Neutrino Effects on Atomic Measurements of the Weinberg Angle

Abstract

We derive a complete expression for the neutrino-mediated quantum force beyond the four-Fermi approximation within the Standard Model. Using this new result, we study the effect of atomic parity violation caused by neutrinos. We find that the neutrino effect is sizable compared to the current experimental sensitivity and can also significantly affect the value of the Weinberg angle measured in atomic systems. This offers a promising method for detecting the neutrino force in the future and facilitates the application of precision atomic physics as a probe for neutrino physics and the electroweak sector of the Standard Model.

Figures (2)

• Figure 1: Feynman diagrams that contribute to the SM neutrino forces beyond the four-Fermi approximation: self-energy (left), penguin (middle), and box (right), where $\chi_1$ and $\chi_2$ are arbitrary SM fermions. The coupling to neutrino and $W$ boson exists only when $\chi_i$ is a lepton. If both $\chi_1$ and $\chi_2$ are leptons, there is an additional flipped penguin diagram with the vertex correction at $\overline{\chi_2}$. Note that the box diagram only exists for $\chi_1 = \chi_2$.
• Figure 2: The evolution of the SM neutrino force with distances in the middle range $10^{-1}\lesssim m_Z r \lesssim 10$ according to Eqs. (\ref{['eq:VSE']})-(\ref{['eq:Vbox']}).