Reinterpreting the weak mixing angle from atomic parity violation in view of the Cs neutron rms radius measurement from COHERENT

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 ${\sin }^2{\vartheta }_{\text{W}}=0.239{}_{-0.007}^{+0.006}$, to be compared with the Standard Model prediction at low momentum transfer, ${\sin }^2{\vartheta }_{\text{W}}^{\text{SM}}=0.23857(5)$. 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 $R_n=5.42\pm 0.31\text{fm}$ 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.

5 pages, 2 figures

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• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GW170817: Measurements of Neutron Star Radii and Equation of State
• Search for New Physics with Atoms and Molecules
• Observation of Coherent Elastic Neutrino-Nucleus Scattering
• Neutron skins and neutron stars in the multi-messenger era
• DARWIN: towards the ultimate dark matter detector
• Precision Measurement of the Weak Charge of the Proton
• Average CsI neutron density distribution from COHERENT data
• Parity and Time-Reversal Violation in Atomic Systems
• Weak Mixing Angle in the Thomson Limit

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