Abstract
Using the model independent average neutron rms radius of $^{133}\text{Cs}$ and $^{127}\text{I}$ obtained from the analysis of the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we remove the long-standing $1.5\,\sigma$ tension between the Standard Model prediction and the weak mixing angle measurement from the atomic parity violation (APV) in caesium. The updated APV result becomes $\sin^2 \vartheta_{\textrm{W}}=0.239{}^{+0.006}_{-0.007}$, to be compared with the Standard Model prediction at low momentum transfer, $\sin^2 \vartheta_{\text{W}}^{\textrm{SM}} = 0.23857(5)$. Moreover, exploiting the fact that the APV result is highly sensitive to the caesium neutron rms radius, $R_{n}$, and assuming that the Standard Model is correct, we combine the APV and the COHERENT measurements in order to get a better determination of $R_{n}$. The value of $R_{n}=5.42\pm 0.31\,\textrm{fm}$ is obtained, improving significantly the current uncertainty. This result allows to infer a meaningful value of the caesium neutron skin, the difference between the neutron and proton distribution radii, equal to $\Delta R_{np}=0.62\pm 0.31\,\text{fm}$, showing for the first time a $2\, \sigma$ deviation from zero.
Highlights
The weak mixing angle, θW, known as the Weinberg angle, is a fundamental parameter in the theory of the electroweak (EW) interactions included in the standard model (SM) of particle physics [1,2]
The experimental determination of sin2 θW provides a direct probe of physics phenomena not included in the SM, usually referred to as new physics
A summary of the weak mixing angle measurements as a function of the energy scale, Q, is shown in Fig. 1, along with the SM predicted running of sin2 θW, calculated in the so-called modified minimal subtraction (MS) renormalization scheme [1,4,5]
Summary
For clarity we displayed the old APV point to the left and the Tevatron and LHC points horizontally to the left and to the right, respectively. Sin2θSWM 1⁄4 0.23857ð5Þ; ð1Þ motivating a further investigation of all the inputs entering in this measurement. The APV determination of sin θW is derived by measuring the weak charge of 133Cs, QCWs. In the SM, for a nucleus with N neutrons and Z protons, the weak charge including EW corrections is defined as [14]
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