Muon and electron g-2 and proton and cesium weak charges implications on dark $\mathbf{Z_d}$ models

Understand

Theories beyond the standard model involving a sub-GeV-scale vector $Z_d$ mediator have been largely studied as a possible explanation of the experimental values of the muon and electron anomalous magnetic moments.

• Motivated by the recent determination of the anomalous muon magnetic moment performed at Fermilab, we derive the constraints on such a model obtained from the magnetic moment determinations and the measurements of the proton and cesium weak charge, $Q_W$, performed at low-energy transfer.
• In order to do so, we revisit the determination of the cesium $Q_W$ from the atomic parity violation experiment, which depends critically on the value of the average neutron rms radius of $^{133}\text{Cs}$, by determining the latter from a practically model-independent extrapolation from the recent average neutron rms radius of $^{208}\text{Pb}$ performed by the PREX-2 Collaboration.
• From a combined fit of all the aforementioned experimental results, we obtain rather precise limits on the mass and the kinetic mixing parameter of the $Z_d$ boson, namely $m_{Z_d} = 47{}^{+61}_{-16} \, \mathrm{MeV}$ and $\varepsilon = 2.3{}^{+1.1}_{-0.4} \times 10^{-3}$, when marginalizing over the $Z-Z_d$ mass mixing parameter $\delta$.