Refined determination of the weak mixing angle at low energy

The weak mixing angle is a fundamental parameter of the electroweak theory of the standard model whose measurement in the low-energy regime is still not precisely determined. Different probes are sensitive to its value, among which atomic parity violation, coherent elastic neutrino-nucleus scattering and parity-violating electron scattering on different nuclei. In this work, we attempt for the first time to combine all these various determinations by performing a global fit that also keeps into account the unavoidable dependence on the experimentally poorly known neutron distribution radius of the nuclei employed, for which a new measurement using proton-cesium elastic scattering became available. By using all present direct determinations of the neutron distribution radius of cesium we find $\sin^2\!\vartheta_{W} =0.2396^{+0.0020}_{-0.0019}$, which should supersede the previous value determined from atomic parity violation on cesium. When including electroweak only, but also indirect, determinations of the neutron distribution radius of cesium the uncertainty reduces to 0.0017 maintaining the same central value, showing an excellent agreement independently of the method used.