Portable Likelihoods for Experimental Neutrino Physics Analyses with Normalizing Flows

In long-baseline neutrino experiments, the data collected at a near detector constrain the systematic uncertainties affecting the far-detector predictions, requiring a propagation of the near-detector constraints via its likelihood. More generally, the same need arises whenever the result of one simulation-based analysis in the form of a constrained likelihood is used as input to another. In current oscillation analyses it relies either on a Gaussian approximation around the best fit, which discards non-Gaussian features, or on MCMC samples, which form a finite chain rather than an evaluable function. We propose exporting the constrained likelihood as a trained normalizing flow. A hybrid architecture, initialized from the post-fit Gaussian, combines coupling layers for the approximately linear parameters with a conditional autoregressive spline flow for the remainder. On a near-detector replica with 110 systematic parameters, 10 of which explicitly introduce non-Gaussianities, the trained flow reproduces an MCMC reference and reaches a relative effective sample size of $98\%$, against about $5\%$ for the Gaussian approximation. The result is a analytical, portable density that can be inserted into downstream analyses without the original data or simulation.