Precision Determination of Electroweak Coupling from Atomic Parity Violation and Implications for Particle Physics

We carry out high-precision calculation of parity violation in a cesium atom, reducing theoretical uncertainty by a factor of 2 compared to previous evaluations. We combine previous measurements with calculations and extract the weak charge of the ${}^{133}\mathrm{Cs}$ nucleus, $Q_W=-73.16(29{)}_{\mathrm{expt}}(20{)}_{\mathrm{theor}}$. The result is in agreement with the standard model (SM) of elementary particles. This is the most accurate to-date test of the low-energy electroweak sector of the SM. In combination with the results of high-energy collider experiments, we confirm the energy dependence (or “running”) of the electroweak force over an energy range spanning 4 orders of magnitude (from $\sim 10\mathrm{MeV}$ to $\sim 100\mathrm{GeV}$). Additionally, our result places constraints on a variety of new physics scenarios beyond the SM. In particular, we increase the lower limit on the masses of extra $Z$ bosons predicted by models of grand unification and string theories.

Figure 1

Progress in evaluating the PNC amplitude. Points marked Paris ’86, Novosibirsk ’89, Notre Dame ’90 correspond to Refs. 10, 11, 31. Point marked World average ’05 is due to efforts of several groups [12, 13, 14, 15, 16] on sub-1% Breit, QED, and neutron-skin corrections reviewed in Ref. 17. The strip corresponds to a combination of the standard model $Q_W$ with measurements [3, 4]. The edges of the strip correspond to $\pm \sigma$ of the measurement. Here we express $E_{\mathrm{PNC}}$ in conventional units of $i|e|a_B(-Q_W/N)\times {10}^{-11}$, where $e$ is the elementary charge and $a_B$ is the Bohr radius. These units factor out a ratio of $Q_W$ to its approximate value, $-N$.

Figure 2

Deviations of computed values (red filled circles) from experimental data (centered at zero). The upper panel displays combinations of magnetic hyperfine structure constants $\sqrt{A_{n{S}_{1/2}}{A}_{n^{\prime }{P}_{1/2}}}$ which mimic matrix elements of the weak interaction. For these combinations, experimental error bars are negligible compared to the theoretical accuracy. The lower panel exhibits deviations of the computed dipole matrix elements from the most accurate experimental results [23, 32].

Figure 3

Many-body diagrams responsible for the shift of the PNC amplitude compared to previous calculations. Top row: Sample direct contributions of valence triples to matrix elements (wavy capped line) [21]. Bottom row: Iterative equation for line dressing of the hole line in expressions for matrix elements [20] (similar equation holds for particle lines; exchange diagrams are not shown).