Fast Bayesian Inference for Neutrino Non-Standard Interactions at Dark Matter Direct Detection Experiments

TL;DR

The paper tackles the challenge of Bayesian inference in high-dimensional, complex posteriors arising from neutrino non-standard interactions (NSI) in dark matter direct-detection experiments. It combines GPU-accelerated likelihood evaluation, automatic differentiation, and neural-transport reparameterization (NeuTra) to drastically speed up sampling, benchmarking against traditional nested sampling and Hamiltonian Monte Carlo. The authors demonstrate a first full-parameter NSI scan by jointly analyzing XENON1T NR and PandaX-4T ER data, achieving speedups up to factors of $\sim 60$–$\sim 100$ and producing robust multi-dimensional credible regions. This approach not only improves inference efficiency and model comparison via Bayesian evidence, but also generalizes to other astroparticle physics problems with multi-dimensional posteriors, enabling timely global analyses and more comprehensive uncertainty quantification.$

Abstract

Multi-dimensional parameter spaces are commonly encountered in physics theories that go beyond the Standard Model. However, they often possess complicated posterior geometries that are expensive to traverse using techniques traditional to astroparticle physics. Several recent innovations, which are only beginning to make their way into this field, have made navigating such complex posteriors possible. These include GPU acceleration, automatic differentiation, and neural-network-guided reparameterization. We apply these advancements to dark matter direct detection experiments in the context of non-standard neutrino interactions and benchmark their performances against traditional nested sampling techniques when conducting Bayesian inference. Compared to nested sampling alone, we find that these techniques increase performance for both nested sampling and Hamiltonian Monte Carlo, accelerating inference by factors of $\sim 100$ and $\sim 60$, respectively. As nested sampling also evaluates the Bayesian evidence, these advancements can be exploited to improve model comparison performance while retaining compatibility with existing implementations that are widely used in the natural sciences. Using these techniques, we perform the first scan in the neutrino non-standard interactions parameter space for direct detection experiments whereby all parameters are allowed to vary simultaneously. We expect that these advancements are broadly applicable to other areas of astroparticle physics featuring multi-dimensional parameter spaces.

Figures (6)

• Figure 1: Left: Experimental idea. Solar neutrinos collide with the target atoms in a direct detection experiment, causing either the nucleus or the electrons of the atom to recoil. Right: The neutrino non-standard interactions parameterization, which can be used to model new physics phenomena between neutrinos, neutrons ($n$), protons ($p$), and electrons ($e$) Amaral:2023tbs. It is characterized by an overall interaction strength coordinate, $\varepsilon_{\alpha\beta}\xspace$, and two angles describing how strong the interaction is with the neutron ($\eta$) and proton vs. electron ($\varphi$).
• Figure 2: Marginalized representations of the inferred posteriors for our synthetic model, \ref{['eq:toy_model']}, using nested sampling (NS) and the No U-Turn Sampler (NUTS), both with and without neural transport (NeuTra). Left: The $68\%$ and $95\%$ highest posterior density region contours. Middle and Right: Probability density of the samples with $68\%$ equal-tailed intervals indicated as dashed lines. Only $\mu_1$ and $\mathcal{C}_1$ are shown for clarity; the full corner plot is given in \ref{['appendix:corner']}. As desired, our results show a high degree of overlap and all closely match the ground truth, derived in \ref{['appendix:bayesian']}.
• Figure 3: The $68\%$ and $95\%$ contours for the inferred posteriors for the neutrino non-standard interactions parameters. Our sampling methods are nested sampling (NS) and the No U-Turn Sampler (NUTS), both with and without neural transport (NeuTra). Two of the six $\varepsilon_{\alpha\beta}\xspace$ are selected to be shown for visualization purposes; the full corner plot is given in \ref{['appendix:corner']}. As desired, all contours show a high degree of overlap. Probability densities are also shown with $68\%$ equal-tailed intervals indicated as dashed lines. The intervals from all methods are almost identical.
• Figure 4: Log of Bayesian evidence integral $\log \mathcal{Z}$ for synthetic model, \ref{['eq:bayesian']}, with number of integration points per parameter dimension. For this model, the number of dimensions is $k = 3$ and the number of data points is $j = 2$. The integral converges to the quoted value of $\log \mathcal{Z} \approx -11.14$ after approximately $60$ points.
• Figure 5: The same as in \ref{['fig:toy']} but for the full synthetic model parameter space.