Calculation of radiative corrections to the effect of parity nonconservation in heavy atoms

Abstract

We calculate the self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms. The sum of the corrections is of the form ${\cal A}\ln(λ_C/r_0)+{\calB}$, where $\mathcal{A}$ and $\mathcal{B}$ are functions of $Z\alpha$, and ${\lambda }_C$ and $r_0$ are the Compton wavelength and the nuclear radius, respectively. The function $\mathcal{A}$ is calculated exactly in $Z\alpha$ and the function $\mathcal{B}$ is calculated in the leading order. In the leading order $\mathcal{A}\propto \alpha (Z\alpha {)}^2$ and $\mathcal{B}\propto \alpha (Z\alpha )$. The sum of the corrections is -0.85% for Cs and -1.48% for Tl. Using these results we have performed analysis of the experimental data on atomic parity nonconservation. The values obtained for the nuclear weak charge, $Q_W=-72.81(28{)}_{exp}(36{)}_{theor}$ for Cs and $Q_W=-116.8(1.2{)}_{exp}(3.4{)}_{theor}$ for Tl, agree with predictions of the standard model within $0.6\sigma$. As an application of our approach we have also calculated dependence of the Lamb shift on the finite nuclear size.

arXiv comment14 pages, 7 figures

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