$ν^2$-Flows: Fast and improved neutrino reconstruction in multi-neutrino final states with conditional normalizing flows

TL;DR

This paper extends neutrino reconstruction to events with multiple neutrinos by introducing ν^2-Flows, a conditional normalizing-flow framework guided by a transformer-based event encoder with cross-attention. The method handles arbitrary multiplicities and delivers per-event neutrino momentum solutions that closely match truth distributions, reducing biases inherent in traditional approaches. In tt̄ dilepton events, ν^2-Flows substantially improves the statistical precision of unfolded double-differential observables (e.g., $m_{t\bar{t}}$ and $\Delta\phi(\ell^+\ell^-)$) by factors of 1.5–2 over ν-Weighting and up to 4 over Ellipse, while maintaining full event coverage and fast CPU/GPU inference. The approach shows robustness to training samples and demonstrates implicit learning of the top-quark mass relation, with potential applications to background discrimination and extended multiplicities in future analyses.

Abstract

In this work we introduce $ν^2$-Flows, an extension of the $ν$-Flows method to final states containing multiple neutrinos. The architecture can natively scale for all combinations of object types and multiplicities in the final state for any desired neutrino multiplicities. In $t\bar{t}$ dilepton events, the momenta of both neutrinos and correlations between them are reconstructed more accurately than when using the most popular standard analytical techniques, and solutions are found for all events. Inference time is significantly faster than competing methods, and can be reduced further by evaluating in parallel on graphics processing units. We apply $ν^2$-Flows to $t\bar{t}$ dilepton events and show that the per-bin uncertainties in unfolded distributions is much closer to the limit of performance set by perfect neutrino reconstruction than standard techniques. For the chosen double differential observables $ν^2$-Flows results in improved statistical precision for each bin by a factor of 1.5 to 2 in comparison to the Neutrino Weighting method and up to a factor of four in comparison to the Ellipse approach.

Figures (19)

• Figure 1: A schematic of the $\nu^2$-Flows network for learning the conditional likelihood of multiple neutrinos in the event. The network uses a transformer encoder (TE) with cross-attention (CA) with a learnable class token (CT) to embed an event representation for any multiplicity of physics objects. This operation is permutation invariant and can operate on any jet and lepton multiplicity. Each physics object has its own dedicated embedding network and additional event information (Misc) is used to condition the transformer encoder blocks. The representation vector is used to condition the transformation with the normalizing flow.
• Figure 2: The kinematics of the reconstructed (anti-)neutrinos for the three reconstruction methods and $\nu$-Truth (shaded grey). The hashed areas represent statistical uncertainties in the $\nu$-Truth prediction.
• Figure 3: The angular separation in $\eta$ and $\phi$ between the reconstructed neutrino pair per event for the three reconstruction methods and $\nu$-Truth (shaded grey). The hashed areas represent statistical uncertainties in the $\nu$-Truth prediction.
• Figure 4: The reconstructed invariant mass of $W$ bosons (left) and top quarks (middle), as well as the top quark ${p}_\mathrm{T}$ (right) when using the three neutrino reconstruction methods in comparison to $\nu$-Truth (shaded grey).
• Figure 5: The invariant mass, ${p}_\mathrm{T}$, and rapidity of the reconstructed $t\bar{t}$ system when using the three neutrino reconstruction methods in comparison to $\nu$-Truth (shaded grey).