First measurement of inclusive muon neutrino charged current differential cross sections on argon at E_ν ~ 0.8 GeV with the MicroBooNE detector (energy-dependent σ)

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# MicroBooNE νμ CC inclusive σ(Eν) on argon, 0.2–4 GeV (PRL 128, 151801 (2022); HEPData ins1954078 / arXiv ancillary
# files: unfolded σ, covariance and the additional smearing matrix A_c, in data/), compared with the cross sections of
# Newtrinos.jl (module `xsec`): the GENIE tunes (`generator_sigma`, ⁴⁰Ar per nucleon) and the reference model of
# `CorrelatedXsec` with its prior 1σ band. Following the paper, each model is averaged in the true-energy bins with the
# nominal BNB νμ flux at MicroBooNE (data/flux_bnb_numu_uboone.csv, from arXiv:1905.09694) and smeared with A_c
# (σ_smeared = A_c σ_model) before it is compared with the data. The paper's "GENIE v3.00.06" is G18_10a_02_11a, the
# reference tune here, which tests the chain against the paper's own curve (digitised, data/models_smeared_digitized.csv)
# and χ² (18.8 for 10 bins).
# 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, LinearAlgebra

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

readc(f) = CSV.read(f, DataFrame; comment = "#")
D = readc("data/sigma.csv")
C = Matrix{Float64}(CSV.read("data/covariance.csv", DataFrame; comment = "#", header = false))
Ac = Matrix{Float64}(CSV.read("data/Ac.csv", DataFrame; comment = "#", header = false))
paper = readc("data/models_smeared_digitized.csv")
flux = readc("data/flux_bnb_numu_uboone.csv")
edges = vcat(D.E_lo, D.E_hi[end])

# flux-weighted bin average ∫Φσ dE / ∫Φ dE on a fine grid (flux constant within its 50 MeV bins)
Ef = collect(range(0.2, 4.0, length = 3801))
Φ = [flux.flux[clamp(searchsortedlast(flux.E_lo, e), 1, nrow(flux))] for e in Ef]
binidx = [clamp(searchsortedlast(edges, e), 1, nrow(D)) for e in Ef]
fluxavg(σ) = [sum(Φ[binidx .== j] .* σ[binidx .== j]) / sum(Φ[binidx .== j]) for j in 1:nrow(D)]
@printf("flux-weighted bin centres: %s (paper %s)\n", round.(fluxavg(Ef), digits = 3), D.E_center)

tab = X.load_table()
at(v, e) = X.at_energies(tab.E, v, e)
TUNES = Symbol.(sort(tab.tunes))
σ_tune(t, e) = at(sum(X.generator_sigma(t, :Ar, :numu, false, :CC)), e) .* e     # σ per nucleon (σ/E × E)

xs = X.configure(X.CorrelatedXsec())
ref = xs.cfg.reference
sigf = xs.sigma(Ef; flavour = :numu, anti = false, current = :CC, target = :Ar)
model(p) = Ac * fluxavg(sigf(p) .* Ef)
rng = MersenneTwister(1)
draw() = map(p -> p isa Distribution ? rand(rng, p) : p, xs.priors)
samples = [draw() for _ in 1:500]
p0 = xs.params
M = reduce(hcat, [model(p) for p in samples])
Ccov = cov(M, dims = 2)

chi2(m, Cm = C) = (r = D.sigma .- m; dot(r, Cm \ r))
rows = [(model = "$(ref) (nominal)", chi2 = chi2(model(p0)), chi2_with_prior = chi2(model(p0), C + Ccov))]
smeared = Dict(t => Ac * fluxavg(σ_tune(t, Ef)) for t in TUNES)
for t in TUNES
    push!(rows, (model = string(t), chi2 = chi2(smeared[t]), chi2_with_prior = NaN))
end
for c in names(paper)[4:end]
    push!(rows, (model = "paper: $(c) (digitised)", chi2 = chi2(paper[!, c]), chi2_with_prior = NaN))
end
out = DataFrame(rows); out.ndf .= nrow(D)
CSV.write("results/chi2.csv", out)
CSV.write("results/smeared.csv", DataFrame(E_lo = D.E_lo, E_hi = D.E_hi, data = D.sigma, err = D.err,
                                           reference = round.(model(p0), digits = 4), prior_1sigma = round.(sqrt.(diag(Ccov)), digits = 4),
                                           paper_GENIE_v3 = paper[!, "GENIE_v3.00.06"]))
show(stdout, out, allrows = true, allcols = true); println()

# figure: σ/⟨E⟩ per bin as in the paper (data, smeared models)
Ec = D.E_center
fig = Figure(size = (820, 500))
ax = Axis(fig[1, 1], xlabel = "E_ν (GeV)", ylabel = "σ / ⟨E_ν⟩ (10⁻³⁸ cm²/GeV per nucleon)", limits = (0.2, 4.0, 0.3, 1.45),
          title = "MicroBooNE νμ CC inclusive on argon (models A_c-smeared)")
stairs_ = (y) -> (vcat(edges[1], repeat(edges[2:end-1], inner = 2), edges[end]), repeat(y, inner = 2))
lo, hi = [quantile(r, 0.16) for r in eachrow(M)], [quantile(r, 0.84) for r in eachrow(M)]
band!(ax, stairs_(lo ./ Ec)[1], stairs_(lo ./ Ec)[2], stairs_(hi ./ Ec)[2], color = (:dodgerblue, 0.25), label = "CorrelatedXsec prior 1σ")
for (i, t) in enumerate(TUNES)
    lines!(ax, stairs_(smeared[t] ./ Ec)..., color = (Makie.wong_colors()[mod1(i, 7)], 0.8), linewidth = 1, label = "GENIE $(t)")
end
lines!(ax, stairs_(model(p0) ./ Ec)..., color = :dodgerblue, linewidth = 2.5, label = "nominal ($(ref))")
scatter!(ax, Ec, paper[!, "GENIE_v3.00.06"] ./ Ec, marker = :xcross, color = :red, markersize = 10, label = "paper: GENIE v3 (G18_10a_02_11a)")
errorbars!(ax, Ec, D.sigma ./ Ec, D.err ./ Ec, color = :black, whiskerwidth = 4)
scatter!(ax, Ec, D.sigma ./ Ec, color = :black, label = "MicroBooNE")
Legend(fig[1, 2], ax, framevisible = false, labelsize = 9)
save("ours/sigma_enu.png", fig)