nufast

Fast and accurate three-flavor neutrino oscillation probabilities in vacuum and matter.

Rust port of NuFast by Peter Denton.

Features

Vacuum oscillations: Full 3-flavor PMNS oscillation probabilities
Matter effects (MSW): Constant-density matter with arbitrary electron fraction
CP violation: Full δ_CP phase support
Newton refinement: Optional iterative improvement for matter eigenvalues
Zero dependencies: Pure Rust, no external crates required
Fast: Optimized for batch calculations

Installation

[dependencies]
nufast = "0.2"

Quick Start

use nufast::{VacuumParameters, MatterParameters, probability_vacuum_lbl, probability_matter_lbl};
use std::f64::consts::PI;

// Vacuum oscillation example (T2K-like)
let vacuum = VacuumParameters {
    s12sq: 0.307,      // sin²θ₁₂
    s13sq: 0.0218,     // sin²θ₁₃
    s23sq: 0.545,      // sin²θ₂₃
    delta: 1.36 * PI,  // δ_CP in radians
    Dmsq21: 7.42e-5,   // Δm²₂₁ in eV²
    Dmsq31: 2.517e-3,  // Δm²₃₁ in eV² (normal ordering)
    L: 295.0,          // baseline in km
    E: 0.6,            // energy in GeV
};

let probs = probability_vacuum_lbl(&vacuum);
println!("P(νμ → νe) = {:.4}", probs[1][0]);

// Matter oscillation example (DUNE-like)
let matter = MatterParameters {
    s12sq: 0.307,
    s13sq: 0.0218,
    s23sq: 0.545,
    delta: 1.36 * PI,
    Dmsq21: 7.42e-5,
    Dmsq31: 2.517e-3,
    L: 1300.0,         // km
    E: 2.5,            // GeV
    rho: 2.848,        // matter density in g/cm³
    Ye: 0.5,           // electron fraction
    N_Newton: 0,       // Newton iterations (0 = DMP approximation)
};

let probs = probability_matter_lbl(&matter);
println!("P(νμ → νe) in matter = {:.4}", probs[1][0]);

Probability Matrix

The returned [[f64; 3]; 3] matrix is indexed as probs[α][β] = P(ν_α → ν_β):

	e (0)	μ (1)	τ (2)
e	P_ee	P_eμ	P_eτ
μ	P_μe	P_μμ	P_μτ
τ	P_τe	P_τμ	P_ττ

Physics Notes

NuFit 5.2 Best-Fit Values (2022)

// Normal Ordering
let s12sq = 0.307;      // sin²θ₁₂
let s13sq = 0.0218;     // sin²θ₁₃  
let s23sq = 0.545;      // sin²θ₂₃
let delta = 1.36 * PI;  // δ_CP
let Dmsq21 = 7.42e-5;   // eV²
let Dmsq31 = 2.517e-3;  // eV² (positive for NO)

// Inverted Ordering: use Dmsq31 = -2.498e-3 eV²

Matter Effect

The MSW (Mikheyev-Smirnov-Wolfenstein) effect modifies oscillation probabilities in matter. The N_Newton parameter controls accuracy:

N_Newton = 0: DMP approximation (fast, ~0.1% accuracy)
N_Newton = 1: One Newton iteration (~0.01% accuracy)
N_Newton ≥ 2: Machine precision

Antineutrinos

For antineutrinos, flip the sign of δ_CP:

let delta_antinu = -delta;

Performance

Benchmarked on AMD Ryzen 9 5900X:

Vacuum: ~15 ns per calculation
Matter (N_Newton=0): ~25 ns per calculation
Matter (N_Newton=1): ~30 ns per calculation

References

P.B. Denton, NuFast: Fast and Accurate Neutrino Oscillation Probabilities
P.B. Denton, H. Minakata, S.J. Parke, "Compact Perturbative Expressions for Neutrino Oscillations in Matter" (2016)
NuFit 5.2 (2022): http://www.nu-fit.org

License

MIT License - see LICENSE for details.

nufast 0.2.0