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Using the new results on coherent elastic neutrino-nucleus scattering data incesium-iodide provided by the COHERENT experiment, we determine a newmeasurement of the average neutron rms radius of $^{133}\text{Cs}$ and$^{127}\text{I}$. In combination with the atomic parity violation (APV)experimental result, we derive the most precise measurement of the neutron rmsradii of $^{133}\text{Cs}$ and $^{127}\text{I}$, disentangling for the firsttime the contributions of the two nuclei. By exploiting these measurements wedetermine the corresponding neutron skin values for $^{133}\text{Cs}$ and$^{127}\text{I}$. These results suggest a preference for models which predictlarge neutron skin values, as corroborated by the only other electroweakmeasurements of the neutron skin of $^{208}\text{Pb}$ performed by PREXexperiments. Moreover, for the first time, we obtain a data-driven APV+COHERENTmeasurement of the low-energy weak mixing angle with a percent uncertainty,independent of the value of the average neutron rms radius of $^{133}\text{Cs}$and $^{127}\text{I}$, that is allowed to vary freely in the fit. The value ofthe low-energy weak mixing angle that we found is slightly larger than thestandard model prediction.

New insights into nuclear physics and weak mixing angle using electroweak probes