import sys
sys.path.append('../src')
import numpy as np
import oscprob3nu
import hamiltonians3nu
from globaldefs import *
energy = 1.e9 # Neutrino energy [eV]
baseline = 1.3e3 # Baseline [km]
h_vacuum_energy_indep = \
hamiltonians3nu.hamiltonian_3nu_vacuum_energy_independent( S12_NO_BF,
S23_NO_BF,
S13_NO_BF,
DCP_NO_BF,
D21_NO_BF,
D31_NO_BF)
# Units of VCC_EARTH_CRUST: [eV]
h_matter = hamiltonians3nu.hamiltonian_3nu_matter(h_vacuum_energy_indep,
energy, VCC_EARTH_CRUST)
Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt = \
oscprob3nu.probabilities_3nu(h_matter, baseline*CONV_KM_TO_INV_EV)
print("Pee = %6.5f, Pem = %6.5f, Pet = %6.5f" % (Pee, Pem, Pet))
print("Pme = %6.5f, Pmm = %6.5f, Pmt = %6.5f" % (Pme, Pmm, Pmt))
print("Pte = %6.5f, Ptm = %6.5f, Ptt = %6.5f" % (Pte, Ptm, Ptt))
energy*1.e9,
VCC_EARTH_CRUST,
EPS_3)
label_case = r'NSI'
elif (case.lower() == 'liv'):
hamiltonian = hamiltonians3nu.hamiltonian_3nu_liv( \
h_vacuum_energy_independent,
energy*1.e9,
SXI12, SXI23, SXI13, DXICP,
B1, B2, B3, LAMBDA)
label_case = r'CPT-odd LIV'
# Each element of prob: [Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt]
prob = [oscprob3nu.probabilities_3nu( hamiltonian,
l*CONV_KM_TO_INV_EV) \
for l in l_val]
prob_ee = [x[0] for x in prob]
prob_em = [x[1] for x in prob]
prob_et = [x[2] for x in prob]
prob_me = [x[3] for x in prob]
prob_mm = [x[4] for x in prob]
prob_mt = [x[5] for x in prob]
prob_te = [x[6] for x in prob]
prob_tm = [x[7] for x in prob]
prob_tt = [x[8] for x in prob]
# Formatting
mpl.rcParams['xtick.labelsize'] = 26
mpl.rcParams['ytick.labelsize'] = 26
mpl.rcParams['legend.fontsize'] = 26
sys.path.append('../src')
import numpy as np
import oscprob3nu
import hamiltonians3nu
from globaldefs import *
energy = 1.e9 # Neutrino energy [eV]
baseline = 1.3e3 # Baseline [km]
h_vacuum_energy_indep = \
hamiltonians3nu.hamiltonian_3nu_vacuum_energy_independent( S12_NO_BF,
S23_NO_BF,
S13_NO_BF,
DCP_NO_BF,
D21_NO_BF,
D31_NO_BF)
# EPS_3 is the 3x3 matrix of NSI strength parameters, read from
# globaldefs; see that file to find the values
h_nsi = hamiltonians3nu.hamiltonian_3nu_nsi(h_vacuum_energy_indep, energy,
VCC_EARTH_CRUST, EPS_3)
Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt = \
oscprob3nu.probabilities_3nu(h_nsi, baseline*CONV_KM_TO_INV_EV)
print("Pee = %6.5f, Pem = %6.5f, Pet = %6.5f" % (Pee, Pem, Pet))
print("Pme = %6.5f, Pmm = %6.5f, Pmt = %6.5f" % (Pme, Pmm, Pmt))
print("Pte = %6.5f, Ptm = %6.5f, Ptt = %6.5f" % (Pte, Ptm, Ptt))
sys.path.append('../src')
import numpy as np
import oscprob3nu
import hamiltonians3nu
from globaldefs import *
energy = 1.e9 # Neutrino energy [eV]
baseline = 1.3e3 # Baseline [km]
# Use the NuFit 4.0 best-fit values of the mixing parameters pulled from
# globaldefs. NO means "normal ordering"; change NO to IO if you want
# to use inverted ordering.
h_vacuum_energy_indep = \
hamiltonians3nu.hamiltonian_3nu_vacuum_energy_independent( S12_NO_BF,
S23_NO_BF,
S13_NO_BF,
DCP_NO_BF,
D21_NO_BF,
D31_NO_BF)
h_vacuum = np.multiply(1./energy, h_vacuum_energy_indep)
# CONV_KM_TO_INV_EV is pulled from globaldefs; it converts km to eV^{-1}
Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt = \
oscprob3nu.probabilities_3nu( h_vacuum, baseline*CONV_KM_TO_INV_EV)
print("Pee = %6.5f, Pem = %6.5f, Pet = %6.5f" % (Pee, Pem, Pet))
print("Pme = %6.5f, Pmm = %6.5f, Pmt = %6.5f" % (Pme, Pmm, Pmt))
print("Pte = %6.5f, Ptm = %6.5f, Ptt = %6.5f" % (Pte, Ptm, Ptt))
def plot_probability_3nu_vs_energy_compare(output_format='pdf',
output_path='./fig/'):
r"""Generates and saves a plot of 3nu probabilities vs. energy.
Generates and saves a plot of three-neutrino probabilities vs.
energy for oscillations in vacuum, matter, with NSI, and with
CPT-odd LIV. This is the same plot that is included in the paper.
Parameters
----------
output_format : str, optional
File extension of the plot to save (e.g., 'pdf', 'png', 'jpg').
output_path : str, optional
File path where to save the plot.
Returns
-------
None
The plot is generated and saved.
"""
# Baseline (DUNE)
l = 1.3e3 * CONV_KM_TO_INV_EV # [eV^{-1}]
# Neutrino energies
log10_energy_nu_min = log10(5.e-1) # [GeV]
log10_energy_nu_max = log10(3.e1) # [GeV]
log10_energy_nu_npts = 400
log10_energy_nu = np.linspace(log10_energy_nu_min, log10_energy_nu_max,
log10_energy_nu_npts)
energy_nu = [10.**x for x in log10_energy_nu] # [GeV]
# Plot formatting
mpl.rcParams['xtick.labelsize'] = 28
mpl.rcParams['ytick.labelsize'] = 28
mpl.rcParams['legend.fontsize'] = 21
mpl.rcParams['legend.borderpad'] = 0.4
mpl.rcParams['axes.labelpad'] = 10
mpl.rcParams['ps.fonttype'] = 42
mpl.rcParams['pdf.fonttype'] = 42
fig, axes = plt.subplots(3, 1, figsize=[8, 15])
fig.subplots_adjust(hspace=0.05, wspace=0.05)
h_vacuum_energy_indep = \
hamiltonians3nu.hamiltonian_3nu_vacuum_energy_independent( S12_NO_BF,
S23_NO_BF,
S13_NO_BF,
DCP_NO_BF,
D21_NO_BF,
D31_NO_BF)
prob_vacuum = [oscprob3nu.probabilities_3nu( \
np.multiply(1./x/1.e9, h_vacuum_energy_indep), l) \
for x in energy_nu]
# Uncomment to compare to the probability computed with the standard
# ocillation formula in vacuum
# U = hamiltonians3nu.pmns_mixing_matrix( S12_NO_BF,
# S23_NO_BF,
# S13_NO_BF,
# DCP_NO_BF)
# prob_vacuum_std = [hamiltonians3nu.probabilities_3nu_vacuum_std( \
# U, D21_BF, D31_BF, x, l/CONV_KM_TO_INV_EV) \
# for x in energy_nu]
prob_matter = [oscprob3nu.probabilities_3nu( \
hamiltonians3nu.hamiltonian_3nu_matter( \
h_vacuum_energy_indep, x*1.e9, VCC_EARTH_CRUST), l)
for x in energy_nu]
# eps = eps_ee, eps_em, eps_et, eps_mm, eps_mt, eps_tt
prob_nsi = [oscprob3nu.probabilities_3nu( \
hamiltonians3nu.hamiltonian_3nu_nsi( \
h_vacuum_energy_indep, x*1.e9, VCC_EARTH_CRUST, EPS_3),
l)
for x in energy_nu]
prob_liv = [oscprob3nu.probabilities_3nu( \
hamiltonians3nu.hamiltonian_3nu_liv( \
h_vacuum_energy_indep, x*1.e9, SXI12, SXI23, SXI13,
DXICP, B1, B2, B3, LAMBDA), l)
for x in energy_nu]
# Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt
for i, ax in enumerate(np.array(axes).reshape((1, 3))[0]):
if (i == 0): # Pee
p_vacuum = [x[0] for x in prob_vacuum]
# p_vacuum_std = [x[0] for x in prob_vacuum_std]
p_matter = [x[0] for x in prob_matter]
p_nsi = [x[0] for x in prob_nsi]
p_liv = [x[0] for x in prob_liv]
ylabel = r'$P_{\nu_e \to \nu_e}$'
elif (i == 1): # Pme
p_vacuum = [x[3] for x in prob_vacuum]
# p_vacuum_std = [x[3] for x in prob_vacuum_std]
p_matter = [x[3] for x in prob_matter]
p_nsi = [x[3] for x in prob_nsi]
p_liv = [x[3] for x in prob_liv]
ylabel = r'$P_{\nu_\mu \to \nu_e}$'
elif (i == 2): # Pmm
p_vacuum = [x[4] for x in prob_vacuum]
# p_vacuum_std = [x[4] for x in prob_vacuum_std]
p_matter = [x[4] for x in prob_matter]
p_nsi = [x[4] for x in prob_nsi]
p_liv = [x[4] for x in prob_liv]
ylabel = r'$P_{\nu_\mu \to \nu_\mu}$'
ax.set_xlabel(r'Neutrino energy [GeV]', fontsize=27)
ax.set_ylabel(ylabel, fontsize=27)
ax.plot(energy_nu,
p_vacuum,
color='C0',
ls='-',
lw=3.0,
zorder=1,
label=r'Vacuum')
# ax.plot(energy_nu, p_vacuum_std, color='k', ls='-', lw=3.0, zorder=1,
# label=r'Vacuum std.')
ax.plot(energy_nu,
p_matter,
color='C1',
ls='--',
lw=3.0,
zorder=1,
label=r'Matter')
ax.plot(energy_nu,
p_nsi,
color='C2',
ls=':',
lw=3.0,
zorder=1,
label=r'NSI')
ax.plot(energy_nu,
p_liv,
color='C3',
ls='-.',
lw=3.0,
zorder=1,
label=r'CPT-odd LIV')
ax.tick_params('both', length=10, width=2, which='major')
ax.tick_params('both', length=5, width=1, which='minor')
ax.tick_params(axis='both', which='major', pad=10, direction='in')
ax.tick_params(axis='both', which='minor', pad=10, direction='in')
ax.tick_params(axis='x', which='minor', bottom=True)
ax.tick_params(axis='x', which='minor', top=True)
ax.tick_params(axis='y', which='minor', left=True)
ax.tick_params(axis='y', which='minor', right=True)
ax.tick_params(bottom=True, top=True, left=True, right=True)
ax.set_xlim([10.**log10_energy_nu_min, 10.**log10_energy_nu_max])
ax.set_xscale('log')
if (i == 0):
ax.set_xticklabels([])
ax_yticks_major = np.array([0.85, 0.90, 0.95, 1.00])
ax.set_yticks(ax_yticks_major, minor=False)
ax_yticks_minor = np.array([
0.86, 0.87, 0.88, 0.89, 0.91, 0.92, 0.93, 0.94, 0.96, 0.97,
0.98, 0.99
])
ax.set_yticks(ax_yticks_minor, minor=True)
ax.set_ylim([0.85, 1.00])
ax.legend(loc='lower right',
ncol=1,
frameon=False,
columnspacing=1.)
elif (i == 1):
ax.set_xticklabels([])
ax_yticks_major = np.array([0.00, 0.05, 0.10])
ax.set_yticks(ax_yticks_major, minor=False)
ax_yticks_minor = np.array(
[0.01, 0.02, 0.03, 0.04, 0.06, 0.07, 0.08, 0.09, 0.11, 0.12])
ax.set_yticks(ax_yticks_minor, minor=True)
ax.set_ylim([0.00, 0.12])
elif (i == 2):
ax_yticks_major = np.array([0.00, 0.25, 0.50, 0.75])
ax.set_yticks(ax_yticks_major, minor=False)
ax_yticks_minor = np.array([
0.05, 0.10, 0.15, 0.20, 0.30, 0.35, 0.40, 0.45, 0.55, 0.60,
0.65, 0.70, 0.80, 0.85, 0.90, 0.95
])
ax.set_yticks(ax_yticks_minor, minor=True)
ax.set_ylim([0.0, 1.0])
pylab.savefig(output_path + 'prob_3nu_vs_energy_compare.' +
output_format,
bbox_inches='tight',
dpi=300)
return
a fast general-purpose computation method for two and three neutrino
flavors", arXiv:1904.XXXXX.
Created: 2019/04/29 23:22
Last modified: 2019/04/29 23:22
"""
from __future__ import print_function
__version__ = "1.0"
__author__ = "Mauricio Bustamante"
__email__ = "*****@*****.**"
import sys
sys.path.append('../src')
import oscprob3nu
hamiltonian = [[1.0 + 0.0j, 0.0 + 2.0j, 0.0 - 1.0j],
[0.0 - 2.0j, 3.0 + 0.0j, 3.0 + 0.0j],
[0.0 + 1.0j, 3.0 - 0.0j, 5.0 + 0.0j]]
L = 1.0
Pee, Pem, Pet, Pme, Pmm, Pmt, Pte, Ptm, Ptt = \
oscprob3nu.probabilities_3nu(hamiltonian, L)
print("Pee = %6.5f, Pem = %6.5f, Pet = %6.5f" % (Pee, Pem, Pet))
print("Pme = %6.5f, Pmm = %6.5f, Pmt = %6.5f" % (Pme, Pmm, Pmt))
print("Pte = %6.5f, Ptm = %6.5f, Ptt = %6.5f" % (Pte, Ptm, Ptt))