r"""
Transformations in vacuum
=========================
Transitions of neutrino mass states :math:`\nu_i\to\nu_j` in vacuum
"""
from abc import abstractmethod, ABC
import numpy as np
from astropy import units as u
from astropy import constants as c
from snewpy.flavor import FlavorMatrix
from .base import ThreeFlavorTransformation, FourFlavorTransformation
from snewpy.neutrino import MassHierarchy
###############################################################################
# Vacuum transformations
###############################################################################
###############################################################################
[docs]
class NeutrinoDecay(VacuumTransformation, ThreeFlavorTransformation):
"""Decay effect, where the heaviest neutrino decays to the lightest
neutrino. For a description and typical parameters, see A. de Gouvêa et al.,
PRD 101:043013, 2020, arXiv:1910.01127.
"""
def __init__(self, mass=1*u.eV/c.c**2, tau=1*u.day, dist=10*u.kpc):
"""Initialize transformation matrix.
Parameters
----------
mass : astropy.units.quantity.Quantity
Mass of the heaviest neutrino; expect in eV/c^2.
tau : astropy.units.quantity.Quantity
Lifetime of the heaviest neutrino.
dist : astropy.units.quantity.Quantity
Distance to the supernova.
"""
self.m = mass
self.tau = tau
self.d = dist
super().__init__()
def gamma(self, E):
"""Decay width of the heaviest neutrino mass.
Parameters
----------
E : float
Energy of the nu3.
Returns
-------
Gamma : float
Decay width of the neutrino mass, in units of 1/length.
:meta private:
"""
return self.m*c.c / (E*self.tau)
def P_mm(self, t, E)->FlavorMatrix:
decay_factor = np.exp(-self.gamma(E)*self.d)
PND = FlavorMatrix.eye(self.mixing_params.basis_mass, extra_dims=E.shape)
if self.mixing_params.mass_order == MassHierarchy.NORMAL:
PND['NU_1','NU_3'] = 1 - decay_factor
PND['NU_3','NU_3'] = decay_factor
else:
PND['NU_2','NU_2'] = decay_factor
PND['NU_3','NU_2'] = 1 - decay_factor
PND['NU_BAR','NU_BAR'] = PND['NU','NU']
return PND
###############################################################################
[docs]
class QuantumDecoherence(VacuumTransformation, ThreeFlavorTransformation):
"""Quantum Decoherence, where propagation in vacuum leads to equipartition
of states. For a description and typical parameters, see M. V. dos Santos et al.,
2023, arXiv:2306.17591.
"""
def __init__(self, Gamma3=1e-27*u.eV, Gamma8=1e-27*u.eV, dist=10*u.kpc, n=0, E0=10*u.MeV):
"""Initialize transformation matrix.
Parameters
----------
Gamma3 : astropy.units.quantity.Quantity
Quantum decoherence parameter; expect in eV.
Gamma8 : astropy.units.quantity.Quantity
Quantum decoherence parameter; expect in eV.
dist : astropy.units.quantity.Quantity
Distance to the supernova.
n : float
Exponent of power law for energy dependent quantum decoherence parameters,
i.e. Gamma = Gamma0*(E/E0)**n. If not specified, it is taken as zero.
E0 : astropy.units.quantity.Quantity
Reference energy in the power law Gamma = Gamma0*(E/E0)**n. If not specified,
it is taken as 10 MeV. Note that if n = 0, quantum decoherence parameters are independent
of E0.
"""
self.Gamma3 = (Gamma3 / (c.hbar.to('eV s') * c.c)).to('1/kpc')
self.Gamma8 = (Gamma8 / (c.hbar.to('eV s') * c.c)).to('1/kpc')
self.d = dist
self.n = n
self.E0 = E0
super().__init__()
def P_mm(self, t, E)->FlavorMatrix:
PQD = FlavorMatrix.zeros(self.mixing_params.basis_mass, extra_dims=E.shape)
x = (E/self.E0)**self.n
PQD['NU_1','NU_1'] = 1/3 + 1/2 * np.exp(-(self.Gamma3 + self.Gamma8 / 3) * x * self.d) \
+ 1/6 * np.exp(-self.Gamma8 * x * self.d)
PQD['NU_1','NU_2'] = 1/3 - 1/2 * np.exp(-(self.Gamma3 + self.Gamma8 / 3) * x * self.d) \
+ 1/6 * np.exp(-self.Gamma8 * x * self.d)
PQD['NU_1','NU_3'] = 1/3 - 1/3 * np.exp(-self.Gamma8 * x * self.d)
PQD['NU_2',['NU_1','NU_2','NU_3']] = PQD['NU_1',['NU_2','NU_1','NU_3']]
PQD['NU_2','NU_2'] = PQD['NU_1','NU_1']
PQD['NU_2','NU_3'] = PQD['NU_1','NU_3']
PQD['NU_3','NU_1'] = PQD['NU_1','NU_3']
PQD['NU_3','NU_2'] = PQD['NU_2','NU_3']
PQD['NU_3','NU_3'] = 1/3 + 2/3 * np.exp(-self.Gamma8 * x * self.d)
PQD['NU_BAR','NU_BAR'] = PQD['NU','NU']
return PQD