Neutron Skin in CsI and Low-Energy Effective Weak Mixing Angle from COHERENT Data

Abstract

Both the neutron skin thickness $\Delta R_{np}$ of atomic nuclei and the low-energy neutrino-nucleon ($\nu N$) interactions are of fundamental importance in nuclear and particle physics, astrophysics as well as new physics beyond the standard model (SM) but largely uncertain currently, and the coherent elastic neutrino-nucleus scattering (CE$\nu$NS) provides a clean way to extract their information. New physics beyond the SM may cause effectively a shift of the SM weak mixing angle ${\theta }_W$ in low-energy $\nu N$ interactions, leading to an effective weak mixing angle ${\theta }_W^{\ast }$. By analyzing the CE$\nu$NS data of the COHERENT experiment, we find that while a one-parameter fit to the COHERENT data by varying $\Delta R_{np}$ produces $\Delta R_{np}^{\mathrm{CsI}}\simeq 0.68_{-1.13}^{+0.91}$ fm for CsI with an unrealistically large central value by fixing ${\sin }^2{\theta }_W^{\ast }$ at the low-energy SM value of ${\sin }^2{\theta }_W^{\mathrm{SM}}=0.23857$, a two-dimensional fit by varying $\Delta R_{np}$ and ${\sin }^2{\theta }_W^{\ast }$ leads to a strong positive correlation between $\Delta R_{np}$ and ${\sin }^2{\theta }_W^{\ast }$ with significantly smaller central values of $\Delta R_{np}^{\mathrm{CsI}}\simeq 0.24_{-2.03}^{+2.30}$ fm and ${\sin }^2{\theta }_W^{\ast }=0.21_{-0.10}^{+0.13}$. Although the uncertainty is too large to claim a determination of $\Delta R_{np}^{\mathrm{CsI}}$ and ${\sin }^2{\theta }_W^{\ast }$, the present study suggests that the multi-dimensional fit is important in future analyses of high-precision CE$\nu$NS data. The implication of the possible deviation of ${\sin }^2{\theta }_W^{\ast }$ from ${\sin }^2{\theta }_W^{\mathrm{SM}}$ on new physics beyond the SM is also discussed.

Comments: 6 pages, 2 figures. Presentation improved and discussions added. Accepted version to appear in PRD as a Rapid Communication