 275, 1759 (1997)]. However, currently, there is an alarming discrepancy in different determinations of $\beta$. The most recent determination [PRL 123, 073002 (2019)] of $\beta$ claimed an error bar of $\sim 0.2\%$ comparable to that of the earlier measurement [PRL 82, 2484 (1999)]. However, the central values of the two determinations of $\beta$ differ by $\sim 0.7\%$, severely limiting APV interpretation. Here, we re-examine computations of $\beta$ and investigate the role of higher-order, hyperfine interaction induced, corrections to transition polarizabilities.