  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, 1007 (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)].
