Use Python to compute neutrino oscillation probabilities in vacuum and matter at the speed of C!

We use the recently discovered Eigenvalue-Eigenvector and Adjugate Identities to compute oscillation probabilities with minimal algorithmic steps. Implemented using Cython to have the convenience of Python but the speed of C.

Installation

Pytrino is published on PyPI and condaforge.

Using pip

pip install pytrino

or

pip3 install pytrino

or

python -m pip install pytrino

Using conda

conda install pytrino

Building from source

Method one

python setup.py build
python setup.py install

Method two

python -m build

pip install dist/pytrino-[version-no].tar.gz

Build wheels

Usage

Imports

from pytrino import oscprobs

Define your oscillation parameters

baseline = 10 # baseline length L
energy = 2 * 1e-3 # neutrino beam energy E
delmsq31 = 2.5e-3 # mass squared difference 31 in vacuum
delmsq21 = 7.55e-5 # mass squared difference 21 in vacuum
deltacp = np.pi/6 # Dirac CP-violating phase in vacuum
theta13 = np.pi/20 # mixing angle in vacuum
theta12 = np.pi/6 # mixing angle in vacuum
theta23 = np.pi/4 # mixing angle in vacuum
V = 0 # matter (MSW) effect potential

Instantiate probability solver object

Probabilities via diagonalizing Hamiltonian in matter

probsolver = Eigen(baseline, energy, V, delmsq21, delmsq31, deltacp, theta12, theta13, theta23)

pip install pytrino

Probabilities via Cayley-Hamilton formalism
```Python
probsolver = CayleyHamilton(baseline, energy, V, delmsq21, delmsq31, deltacp, theta12, theta13, theta23)

Probabilities using Linear Algebra identities

probsolver = Identities(baseline, energy, 0, delmsq21, delmsq31, deltacp, theta12, theta13, theta23)

Compute probabilities

print(prob.mat_angles_phase()) # prints mixing angles and phase in matter
# (29.988882340423384, 84.48628984963665, 3.5930259417910695, 44.188561816129464)

print(prob.PMNS()) # prints values of PMNS matrix elements
"""
[[ 0.849+0.000e+00j -0.297+0.000e+00j -0.062-4.318e-01j]
 [-0.335+8.346e-02j -0.92 -2.921e-02j -0.184+1.342e-18j]
 [ 0.01 +3.989e-01j  0.214-1.396e-01j -0.881-7.870e-19j]]
"""

print(prob.PMNS() @ prob.PMNS().H) # unitarity check
"""
[[1.000e+00-1.696e-22j 0.000e+00+1.561e-17j 6.939e-18+5.551e-17j]
 [0.000e+00-1.561e-17j 1.000e+00-4.276e-19j 5.551e-17-1.327e-18j]
 [1.388e-17-4.857e-17j 5.551e-17+0.000e+00j 1.000e+00-8.097e-19j]]
"""

print(prob.probabilities()) # prints all 9 probabilities
"""
[[0.97  0.015 0.014]
 [0.014 0.236 0.75 ]
 [0.015 0.749 0.236]]
"""

Contributions

Please open a pull request if you have any improvements/changes that might benefit the package.

Please open an issue if there is any difficulty installing/using the package.

Contact me