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We implement the Bayesian inference to retrieve energy spectra of all neutrinos from a galactic core-collapse supernova (CCSN). To achieve high statistics and full sensitivity to all flavours of neutrinos, we adopt a combination of several reaction channels from different large-scale neutrino observatories, namely inverse beta decay on proton and elastic scattering on electron from Hyper-Kamiokande (Hyper-K), charged current absorption on Argon from Deep Underground Neutrino Experiment (DUNE) and coherent elastic scattering on Lead from RES-NOVA. Assuming no neutrino oscillation or specific oscillation models, we obtain mock data for each channel through Poisson processes with the predictions, for a typical source distance of 10 kpc in our Galaxy, and then evaluate the probability distributions for all spectral parameters of theoretical neutrino spectrum model with Bayes' theorem. Although the results for either the electron-neutrinos or electron-antineutrinos reserve relatively large uncertainties (according to the neutrino mass hierarchy), a precision of a few percent (i.e., $\pm 1 \% \sim \pm 4 \%$ at a credible interval of $2 \sigma$) is achieved for primary spectral parameters (e.g., mean energy and total emitted energy) of other neutrino species. Moreover, the correlation coefficients between different parameters are computed as well and interesting patterns are found. Especially, the mixing-induced correlations are sensitive to the neutrino mass hierarchy, which potentially makes it a brand new probe to determine the neutrino mass hierarchy in the detection of galactic supernova neutrinos. Finally, we discuss the origin of such correlation patterns and perspectives for further improvement on our results., Comment: 25 pages, 7 figures, 4 tables, published version

A precise and model-independent determination of the neutron distribution radius $R_{\rm n}$ and thus the neutron skin thickness $R_{\rm skin}$ of atomic nuclei is of fundamental importance in nuclear physics, particle physics and astrophysics but remains a big challenge in terrestrial labs. We argue that the nearby core-collapse supernova (CCSN) in our Galaxy may render a neutrino flux with unprecedentedly high luminosity, offering perfect opportunity to determine the $R_{\rm n}$ and $R_{\rm skin}$ through the coherent elastic neutrino-nucleus scattering (CE$\nu$NS). We evaluate the potential of determining the $R_{\rm n}$ of lead (Pb) via CE$\nu$NS with the nearby CCSN neutrinos in the RES-NOVA project which is designed to hunt CCSN neutrinos using an array of archaeological Pb based cryogenic detectors. We find that an ultimate precision of $\sim 0.1 \%$ for the $R_{\rm n}$ ($\sim 0.006$ fm for the $R_{\rm skin}$) of Pb can be achieved via RES-NOVA in the most optimistic case that the CCSN explosion were to occur at a distance of $\sim 1$ kpc from the Earth., Comment: 7 pages, 3 figures, 1 table. Discussions on nearby CCSN rate and neutrino detection added. Accepted version to appear in PRD

Core-collapse supernova (CCSN) provides a unique astrophysical site for studying neutrino-matter interactions. Prior to the shock-breakout neutrino burst during the collapse of the iron core, a preshock $\nu_e$ burst arises from the electron capture of nuclei and it is sensitive to the low-energy coherent elastic neutrino-nucleus scattering (CE$\nu$NS) which dominates the neutrino opacity. Since the CE$\nu$NS depends strongly on the non-standard neutrino interactions (NSI) which are completely beyond the standard model and yet to be determined, the detection of the preshock burst thus provides a clean way to extract the NSI information. Within the spherically symmetric general-relativistic hydrodynamic simulation for the CCSN, we investigate the NSI effects on the preshock burst. We find that the NSI can maximally enhance the peak luminosity of the preshock burst almost by a factor of three, reaching a value comparable with that of the shock-breakout burst. Future detection of the preshock burst will have critical implications on astrophysics, neutrino physics and physics beyond the standard model., Comment: 7 pages, 3 figures. Presentation improved and discussions added. Accepted version to appear in ApJL

We use both mass and internal energy specified rubidium atoms to jointly test the weak equivalence principle (WEP). We improve the four-wave double-diffraction Raman transition method (FWDR) we proposed before to select atoms with certain mass and angular momentum state, and perform dual-species atom interferometer. By combining $^{87}$Rb and $^{85}$Rb atoms with different angular momenta, we compare the differential gravitational acceleration of them, and determine the value of E\"{o}tv\"{o}s parameter, $\eta$, which measures the strength of the violation of WEP. For one case ($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statistical uncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s. With various systematic errors correction, the final value is $\eta=(-4.4 \pm 6.7) \times 10^{-10}$. Comparing with the previous WEP test experiments using atoms, this work gives a new upper limit of WEP violation for $^{87}$Rb and $^{85}$Rb atom pairs., Comment: 5 pages, 3 figures

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