Measuring the Low-Energy Weak Mixing Angle with Supernova Neutrinos

TL;DR

This work proposes using coherent elastic neutrino-nucleus scattering (CEvNS) in the Argo detector to measure the low-energy weak mixing angle $sin^2(theta_W)$ with MeV-scale supernova neutrinos. It models the core-collapse supernova flux via the Garching quasi-thermal parameterization and predicts CEvNS event rates in a 362.7-ton argon detector, accounting for detector thresholds, form factors, and pile-up. A chi-squared framework shows that, for a nearby galactic SN, a precision of a few percent on $sin^2(theta_W)$ is achievable (roughly 2.8% at 3 kpc, down to 1.3% at 1 kpc, and 4.5% at 5 kpc), with flux uncertainties from external SN measurements currently dominating the error budget. The results indicate strong potential for low-energy electroweak tests and for constraining neutrino non-standard interactions, highlighting the scientific value of multi-detector, multi-messenger calibration of the next galactic SN.

Abstract

The weak mixing angle $θ_W$ is a fundamental parameter in the electroweak theory with a value running according to the energy scale, and its precision measurement in the low-energy regime is still ongoing. We propose a method to measure the low-energy $\sin{^2θ_W}$ by taking advantage of Argo, a future ton-scale liquid argon dark matter detector, and the neutrino flux from a nearby core-collapse supernova (CCSN). We evaluate the expected precision of this measurement through the coherent elastic neutrino-nucleus scattering (CE$ν$NS) channel. We show that Argo is potentially capable of achieving a few percent determination of $\sin{^2θ_W}$, at the momentum transfer of $q \sim 20$ MeV, in the observation of a CCSN within $\sim 3$ kpc from the Earth. Such a measurement is valuable for both the precision test of the electroweak theory and searching for new physics beyond the standard model in the neutrino sector.

Figures (5)

• Figure 1: Temporal evolution of supernova neutrino spectral parameters for the models s11.2-S (dashed-dotted lines) and s27.0-L (solid lines). $\nu_e$, $\Bar{\nu}_e$, and $\nu_x$ ($\nu_x$ denotes one of $\nu_\mu$, $\Bar{\nu}_\mu$, $\nu_\tau$, and $\Bar{\nu}_\tau$) are colored blue, red, and purple, respectively. Upper panel: neutrino mean energies $\langle E_{\nu_\beta} \rangle$. Middle panel: neutrino luminosities $\mathcal{L}_{\nu_\beta}$. The total neutrino luminosities are also shown in black. Lower panel: shape parameter $\alpha_\beta$. Note that the feature appearing in all curves at $\sim\!0.5\,\rm s$ is due to the artificial triggering of the explosion models (see more discussion in the text) Mirizzi:2015eza
• Figure 2: Expected event counts of CE$\nu$NS in Argo for the 4 models, evaluated at $d=10{\,\text{kpc}}$. Upper panel: scattering rate $\mathrm{d}\mathcal{N}/\mathrm{d}t$. Lower panel: cumulative event counts $\mathcal{N}$ over time
• Figure 3: Simulated event pile-up in Argo with $\sin^2{\theta_W}=0.23863$. For each set of Monte Carlo simulations at a certain value of $d$, $3\times10^4$ individual mock triggers are generated. Upper panel: mean portion of pile-up events $\langle \mathcal{N}_\text{bias} \rangle/ \mathcal{N}_\text{true}$ (in percentage). Lower panel: $1\sigma$ variation of pile-up events $\sigma_{\text{bias}}/ \mathcal{N}_\text{true}$
• Figure 4: Expected sensitivity of Argo to the variation in low-energy $\sin{^2\theta_W}$ from the SM value of $0.23863$ (indicated by the vertical black dashed-dotted line), at a few benchmark values of $d$. The $1\sigma$ and $2\sigma$ confidence levels are indicated by the horizontal grey dotted lines. The model s27.0-L and NMO are assumed
• Figure 5: Comparison between the expected precision of low-energy $\sin{^2\theta_W}$ measurement by Argo and other measurements ParticleDataGroup:2024cfk, at the $1\sigma$ confidence level, at different momentum transfers $q$. Measurements from recent CE$\nu$NS experiments AtzoriCorona:2022qrfDeRomeri:2022twgDeRomeri:2025csu are also shown in colors