Optical-rotation technique used for a high-precision measurement of parity nonconservation in atomic lead

We have measured the parity-nonconserving (PNC) optical rotation near the 1.279-μm ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ ${\to }^3$ ${\mathit{P}}_1$ magnetic-dipole absorption line in atomic lead vapor. We measure the quantity scrR≡Im(${\mathit{scrE}}_{\mathrm{PNC}}$/scrM), where scrM is the magnetic-dipole amplitude of the absorption line and ${\mathit{scrE}}_{\mathrm{PNC}}$ is the electric-dipole amplitude coupled into the same line by the PNC interaction within the lead atom. We find scrR to be (-9.86±0.04±0.11)×${10}^{\mathrm{-}8}$, where the first error is statistical and the second is systematic. The statistical errors are due to incompletely subtracted background fluctuations, and the systematic errors are caused by line-shape uncertainties and calibration error. Our value is consistent with the atomic PNC calculations for lead, which give scrR=(-10.7±0.8)×${10}^{\mathrm{-}8}$ for the standard electroweak model with ${\sin }^2$ ${\mathrm{\theta }}_{\mathit{W}}$=0.23 and no electroweak radiative corrections. Including radiative corrections yields the value S=-3±8 for the isospin-conserving electroweak parameter, with difficulties in the atomic theory of lead presently limiting the extent to which our result tests the standard model. This same technique can also be applied to thallium, where the atomic theory is currently accurate to 3%. By searching for a difference in scrR for the two hyperfine components of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, we find the amplitude of the nuclear spin-dependent PNC rotation to be less than 2×${10}^{\mathrm{-}2}$ of the nuclear spin-independent rotation.