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

Both the neutron skin thickness $\mathrm{\Delta }{R}_{np}$ 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 $\mathrm{\Delta }{R}_{np}$ produces $\mathrm{\Delta }{R}_{np}^{\mathrm{C}\mathrm{s}\mathrm{I}}\simeq 0.68_{-1.13}^{+0.91}$ fm for CsI with an unrealistically large central value by fixing ${\sin }^2{\theta }_W^{\ast }$ at the low-energy SM value of ${\sin }^2{\theta }_W^{\mathrm{S}\mathrm{M}}=0.23857$, a two-dimensional fit by varying $\mathrm{\Delta }{R}_{np}$ and ${\sin }^2{\theta }_W^{\ast }$ leads to a strong positive correlation between $\mathrm{\Delta }{R}_{np}$ and ${\sin }^2{\theta }_W^{\ast }$ with significantly smaller central values of $\Delta R^{\rm {CsI}}{np} \simeq 0.24{-2.03}^{+2.30}$fmand$\sin^2 \theta^W = 0.21{-0.10}^{+0.13}$. Although the uncertainty is too large to claim a determination of $\Delta R^{\rm{CsI}}_{np}$and$\sin^2 \theta^_W$, 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 $\sin^2 \theta^*_W$from$\sin^2\theta_W^{\rm{SM}}$ on new physics beyond the SM is also discussed.