# Weak charge

In the nuclear physics, and atomic physics weak charge refers to the standard model vector coupling of nucleons to the Z boson, namely ${\displaystyle 2T_{3}-4Q\sin ^{2}\theta _{W}}$, where T3 is the weak isospin, Q the charge, and θ the weak mixing angle. Thus, it is approximately -0.99 for a neutron and +0.07 for a proton.[1]

It further affects parity violating electron scattering. The weak charge may be summed in atomic nuclei, so that the predicted weak charge for 133Cs (55 protons, 78 neutrons) is -73.23 , while the experimentally deduced value was -72.58.[2]

A recent study using four even-numbered isotopes of ytterbium was found consistent, to a 0.1% level of accuracy, with the formula weak charge Qw = −0.989 N + 0.071 Z, the latter two variables corresponding to the respective numbers of neutrons and protons in 170Yb, 172Yb, 174Yb, and 176Yb.[3] In the ytterbium system, atoms were excited by laser light in the presence of electric and magnetic fields, and the resulting parity violation was observed.[4] The specific transition observed was the forbidden transition from 6s2 1S0 to 5d6s 3D1 (24489 cm−1). The latter state was mixed, due to weak interaction, with 6s6p 1P1 (25068 cm−1) to a degree proportional to the nuclear weak charge.[3]

## References

1. ^ Hagen, G.; Ekström, A.; Forssén, C.; Jansen, G. R.; Nazarewicz, W.; Papenbrock, T.; Wendt, K. A.; Bacca, S.; Barnea, N.; Carlsson, B.; Drischler, C.; Hebeler, K.; Hjorth-Jensen, M.; Miorelli, M.; Orlandini, G.; Schwenk, A.; Simonis, J. (2016). "Charge, neutron, and weak size of the atomic nucleus". Nature Physics. 12 (2): 186–190. arXiv:1509.07169. doi:10.1038/nphys3529.
2. ^ Dzuba, V. A.; Berengut, J. C.; Flambaum, V. V.; Roberts, B. (2012). "Revisiting Parity Nonconservation in Cesium". Physical Review Letters. 109 (20): 203003. arXiv:1207.5864. doi:10.1103/PhysRevLett.109.203003. PMID 23215482.
3. ^ a b Antypas, D.; Fabricant, A.; Stalnaker, J. E.; Tsigutkin, K.; Flambaum, V. V.; Budker, D. (2018). "Isotopic variation of parity violation in atomic ytterbium". Nature Physics. arXiv:1804.05747. doi:10.1038/s41567-018-0312-8.
4. ^ "Atomic parity violation research reaches new milestone" (Press release). Universitaet Mainz. 2018-11-12. Retrieved 2018-11-13.