NuOscProbExact: a fast, general-purpose code to compute exact two-, three-, and four-flavor neutrino oscillation probabilities

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# Newtrinos.jl oscillation probabilities (module `osc`: three flavours in vacuum and matter, 3+1 sterile through the
# Earth) compared with NuOscProbExact (M. Bustamante, arXiv:1904.12391), an exact solver for arbitrary Hamiltonians.
# The NuOscProbExact reference values are produced by data/nuoscprobexact_reference.py (pip install nuoscprobexact).
# 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, StructArrays, ArraysOfArrays

cd(@__DIR__); mkpath("ours"); mkpath("results")
pj = CSV.read("data/ref_parameters.csv", DataFrame)[1, :]
p3 = (θ₁₂ = asin(pj["s12"]), θ₁₃ = asin(pj["s13"]), θ₂₃ = asin(pj["s23"]), δCP = pj["dcp"], Δm²₂₁ = pj["d21"], Δm²₃₁ = pj["d31"])
p4 = (; p3..., Δm²₄₁ = pj["d41"], θ₁₄ = asin(pj["s14"]), θ₂₄ = asin(pj["s24"]), θ₃₄ = asin(pj["s34"]))

# ---------------- (1) three flavours, L = 1300 km: vacuum and constant density ρ = 3 g/cm³, Yₑ = 0.5 ----------------
ref = CSV.read("data/ref_3nu_1300km.csv", DataFrame)
E = ref.E_GeV
vac = Newtrinos.osc.configure(Newtrinos.osc.OscillationConfig())
mat = Newtrinos.osc.configure(Newtrinos.osc.OscillationConfig(interaction = Newtrinos.osc.SI()))
crust = StructArray{Newtrinos.Layer}(([7000.0], [1.5], [1.5]))
path = VectorOfVectors{Newtrinos.Path}([StructArray{Newtrinos.Path}(([1300.0], [1]))])
P = (vacuum = vac.osc_prob(E, [1300.0], p3)[:, 1, :, :], matter = mat.osc_prob(E, path, crust, p3)[:, 1, :, :])
CH = [("Pee", 1, 1), ("Pem", 1, 2), ("Pet", 1, 3), ("Pme", 2, 1), ("Pmm", 2, 2), ("Pmt", 2, 3), ("Pte", 3, 1), ("Ptm", 3, 2), ("Ptt", 3, 3)]
rows = [(case = String(c), channel = n, max_abs_diff = maximum(abs.(P[c][:, a, b] .- ref[!, "$(c)_$n"]))) for c in (:vacuum, :matter) for (n, a, b) in CH]

fig = Figure(size = (720, 980))
for (k, (n, a, b, lab)) in enumerate((("Pee", 1, 1, "P(νe → νe)"), ("Pme", 2, 1, "P(νμ → νe)"), ("Pmm", 2, 2, "P(νμ → νμ)")))
    ax = Axis(fig[2k - 1, 1], xscale = log10, ylabel = lab, xticklabelsvisible = false, limits = (0.5, 30, nothing, nothing))
    for (c, col, lb) in ((:vacuum, :dodgerblue, "vacuum"), (:matter, :darkorange, "matter"))
        lines!(ax, E, P[c][:, a, b], color = col, linewidth = 2.5, label = "Newtrinos, $lb")
        lines!(ax, E, ref[!, "$(c)_$n"], color = :black, linestyle = :dash, linewidth = 1, label = c == :vacuum ? "NuOscProbExact" : nothing)
    end
    k == 1 && axislegend(ax, position = :rb, framevisible = false, labelsize = 11)
    axd = Axis(fig[2k, 1], xscale = log10, yscale = log10, ylabel = "|ΔP|", limits = (0.5, 30, 1e-17, 1e-11),
               xlabel = k == 3 ? "E_ν (GeV)" : "", xticklabelsvisible = k == 3, yticks = LogTicks(-17:2:-11))
    for (c, col) in ((:vacuum, :dodgerblue), (:matter, :darkorange))
        lines!(axd, E, max.(abs.(P[c][:, a, b] .- ref[!, "$(c)_$n"]), 1e-17), color = col)
    end
    rowsize!(fig.layout, 2k, Relative(0.1))
end
save("ours/fig_prob_3nu_vs_energy.png", fig)

# ---------------- (2) 3+1: ν̄μ survival through the Earth (default four-zone Newtrinos Earth) ----------------
ref4 = CSV.read("data/ref_3p1_earth_numubar.csv", DataFrame)
CZ, E4 = unique(ref4.cz), unique(ref4.E_GeV)
Pref = permutedims(reshape(ref4.Pmm_bar, length(E4), length(CZ)))          # [cz, E]
earth = Newtrinos.earth_layers.configure()
layers = earth.compute_layers()
ster = Newtrinos.osc.configure(Newtrinos.osc.OscillationConfig(flavour = Newtrinos.osc.Sterile(), interaction = Newtrinos.osc.SI()))
Pn = permutedims(ster.osc_prob(E4, earth.compute_paths(CZ, layers), layers, p4; anti = true)[:, :, 2, 2])   # [cz, E]
push!(rows, (case = "3+1 Earth", channel = "P(ν̄μ → ν̄μ)", max_abs_diff = maximum(abs.(Pn .- Pref))))

fig = Figure(size = (1100, 470))
ax = Axis(fig[1, 1], yscale = log10, xlabel = "cos θ_z", ylabel = "antineutrino energy (TeV)",
          title = "Newtrinos: P(ν̄μ → ν̄μ), 3+1, Δm²₄₁ = 1 eV², sin²θ₁₄ = sin²θ₂₄ = 0.1")
hm = heatmap!(ax, CZ, E4 ./ 1e3, Pn, colormap = :viridis, colorrange = (0, 1))
Colorbar(fig[1, 2], hm)
ax2 = Axis(fig[1, 3], yscale = log10, xlabel = "cos θ_z", title = "|Newtrinos − NuOscProbExact|")
hm2 = heatmap!(ax2, CZ, E4 ./ 1e3, log10.(max.(abs.(Pn .- Pref), 1e-17)), colormap = :magma, colorrange = (-16, -10))
Colorbar(fig[1, 4], hm2, label = "log₁₀ |ΔP|")
save("ours/fig_sterile_earth.png", fig)

tab = DataFrame(rows)
CSV.write("results/max_abs_differences.csv", tab)
show(stdout, tab, allrows = true); println()