A Simulation-Based Inference Evaluation of Tension Between MicroBooNE and MiniBooNE Results in a 3+1 Sterile Neutrino Global Fit

Compatibility between different datasets in a global fit is essential for determining whether a chosen model adequately describes the data. In a 3+1 sterile neutrino global fit, long-standing tensions between datasets sensitive to $\nu_e$ appearance and $\nu_e/\nu_\mu$ disappearance indicate a failure of the model to explain the observed data, despite an overall $>5\sigma$ improvement over the $3\nu$ Standard Model (SM) based on a $\chi^2$ fit. Overall, a global preference for the 3+1 sterile-neutrino hypothesis with significant tension between experiments motivates consideration of more complex models, but these are currently computationally prohibitive to evaluate. This paper is the third in a series aimed at reducing computational cost by developing a Simulation-Based Inference (SBI) framework for global fits. Previous papers focused on rapidly fitting the data sets using frequentist (Feldman-Cousins) and Bayesian approaches, while in this work, we formalize a definition of tension within the SBI framework. As an example, we perform a full 3+1 fit to the charged-current quasi-elastic neutrino data from the MiniBooNE experiment and the inclusive neutrino data from the MicroBooNE experiment, located on the same beamline. Using experiment-supplied systematics as is, we find these data sets favor 3+1 at $3.6\sigma$ and $1.8\sigma$ respectively, while the tension between the two is $3.3\sigma$, when fit with the SBI procedure. After correcting for normalization differences between data and Monte Carlo in the MicroBooNE $\nu_\mu$ samples, the tension relaxes to $2.2\sigma$, indicating reduced but non-negligible disagreement. The observed tension may reflect both limitations of the 3+1 model in describing the datasets and the presence of systematic effects that impact the experiments differently.