Neutrino and antineutrino inclusive charged-current cross section measurements with the MINOS near detector

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# MINOS νμ and ν̄μ inclusive CC cross sections per nucleon of isoscalar iron, σ/E for 3–50 GeV, and their ratio
# (PRD 81, 072002 (2010); tables from the arXiv:0910.2201 source in data/), compared with the cross sections of
# Newtrinos.jl (module `xsec`): the GENIE tunes (`generator_sigma`, ⁵⁶Fe, corrected to an isoscalar nucleon with each
# tune's free p/n cross sections, `isoscalar_correction`) and the reference model of `CorrelatedXsec` with its prior
# 1σ band (ν, ν̄ and their ratio sampled jointly).
# Run from this directory with the Newtrinos.jl environment at the pinned commit:
#   julia --project=<path to Newtrinos.jl> reproduce.jl
using Newtrinos, CairoMakie, CSV, DataFrames, Printf, Statistics, Random, Distributions

cd(@__DIR__); mkpath("ours"); mkpath("results")
const X = Newtrinos.xsec

d = CSV.read("data/minos_table.csv", DataFrame; comment = "#")
r = CSV.read("data/minos_ratio.csv", DataFrame; comment = "#")
dn, db = d[d.nu .== "nu", :], d[d.nu .== "nubar", :]

tab = X.load_table()
E = 10 .^ range(log10(0.2), log10(60), length = 300)   # down to the threshold region
at(v, e = E) = X.at_energies(tab.E, v, e)
TUNES = Symbol.(sort(tab.tunes))
iso(t, anti, e = E) = at(X.isoscalar_correction(t, 26, 56, :numu, anti), e)
σ_tune(t, anti, e = E) = at(sum(X.generator_sigma(t, :Fe, :numu, anti, :CC)), e) .* iso(t, anti, e)

xs = X.configure(X.CorrelatedXsec())
ref = xs.cfg.reference
sig = Dict(anti => (f = xs.sigma(E; flavour = :numu, anti, current = :CC, target = :Fe); c = iso(ref, anti); p -> f(p) .* c) for anti in (false, true))
# bin averages (flat in E) for the data bins, and the model at the bin-average energies for the ratio
binE(lo, hi) = collect(range(lo, hi, length = 21))
sig_bins(dd, anti) = [(f = xs.sigma(binE(lo, hi); flavour = :numu, anti, current = :CC, target = :Fe); c = iso(ref, anti, binE(lo, hi)); p -> mean(f(p) .* c))
                      for (lo, hi) in zip(dd.E_lo, dd.E_hi)]
bins = (nu = sig_bins(dn, false), nubar = sig_bins(db, true))
sig_r = Dict(anti => (f = xs.sigma(r.E_mean; flavour = :numu, anti, current = :CC, target = :Fe); c = iso(ref, anti, r.E_mean); p -> f(p) .* c) for anti in (false, true))

rng = MersenneTwister(1)
draw() = map(p -> p isa Distribution ? rand(rng, p) : p, xs.priors)
samples = [draw() for _ in 1:500]
q(M, a) = [quantile(filter(!isnan, row), a) for row in eachrow(M)]   # ratios are undefined where a draw has σ = 0
band = Dict(anti => (M = reduce(hcat, [sig[anti](p) for p in samples]); (lo = q(M, 0.16), hi = q(M, 0.84))) for anti in (false, true))
Rs = reduce(hcat, [sig[true](p) ./ sig[false](p) for p in samples])
rband = (lo = q(Rs, 0.16), hi = q(Rs, 0.84))
p0 = xs.params

ticks = ([0.2, 0.5, 1, 2, 5, 10, 20, 50], ["0.2", "0.5", "1", "2", "5", "10", "20", "50"])
function panel_sigma(pos, anti, dd, lab, lims)
    ax = Axis(pos, xscale = log10, xlabel = "E_ν (GeV)", ylabel = "$lab CC σ / E (10⁻³⁸ cm²/GeV per nucleon)",
              title = "MINOS $lab, isoscalar Fe", limits = (0.2, 60, lims...), xticks = ticks)
    band!(ax, E, band[anti].lo, band[anti].hi, color = (:dodgerblue, 0.25), label = "CorrelatedXsec prior 1σ")
    for (i, t) in enumerate(TUNES)
        lines!(ax, E, σ_tune(t, anti), color = (Makie.wong_colors()[mod1(i, 7)], 0.8), linewidth = 1, label = "GENIE $(t)")
    end
    lines!(ax, E, sig[anti](p0), color = :dodgerblue, linewidth = 2.5, label = "nominal ($(ref))")
    errorbars!(ax, dd.E_mean, dd.sigma_over_E, dd.total, color = :black, whiskerwidth = 4)
    scatter!(ax, dd.E_mean, dd.sigma_over_E, color = :black, label = "MINOS (stat ⊕ syst ⊕ norm)")
    ax
end
function panel_ratio(pos)
    ax = Axis(pos, xscale = log10, xlabel = "E_ν (GeV)", ylabel = "σ(ν̄μ) / σ(νμ)", title = "MINOS ratio r, isoscalar Fe",
              limits = (0.2, 60, 0.2, 0.6), xticks = ticks)
    band!(ax, E, rband.lo, rband.hi, color = (:dodgerblue, 0.25), label = "CorrelatedXsec prior 1σ")
    for (i, t) in enumerate(TUNES)
        lines!(ax, E, σ_tune(t, true) ./ σ_tune(t, false), color = (Makie.wong_colors()[mod1(i, 7)], 0.8), linewidth = 1, label = "GENIE $(t)")
    end
    lines!(ax, E, sig[true](p0) ./ sig[false](p0), color = :dodgerblue, linewidth = 2.5, label = "nominal ($(ref))")
    errorbars!(ax, r.E_mean, r.r, r.total, color = :black, whiskerwidth = 4)
    scatter!(ax, r.E_mean, r.r, color = :black, label = "MINOS (total)")
    ax
end
for (name, mk) in (("nu", pos -> panel_sigma(pos, false, dn, "νμ", (0.0, 1.05))),
                   ("nubar", pos -> panel_sigma(pos, true, db, "ν̄μ", (0.0, 0.42))), ("ratio", panel_ratio))
    fig = Figure(size = (800, 470))
    ax = mk(fig[1, 1])
    Legend(fig[1, 2], ax, framevisible = false, labelsize = 9)
    save("ours/$(name).png", fig)
end

# χ²: σ/E with stat ⊕ syst (MINOS normalised ν above 30 GeV to the world average; the normalisation error is common
# to all bins and is left out), and the ratio with its total errors; reference with and without its prior band
chi2(data, err, m, extra = 0) = sum((data .- m) .^ 2 ./ (err .^ 2 .+ extra .^ 2))
err_ss(dd) = sqrt.(dd.stat .^ 2 .+ dd.sys .^ 2)
mref = (nu = [f(p0) for f in bins.nu], nubar = [f(p0) for f in bins.nubar])
msd = (nu = [std([f(p) for p in samples]) for f in bins.nu], nubar = [std([f(p) for p in samples]) for f in bins.nubar])
rref = sig_r[true](p0) ./ sig_r[false](p0)
rsd = [std(col) for col in eachrow(reduce(hcat, [sig_r[true](p) ./ sig_r[false](p) for p in samples]))]
rows = [(model = "$(ref) (nominal)", chi2_nu = chi2(dn.sigma_over_E, err_ss(dn), mref.nu), chi2_nubar = chi2(db.sigma_over_E, err_ss(db), mref.nubar),
         chi2_ratio = chi2(r.r, r.total, rref), chi2_nu_band = chi2(dn.sigma_over_E, err_ss(dn), mref.nu, msd.nu),
         chi2_nubar_band = chi2(db.sigma_over_E, err_ss(db), mref.nubar, msd.nubar), chi2_ratio_band = chi2(r.r, r.total, rref, rsd))]
binavg(t, anti, dd) = [mean(σ_tune(t, anti, binE(lo, hi))) for (lo, hi) in zip(dd.E_lo, dd.E_hi)]
for t in TUNES
    push!(rows, (model = string(t), chi2_nu = chi2(dn.sigma_over_E, err_ss(dn), binavg(t, false, dn)),
                 chi2_nubar = chi2(db.sigma_over_E, err_ss(db), binavg(t, true, db)),
                 chi2_ratio = chi2(r.r, r.total, σ_tune(t, true, r.E_mean) ./ σ_tune(t, false, r.E_mean)),
                 chi2_nu_band = NaN, chi2_nubar_band = NaN, chi2_ratio_band = NaN))
end
out = DataFrame(rows)
out.ndf_nu .= nrow(dn); out.ndf_nubar .= nrow(db); out.ndf_ratio .= nrow(r)
CSV.write("results/chi2.csv", out)
CSV.write("results/ratio.csv", DataFrame(E = r.E_mean, data = r.r, err = r.total, reference = round.(rref, digits = 4), prior_1sigma = round.(rsd, digits = 4)))
show(stdout, out, allrows = true, allcols = true); println()