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.
pip install pytrinofrom pytrino import oscprobsbaseline = 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 potentialProbabilities 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)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]]
"""