Data release: Atmospheric neutrino oscillation analysis with neutron tagging and an expanded fiducial volume in Super-Kamiokande I-V

// ----------------------------------------------------------------------------
//
// Super-Kamiokande I-V Atmospheric Neutrino Data Release
// Associated publication: "Atmospheric neutrino oscillation analysis with
//   neutron tagging and an expanded fiducial volume in Super-Kamiokande I-V"
// Corresponding author: Roger Wendell, <wendell.roger.4s@kyoto-u.ac.jp>
// DOI: 10.5281/zenodo.8401262
//
// ----------------------------------------------------------------------------

// Changelog, v2 [2026-11-03]

Corrections to the MC summary statistics and bin definitions in `bins/`, and
trimmed chi2 tables. Data counts are unchanged.

- MC counts include events previously omitted from some bins (+0.09% total,
  at most ~1% in any bin). MCTotal now equals the sum over neutrino types.
- MC averages, RMS values and quantiles are recomputed. Energy quantiles no
  longer carry a bias from linear binning, which mainly affected the
  PC and Upmu samples.
- Three bins had an incorrect upper CosZ edge (sk1-5_upmu_thru_*: now 0.0;
  sk4-5_fc_subgev_1ring_numubarlike, LogP 3.0-3.2: now 1.0). Bin edges in
  the text file are now given to four decimal places.
- Removed `sk_2023_MCTotal.txt` from `normal/` and `inverted/`; these
  duplicated `sk_2023_MCTotalNO.txt` and `sk_2023_MCTotalIO.txt`.
- chi2 listings now start at Delta m^2 = 1.6e-3 eV^2. Grid nodes at 1.0-1.5e-3
  (theta13-constrained) and 1.2-1.5e-3 (theta13-free) were removed. These
  included non-converged fits, previously listed as inf, and otherwise had
  Delta chi^2 values above 29 throughout. All remaining values are unchanged.

Overview

This data release accompanies the publication "Atmospheric neutrino oscillation
analysis with neutron tagging and an expanded fiducial volume in
Super-Kamiokande I-V." The information provided is divided into two
sub-directories:

    - bins: Contains data & MC counts in each analysis bin for different
            oscillation configurations
    - chi2: Contains listings of chisquare values at each point in the
            oscillation parameter space scanned for the analyses described in
            the accompanying publication

Bin Information

This section describes the provided bin information. The `bins/` subdirectory
includes a ROOT file which contains binning information, data, and MC counts
and MC summary statistics in each bin in the form of several ROOT trees. The
contents of the ROOT file are also provided as text files within the same
subdirectory.

There are 930 bins used for atmospheric neutrino data in the analysis. Each
ROOT tree and text file contains sequential listing of information for each of
the 930 bins, i.e. the first entry or line of each tree and text file
corresponds to the first bin, and so on.

DISCLAIMER: The data and MC counts and summary statistics provided are not
expected to be sufficient to identically reproduce the publication fit results.
The publication fit results rely on response functions of the bins to
variations in the systematic uncertainty parameters which are not included in
this release. Additionally, the MC oscillation probabilities used in the
publication were computed individually for each MC event and are not possible
to reproduce exactly using the binned event information provided with this
release.

 Bin Definitions

The ROOT file contains a `BinInfoTree` which lists the sample name associated
with each bin, and the upper and lower bin edges of the 2D binning scheme used
to bin atmospheric neutrino events. The sample names describe the selections
used to place events in each bin, e.g. "subgev" and "multigev" for sub-GeV and
multi-GeV events, respectively. Since data from the different SK phases are
divided into different analysis samples, each sample name also lists the range
of SK phases included in the same, e.g. sk1-5 for SK I, SK II, SK III, SK IV,
and SK V, or sk4-5 for SK IV and SK V only. The contents of this tree are also
listed in the `bins/sk_2023_BinInfo.txt` file.

Data Counts

Observed atmospheric neutrino data counts in each bin are listed in the
`DataTree` within the ROOT file. The contents of this tree are also listed in
the `bins/sk_2023_Data.txt` file.

MC Counts and Summary Statistics

MC counts and summary statistics of the true MC energies and directions are
provided for each true neutrino type in the ROOT trees named `MC*Tree`. The
information is provided for three oscillation configurations: The
theta13-constrained best-fit oscillation parameters in the normal (NO) and
inverted (IO) orderings, and without oscillations (NoOsc).

The following summary statistics are provided for both the true neutrino
energies and directions (cosine zenith angle) of MC events in each bin:
Average, RMS, 2.3%, 15.9%, 50%, 84.1%, and 97.7% quantiles. The quantiles
approximately correspond to -2, -1, 0, +1, and +2 sigma deviations from the
median.

The ROOT tree MC information is duplicated in the text files found under the
`bins/[normal,inverted,unoscillated]` subdirectories, corresponding to the three
oscillation scenarios.

Chisquare Information

We provide listings of the relative chisquare values with respect to the
best-fit point in each ordering. The listings are provided as text files: The
first columns correspond to the oscillation parameters at each grid point,
while the final column lists the chisquare value. Chisquare values are provided
for both the theta13-free and theta13-constrained analyses. Adding 5.2283 for
the theta13-free and 5.6905 for the theta13-constrained inverted ordering chi2
values place the inverted values with respect to the best fit in the normal
ordering.  The convention used is delta_m^2_{32} for the normal ordering, and
|delta_m^2_{31}| for the inverted ordering.

ROOT files containing the 1D delta chisquare profiles for delta CP, and 2D
delta chisquare profiles for allowed values of delta m^2 versus sin2 theta23 at
68% and 90% are also provided. There are two ROOT files corresponding to the
contours from the theta13-free and theta13-constrained fits.

A ROOT macro which draws the contours is also provided. It can be run using the
following command from the chi2 directory:

```
> root draw_sk_contours.cc
```