Neutrino Interferometry - nu-waves

What is it?

Neutrino Interferometry, or nu_waves, is a simple Python library that calculate flavor oscillation of neutrinos. You can input your own parameters and get the oscillation probabilities.

How to install?

pip install nu-waves

Features

• Embedded GPU acceleration (MPS, CUDA)
• Oscillation framework with N neutrinos
• Vacuum oscillations
• Custom smearing function (L and E)
• Constant matter MSW
• Multi-layer matter MSW
• Earth model (PREM) with cosz
• Adiabatic transitions

Oscillation convention

The active three-flavor PMNS matrix uses the PDG convention, U_e3 = sin(theta13) * exp(-1j * deltaCP). The evolution operator stores S[energy, detected, emitted], while public probabilities retain the order P[energy, emitted, detected] = abs(S[energy, detected, emitted])**2 (singleton axes may be squeezed). Antineutrinos conjugate the mixing matrix and reverse the matter potential. Matter layers are ordered from source to detector.

The CP convention correction changes predictions from earlier implementations that transposed transition amplitudes. Remove any external phase-sign or channel-swap workarounds when adopting this correction, and regenerate affected predictions. The notebook notebooks/04_vacuum_executor_benchmarks.ipynb checks an independent PDG amplitude before benchmarking; tests/TestPdgConvention.py also covers matter, antineutrinos, layer ordering and decoherence.

Some nice pictures

Examples

2 flavors oscillation in vacuum

import numpy as np
import matplotlib.pyplot as plt
from nu_waves.models.mixing import Mixing
from nu_waves.models.spectrum import Spectrum
from nu_waves.propagation.oscillator import Oscillator
from nu_waves.hamiltonian import vacuum
from nu_waves.utils import flavors

# sterile test
osc_amplitude = 0.1  # sin^2(2\theta)
angles = {(1, 2): np.arcsin(np.sqrt(osc_amplitude)) / 2}
dm2={(2, 1): 1}

mixing = Mixing(n_neutrinos=2, mixing_angles=angles)
spectrum = Spectrum(n_neutrinos=2, m_lightest=0., dm2={(2, 1): 1})
H = vacuum.Hamiltonian(
    mixing=mixing,
    spectrum=spectrum,
    antineutrino=False
)

# oscillator object that calculates the oscillation probability
osc = Oscillator(hamiltonian=H)

# get the oscillation probabilities
E_fixed = 3E-3
L_min, L_max = 1e-3, 20e-3
L_list = np.linspace(L_min, L_max, 200)
print(L_list)
P = osc.probability(
    L_km=L_list, E_GeV=E_fixed,
    flavor_emit=flavors.electron,
    flavor_det=flavors.electron  # muon could be sterile
)

# draw it
plt.figure(figsize=(6.5, 4.0))

plt.plot(L_list * 1000, P, label=r"$P_{e e}$ disappearance", lw=2)
plt.plot(L_list * 1000, [1] * len(L_list), "--", label="Total probability", lw=1.5)

plt.xlabel(r"$L_\nu$ [m]")
plt.ylabel(r"Probability")
plt.title(f"eV$^2$ sterile with $E_\\nu$ = {E_fixed * 1000} MeV")
# plt.xlim(L_min, L_max)
plt.ylim(0, 1.05)
plt.legend()
plt.tight_layout()
plt.show()