# non-resonant leptogenesis with three decaying sterile neutrino using the density matrix equations. Equations from 1112.4528 including the scattering term from 0401240 and effect of right-handed tau participation in kinetic equations.
import ulysses
import numpy as np
from odeintw import odeintw
from numba import jit
@jit
def fast_RHS(y0,eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me,eps3tt,eps3mm,eps3ee,eps3tm,eps3te,eps3me, C, W, d1,d2,d3,w1,w2,w3,n1eq,n2eq,n3eq):
N1, N2, N3, Ntt, Nmm, Nee, Ntm, Nte, Nme, Ntr = y0
c1t,c1m,c1e,c2t,c2m,c2e,c3t,c3m,c3e = C
widtht,widthm = W
c1tc = np.conjugate(c1t)
c1mc = np.conjugate(c1m)
c1ec = np.conjugate(c1e)
c2tc = np.conjugate(c2t)
c2mc = np.conjugate(c2m)
c2ec = np.conjugate(c2e)
c3tc = np.conjugate(c3t)
c3mc = np.conjugate(c3m)
c3ec = np.conjugate(c3e)
#define the different RHSs for each equation
rhs1 = - d1 * (N1-n1eq)
rhs2 = - d2 * (N2-n2eq)
rhs3 = - d3 * (N3-n3eq)
rhs4 = (eps1tt * d1 * (N1-n1eq) + eps2tt * d2 * (N2-n2eq) + eps3tt * d3 * (N3-n3eq)
- 0.5 * w1 * (2 * c1t * c1tc * Ntt + c1m * c1tc * Ntm + c1e * c1tc * Nte + np.conjugate(c1m * c1tc * Ntm + c1e * c1tc * Nte))
- 0.5 * w2 * (2 * c2t * c2tc * Ntt + c2m * c2tc * Ntm + c2e * c2tc * Nte + np.conjugate(c2m * c2tc * Ntm + c2e * c2tc * Nte))
- 0.5 * w3 * (2 * c3t * c3tc * Ntt + c3m * c3tc * Ntm + c3e * c3tc * Nte + np.conjugate(c3m * c3tc * Ntm + c3e * c3tc * Nte))
- 2 * widtht * Ntt + 4 * widtht * Ntr)
rhs5 = (eps1mm * d1 * (N1-n1eq) + eps2mm * d2 * (N2-n2eq) + eps3mm * d3 * (N3-n3eq)
- 0.5 * w1 * (2 * c1m * c1mc * Nmm + c1m * c1tc * Ntm + c1e * c1mc * Nme + np.conjugate(c1m * c1tc * Ntm + c1e * c1mc * Nme))
- 0.5 * w2 * (2 * c2m * c2mc * Nmm + c2m * c2tc * Ntm + c2e * c2mc * Nme + np.conjugate(c2m * c2tc * Ntm + c2e * c2mc * Nme))
- 0.5 * w3 * (2 * c3m * c3mc * Nmm + c3m * c3tc * Ntm + c3e * c3mc * Nme + np.conjugate(c3m * c3tc * Ntm + c3e * c3mc * Nme)))
rhs6 = (eps1ee * d1 * (N1-n1eq) + eps2ee * d2 * (N2-n2eq) + eps3ee * d3 * (N3-n3eq)
- 0.5 * w1 * (2 * c1e * c1ec * Nee + c1e * c1mc * Nme + c1e * c1tc * Nte + np.conjugate(c1e * c1mc * Nme + c1e * c1tc * Nte))
- 0.5 * w2 * (2 * c2e * c2ec * Nee + c2e * c2mc * Nme + c2e * c2tc * Nte + np.conjugate(c2e * c2mc * Nme + c2e * c2tc * Nte))
- 0.5 * w3 * (2 * c3e * c3ec * Nee + c3e * c3mc * Nme + c3e * c3tc * Nte + np.conjugate(c3e * c3mc * Nme + c3e * c3tc * Nte)))
rhs7 = (eps1tm * d1 * (N1-n1eq) + eps2tm * d2 * (N2-n2eq) + eps3tm * d3 * (N3-n3eq)
- 0.5 * ((w1 * c1t * c1mc + w2 * c2t * c2mc + w3 * c3t * c3mc) * Nmm
+ (w1 * c1e * c1mc + w2 * c2e * c2mc + w3 * c3e * c3mc) * Nte
+ (w1 * c1m * c1mc + w2 * c2m * c2mc + w3 * c3m * c3mc) * Ntm
+ (w1 * c1mc * c1t + w2 * c2mc * c2t + w3 * c3mc * c3t) * Ntt
+ (w1 * c1t * c1tc + w2 * c2t * c2tc + w3 * c3t * c3tc + 2 * widtht + 2 * widthm) * Ntm
+ (w1 * c1t * c1ec + w2 * c2t * c2ec + w3 * c3t * c3ec) * np.conjugate(Nme)))
rhs8 = (eps1te * d1 * (N1-n1eq) + eps2te * d2 * (N2-n2eq) + eps3te * d3 * (N3-n3eq)
- 0.5 * ((w1 * c1t * c1ec + w2 * c2t * c2ec + w3 * c3t * c3ec) * Nee
+ (w1 * c1e * c1ec + w2 * c2e * c2ec + w3 * c3e * c3ec) * Nte
+ (w1 * c1m * c1ec + w2 * c2m * c2ec + w3 * c3m * c3ec) * Ntm
+ (w1 * c1t * c1ec + w2 * c2t * c2ec + w3 * c3t * c3ec) * Ntt
+ (w1 * c1t * c1mc + w2 * c2t * c2mc + w3 * c3t * c3mc) * Nme
+ (w1 * c1t * c1tc + w2 * c2t * c2tc + w3 * c3t * c3tc + 2 * widtht) * Nte))
rhs9 = (eps1me * d1 * (N1-n1eq) + eps2me * d2 * (N2-n2eq) + eps3me * d3 * (N3-n3eq)
- 0.5 * ((w1 * c1m * c1ec + w2 * c2m * c2ec + w3 * c3m * c3ec) * Nee
+ (w1 * c1e * c1ec + w2 * c2e * c2ec + w3 * c3e * c3ec + 2 * widthm) * Nme
+ (w1 * c1m * c1ec + w2 * c2m * c2ec + w3 * c3m * c3ec) * Nmm
+ (w1 * c1t * c1ec + w2 * c2t * c2ec + w3 * c3t * c3ec) * np.conjugate(Ntm)
+ (w1 * c1m * c1mc + w2 * c2m * c2mc + w3 * c3m * c3mc) * Nme
+ (w1 * c1m * c1tc + w2 * c2m * c2tc + w3 * c3m * c3tc) * Nte))
rhs10 = 2 * widtht * (Ntt - 2 * Ntr)
RHStemp = [rhs1, rhs2, rhs3, rhs4, rhs5, rhs6, rhs7, rhs8, rhs9, rhs10]
return RHStemp
[docs]class EtaB_3DS_Scattering_RHtaur(ulysses.ULSBase):
"""
Density matrix equation (DME) with three decaying steriles including
scatterings and effect of right-handed tau participation in kinetic equations.
See hep-ph/0401240 and arxiv:0807.1408.
"""
[docs] def RHS(self, y0, zzz, ETA, C, K, W):
(eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me,eps3tt,eps3mm,eps3ee,eps3tm,eps3te,eps3me) = ETA
k1term,k2term,k3term = K
# Turns out, the Bessel functions are expensive, so let's just
# evaluate them for every new zzz
if zzz != self._currz or zzz == self.zmin:
self._d1 = np.real(self.DS(k1term, zzz))
self._w1 = self.scat(zzz)*np.real(self.W1(k1term, zzz))
self._d2 = np.real(self.D2(k2term, zzz))
self._w2 = np.real(self.W2(k2term, zzz))
self._d3 = np.real(self.D3(k3term, zzz))
self._w3 = np.real(self.W3(k3term, zzz))
self._n1eq = self.N1Eq(zzz)
self._n2eq = self.N2Eq(zzz)
self._n3eq = self.N3Eq(zzz)
self._currz=zzz
return fast_RHS(y0,eps1tt,eps1mm,eps1ee,eps1tm,eps1te,eps1me,eps2tt,eps2mm,eps2ee,eps2tm,eps2te,eps2me,eps3tt,eps3mm,eps3ee,eps3tm,eps3te,eps3me, C, W,
self._d1,self._d2,self._d3,self._w1,self._w2,self._w3,self._n1eq,self._n2eq,self._n3eq)
@property
def EtaB(self):
#Define fixed quantities for BEs
_ETA = [
np.real(self.epsilon1ab(2,2)),
np.real(self.epsilon1ab(1,1)),
np.real(self.epsilon1ab(0,0)),
self.epsilon1ab(2,1) ,
self.epsilon1ab(2,0) ,
self.epsilon1ab(1,0) ,
np.real(self.epsilon2ab(2,2)),
np.real(self.epsilon2ab(1,1)),
np.real(self.epsilon2ab(0,0)),
self.epsilon2ab(2,1) ,
self.epsilon2ab(2,0) ,
self.epsilon2ab(1,0) ,
np.real(self.epsilon3ab(2,2)),
np.real(self.epsilon3ab(1,1)),
np.real(self.epsilon3ab(0,0)),
self.epsilon3ab(2,1) ,
self.epsilon3ab(2,0) ,
self.epsilon3ab(1,0)]
_C = [self.c1a(2), self.c1a(1), self.c1a(0),
self.c2a(2), self.c2a(1), self.c2a(0),
self.c3a(2), self.c3a(1), self.c3a(0)]
_K = [np.real(self.k1), np.real(self.k2), np.real(self.k3)]
_W = [ 485e-10*self.MP/self.M1, 1.7e-10*self.MP/self.M1]
y0 = np.array([0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j,0+0j], dtype=np.complex128)
ys, _ = odeintw(self.RHS, y0, self.zs, args = tuple([_ETA, _C , _K, _W]), full_output=1)
nb = np.real(self.sphalfact*(ys[-1,3]+ys[-1,4]+ys[-1,5]))
self.ys = np.real(ys[:, [3,4,5]])
return np.real(nb)