[Paper Review] Calculation of parity nonconservation in cesium and possible deviation from the Standard Model

V. A. Dzuba, V. V. Flambaum+1 more|ArXiv.org|Nov 2, 2001

Radioactive element chemistry and processing1 references3 citations

TL;DR

This paper presents a high-precision calculation of the parity nonconserving (PNC) E1 transition amplitude in cesium using many-body perturbation theory in the screened Coulomb interaction, including Breit and radiative corrections. The result, $ E_{PNC} = 0.902(0.7\/)iea_B(Q_W/N) $, yields a nuclear weak charge of $ Q_W = -72.39(0.4\%\text{ exp} \pm 0.7\%\text{ theory}) $, showing no significant deviation from the Standard Model value of $-73.09(3)$.

ABSTRACT

We have calculated the 6s-7s parity nonconserving E1 transition amplitude (E_{PNC}) in cesium. This calculation has been performed with higher numerical accuracy than our 1989 calculation [V.A. Dzuba, V.V. Flambaum, and O.P. Sushkov, Phys. Lett. A {\bf 141}, 147]. Also the Breit interaction has been included and the radiative corrections estimated. Our final result is E_{PNC}=0.902 (1 +/- 0.7%)iea_{B}(Q_{W}/N). This represents an improvement in the accuracy of the calculation from the 1% error claimed in 1989. This result corresponds to a nuclear weak charge for Cs, Q_{W}=-72.39 (1 +/- 0.4% (exp) +/- 0.7% (theory)). We conclude that there is no significant deviation from the Standard Model value -73.09(3).

Motivation & Objective

• To improve the theoretical accuracy of the $6s-7s$ parity nonconserving E1 transition amplitude in cesium beyond the 1% level achieved in 1989.
• To assess whether the previously reported 2.5σ deviation from the Standard Model weak charge was due to underestimated theoretical uncertainties.
• To include higher-order corrections such as the Breit interaction and radiative corrections of order $Z\alpha^2$ and $Z^2\alpha^3\ln^2(\lambda/R_n)$.
• To evaluate the impact of improved nuclear charge and neutron distribution models on the PNC amplitude.
• To provide a robust theoretical estimate of $Q_W$ for comparison with high-precision experimental measurements.

Proposed method

• Employed many-body perturbation theory in the screened Coulomb interaction, an all-order technique that systematically includes dominant electron correlation effects.
• Used energy-fitted correlation potentials ($\hat{\Sigma}^{(2)}$ and $\hat{\Sigma}$) to improve accuracy of matrix elements and energy levels.
• Calculated the Breit interaction contribution to $E_{PNC}$, finding a correction of $-0.0055$ in atomic units.
• Estimated radiative corrections from the Uehling potential and other $Z^2\alpha^3\ln^2(\lambda/R_n)$-type terms, yielding a net radiative correction of $0.000 \pm 0.004$.
• Incorporated structural radiation and normalization corrections in the matrix element calculations.
• Used a refined nuclear charge distribution and accounted for the neutron distribution's small effect, contributing $-0.0018$ to $E_{PNC}$.

Experimental results

Research questions

• RQ1 Does the previously observed 2.5σ deviation of the cesium weak charge from the Standard Model arise from underestimated theoretical uncertainties?
• RQ2 What is the impact of the Breit interaction on the PNC amplitude in cesium, and how does it affect the weak charge extraction?
• RQ3 What are the contributions of higher-order radiative corrections to the PNC amplitude, particularly those of order $Z^2\alpha^3\ln^2(\lambda/R_n)$?
• RQ4 How does improved numerical accuracy and energy fitting affect the stability and reliability of the PNC amplitude calculation?
• RQ5 To what extent do corrections from the neutron distribution and refined charge distributions alter the PNC amplitude?

Key findings

• The $6s-7s$ PNC amplitude is calculated as $ E_{PNC} = 0.902(0.7\%\text{ theory})iea_B(Q_W/N) $, representing a significant improvement in theoretical accuracy.
• The Breit interaction contributes $-0.0055$ to $E_{PNC}$, confirming earlier estimates and reducing the previous deviation from the Standard Model.
• Radiative corrections of order $Z^2\alpha^3\ln^2(\lambda/R_n)$ contribute $+0.004$, with additional corrections of similar magnitude from energy intervals and E1 amplitudes, leading to a net radiative correction of $0.000 \pm 0.004$.
• The neutron distribution correction shifts $E_{PNC}$ by $-0.0018$, consistent with prior results and negligible at the current precision level.
• The final theoretical uncertainty on $E_{PNC}$ is $0.7\%$, with experimental uncertainty $0.4\%$, yielding a total uncertainty of $0.8\%$ on $Q_W$.
• The extracted weak charge $Q_W = -72.39(0.4\%\text{ exp} \pm 0.7\%\text{ theory})$ deviates from the Standard Model value $-73.09(3)$ by only $1.0\% \pm 0.7\%$, which is not statistically significant.