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 $\theta^*_W$. 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 $\Delta R^{\rm{CsI}}_{np} \simeq 0.68^{+0.91}_{-1.13}$ fm for CsI with an unrealistically large central value by fixing $\sin^2 \theta^*_W$ at the low-energy SM value of $\sin^2\theta_W^{\rm{SM}} = 0.23857$, a two-dimensional fit by varying $\Delta R_{np}$ and $\sin^2 \theta^*_W$ leads to a strong positive correlation between $\Delta R_{np}$ and $\sin^2 \theta^*_W$ with significantly smaller central values of $\Delta R^{\rm {CsI}}_{np} \simeq 0.24_{-2.03}^{+2.30}$ fm and $\sin^2 \theta^*_W = 0.21_{-0.10}^{+0.13}$. 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.
Highlights
Compared to the results using one-parameter fit with sin2 θÃW fixed at sin2θSWM, we find a strong positive correlation between ΔRnp and sin2θÃW with significantly smaller central values of ΔRCnpsI ≃ 0.24þ−22..0330 fm and sin2θÃW 1⁄4 0.21þ−00..1103 at Q ≃ 0.05 GeV, indicating that the sin2θÃW may play an important role in extracting neutron skin information from analyzing the CEνNS data
We have demonstrated that the low-energy effective weak mixing angle θÃW plays an important role in the extraction of neutron skin information of atomic nuclei from the CEνNS experiments
Data of the COHERENT experiment, we have found that while a one-parameter fit to the COHERENT data produces ΔRCnpsI ≃ 0.68þ−10..1931 fm with sin2θÃW 1⁄4 sin2θSWM 1⁄4 0.23857, a two-dimensional fit by varying ΔRnp and sin2θÃW leads to a strong positive correlation between ΔRnp and sin2θÃW with significantly smaller central values of ΔRCnpsI ≃ 0.24þ−22..0330 fm and sin2θÃW 1⁄4 0.21þ−00
Summary
The neutron skin thickness of atomic nuclei, defined as ΔRnp 1⁄4 Rn − Rp where RnðpÞ 1⁄4 hr2nðpÞi1=2 is the neutron (proton) rms radius of the nucleus, provides a good probe of the equation of state (EOS) for isospin asymmetric nuclear matter [1,2,3,4,5,6,7,8,9,10], which is critically important due to its multifaceted roles in nuclear physics and astrophysics [11,12,13,14] as well as some issues of new physics beyond the standard model (SM) [15,16,17,18,19]. [20,21,22]), the Rn is largely uncertain since it is usually determined from strong processes, which is generally model dependent due to the complicated nonperturbative effects This provides a strong motivation for the lead radius experiment (PREX) being performed at the Jefferson Laboratory to determine the Rn of 208Pb to about 1% accuracy by measuring the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from 208Pb [23]. Compared to the results using one-parameter fit with sin θÃW fixed at sin2θSWM, we find a strong positive correlation between ΔRnp and sin2θÃW with significantly smaller central values of ΔRCnpsI ≃ 0.24þ−22..0330 fm and sin2θÃW 1⁄4 0.21þ−00..1103 at Q ≃ 0.05 GeV (corresponding to the energy scale of COHERENT experiment), indicating that the sin2θÃW may play an important role in extracting neutron skin information from analyzing the CEνNS data
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