Determination of the Scalar and Vector Polarizabilities of the Cesium $6s{{}^{2}S}_{1/2}\to 7s{{}^{2}S}_{1/2}$ Transition and Implications for Atomic Parity Nonconservation

Using recent high-precision measurements of electric dipole matrix elements of atomic cesium, we make an improved determination of the scalar ($\alpha$) and vector ($\beta$) polarizabilities of the cesium $6s{{}^{2}S}_{1/2}\to 7s{{}^{2}S}_{1/2}$ transition calculated through a sum-over-states method. We report values of $\alpha =-268.82(30)a_0^3$ and $\beta =27.139(42)a_0^3$ with the highest precision to date. We find a discrepancy between our value of $\beta$ and the past preferred value, resulting in a significant shift in the value of the weak charge $Q_w$ of the cesium nucleus. Future work to resolve the differences in the polarizability will be critical for interpretation of parity nonconservation measurements in cesium, which have implications for physics beyond the standard model.

Figure 1

A graphical summary of the current status of the measured and calculated matrix elements $⟨n{p}_J\parallel r\parallel m{s}_{1/2}⟩$, where $m$, $n=6$ or 7, and $J=1/2$ and $3/2$ in atomic cesium. The error bars show the magnitudes of the uncertainty of the measurements. The data points show the deviation between the most recent calculations of the matrix elements and the measured value. (Deviation $>0$ indicates the theoretical value is greater than the experimental value.) The calculated values are from Ref. [34] ($\circ$), [25, 28] ($*$), and [4] ($\times$).

Figure 2

A summary of the current status of $\beta$ determinations. The $\beta$ values shown on the left (o) are determined through a sum-over-states of $\alpha$ and the ratio $\alpha /\beta$. The two values on the right (x) are determined through an experimental determination of $M{1}_{hf}/\beta$ and a theory value of $M{1}_{hf}$. Refer to Table 2 for references to these values.

Figure 3

A summary of the current status of $Q_w$ determinations. The two horizontal lines denote the standard model prediction $Q_{\mathrm{SM}}^{2018}$ [59]. Past determinations are Vas02 [35], Dzu02 [28], Fla05 [29], Por10 [4], and Dzu12 [5].