This paper reports the first combined analysis that fits multiple public atmospheric neutrino datasets together with reactor data. The authors bring Super‑Kamiokande, IceCube‑DeepCore and KM3NeT‑ORCA atmospheric samples together with precise reactor results from Daya Bay. They show a single physics model can describe all of these datasets at once and extract competitive numbers for the basic neutrino oscillation parameters.

The team performed a very large joint fit. They used 839,048 recorded events divided into 1,536 analysis bins and adjusted 91 fit parameters. The fit compares predicted event rates to the data while allowing the model to shift detector responses and other nuisance terms. Combining the experiments this way has long been viewed as hard outside the experimental collaborations; the paper demonstrates it can be done with public information, albeit with careful approximations.

At a high level the method reweights Monte Carlo predictions for the neutrino flux and interactions, and then applies detector “smearing” to connect true neutrino energy and angle to what each detector measures. For Super‑K they reconstructed smearing with log‑normal and von Mises–Fisher functions and added energy dependence to the angular resolution. For DeepCore and ORCA they used the provided response matrices and the experiment‑supplied detector systematics when available. For the reactor experiment Daya Bay the authors used the full published covariance matrix, so no extra detector parameters were needed for that dataset.

The combined fit produces concrete numbers. The paper reports a value of the CP‑violating phase δCP ≈ 3.78 with uncertainties +0.89/−0.884. CP stands for charge–parity and a non‑zero δCP would mean neutrinos and antineutrinos behave differently. The fit finds the reactor mixing angle θ13 ≈ 0.149, the atmospheric mixing angle θ23 ≈ 0.785, and the atmospheric mass splitting |Δm2 31| ≈ 2.51×10−3 eV2, with stated uncertainties. The analysis prefers the Normal Mass Ordering (the hypothesis that the third neutrino state is heaviest) over the Inverted Ordering by Δχ2IO−NO = 9.11. It also disfavors the absence of CP violation (δCP = 0) with Δχ2 = 8.06. In this context a larger positive Δχ2IO−NO means the normal ordering fits the combined data better than the inverted ordering.