Nuclear neutron radius and weak mixing angle measurements from latest COHERENT CsI and atomic parity violation Cs data

The COHERENT collaboration observed coherent elastic neutrino nucleus scattering using a 14.6 kg cesium-iodide (CsI) detector in 2017 and recently published the updated results before decommissioning the detector. Here, we present the legacy determination of the weak mixing angle and of the average neutron rms radius of $^{133}\mathrm{Cs}$ and $^{127}\mathrm{I}$ obtained with the full CsI dataset, also exploiting the combination with the atomic parity violation (APV) experimental result, that allows us to achieve a precision as low as $\sim$4.5% and to disentangle the contributions of the $^{133}\mathrm{Cs}$ and $^{127}\mathrm{I}$ nuclei. Interestingly, we show that the COHERENT CsI data show a 6$\sigma$ evidence of the nuclear structure suppression of the full coherence. Moreover, we derive a data-driven APV+COHERENT measurement of the low-energy weak mixing angle with a percent uncertainty, independent of the value of the average neutron rms radius of $^{133}\mathrm{Cs}$ and $^{127}\mathrm{I}$, that is allowed to vary freely in the fit. Additionally, we extensively discuss the impact of using two different determinations of the theoretical parity non-conserving amplitude in the APV fit. Our findings show that the particular choice can make a significant difference, up to 6.5% on $R_n$(Cs) and 11% on the weak mixing angle. Finally, in light of the recent announcement of a future deployment of a 10 kg and a $\sim$700 kg cryogenic CsI detectors, we provide future prospects for these measurements, comparing them with other competitive experiments that are foreseen in the near future.