def sterile_quark_neutral(theta=1., sterile=None, active=None, quark=None, kind=None):
""" \begin{align}
N_S + \overline{\nu} &\to q + \overline{q}
\end{align}
"""
if quark.Q == 2./3.:
g_R = CONST.g_R
if quark.Q == -1./3.:
g_R = CONST.g_R / 2.
x = (3 - 4 * g_R)
return CrossGeneratingInteraction(
name="Sterile-quarks neutral channel interaction",
particles=((sterile, active), (quark, quark)),
antiparticles=((False, True), (False, True)),
Ms=(
SterileM(theta=theta, K1=16. / 9. * g_R**2, order=(0, 2, 1, 3)),
SterileM(theta=theta, K1=1. / 9. * x**2, order=(0, 3, 1, 2)),
SterileM(theta=theta, K2=-4. / 9. * g_R * x, order=(2, 3, 0, 1)),
),
integral_type=FourParticleIntegral,
kind=kind
)
def neutrinos_to_leptons(neutrino=None,
lepton=None,
g_L=CONST.g_R + 0.5,
kind=None):
""" \begin{align}
\nu_\alpha + \overline{\nu_\alpha} &\to e^- + e^+
\end{align}
\begin{align}
|\mathcal{M}|^2 = 32 G_F^2 \left(
\\ 4 \, g_L^2 \, (p_0 \cdot p_3) (p_1 \cdot p_2) +
\\ +4 \, g_R^2 \, (p_0 \cdot p_2) (p_1 \cdot p_3) +
\\ +4 \, g_L g_R \, m_2 m_3 (p_0 \cdot p_1)
\\ \right)
\end{align}
Depending of the neutrino generations involved, $g_L$ can either be equal to \
$g_R + \frac12$ (for $\nu_e$) or $g_R - \frac12$ (for others).
"""
return CrossGeneratingInteraction(
name="Neutrino pair annihilation into lepton pair",
particles=((neutrino, neutrino), (lepton, lepton)),
antiparticles=((False, True), (False, True)),
washout_temperature=0 * UNITS.MeV,
Ms=(
WeakM(K1=4 * CONST.g_R**2, order=(0, 3, 1, 2)),
WeakM(K1=4 * g_L**2, order=(0, 2, 1, 3)),
WeakM(K2=4 * g_L * CONST.g_R, order=(2, 3, 0, 1)),
),
integral_type=FourParticleIntegral,
kind=kind)
def neutral_vector_meson(theta=1., sterile=None, active=None, meson=None, kind=None):
""" \begin{align}
N \to \nu + meson
\end{align}
"""
if meson.name == 'Neutral rho':
kappa = 1. - 2. * CONST.sin_theta_w_2
if meson.name == 'Omega':
kappa = 4. * CONST.sin_theta_w_2 / 3.
if meson.name == 'Phi':
kappa = 4. * CONST.sin_theta_w_2 / 3. - 1.
return [CrossGeneratingInteraction(
name="Sterile neutrino decay to neutral vector meson and neutrino",
particles=((sterile, ), (active, meson)),
antiparticles=antiparticles,
Ms=(ThreeParticleM(K=(CONST.G_F * theta * meson.decay_constant * kappa)**2
* sterile.mass**4 * (1 + 2 * (meson.mass / sterile.mass)**2)
* (1 - (meson.mass / sterile.mass)**2)), ),
integral_type=ThreeParticleIntegral,
kind=kind
) for antiparticles in [
((False, ), (False, False)),
((True, ), (True, False))
]]
def decay_neutral_pion(meson=None, photon=None, kind=None):
return [
CrossGeneratingInteraction(
name="Neutral pion decay into two photons",
particles=((meson, ), (photon, photon)),
antiparticles=((False, ), (False, False)),
Ms=(ThreeParticleM(
K=CONST.alpha**2 * meson.mass**4 /
(2 * np.pi**2 * meson.decay_constant**2)), ),
integral_type=ThreeParticleIntegral,
kind=kind)
]
def leptons_CC(active1=None,
active2=None,
lepton1=None,
lepton2=None,
kind=None):
return CrossGeneratingInteraction(
name="Charged current lepton-neutrino interactions",
particles=((lepton1, lepton2), (active1, active2)),
antiparticles=((False, True), (False, True)),
Ms=(WeakM(K1=4., order=(0, 3, 1, 2)), ),
integral_type=FourParticleIntegral,
kind=kind)
def three_particle_meson_decay(parts=None,
antiparts=None,
ME=None,
kind=None):
return [
CrossGeneratingInteraction(
name="Meson decay",
particles=((parts[0], ), (parts[1], parts[2])),
antiparticles=((antiparts[0], ), (antiparts[1], antiparts[2])),
Ms=(ThreeParticleM(K=ME), ),
integral_type=ThreeParticleIntegral,
kind=kind)
]
def baryons_interaction(cls,
neutron=None,
proton=None,
neutrino=None,
electron=None):
return CrossGeneratingInteraction(
name="Baryons interaction",
particles=((neutron, ), (proton, electron, neutrino)),
antiparticles=((False, ), (False, False, True)),
washout_temperature=0 * UNITS.MeV,
Ms=(WeakM(K1=2. * particles.quarks.CKM[(1, 1)]**2,
order=(0, 1, 2, 3)), ),
integral_type=FourParticleIntegral)
def four_particle_meson_decay(parts=None,
antiparts=None,
ME=None,
kind=None):
return [
CrossGeneratingInteraction(
name="Meson decay",
particles=((parts[0], parts[1]), (parts[2], parts[3])),
antiparticles=((antiparts[0], antiparts[1]), (antiparts[2],
antiparts[3])),
Ms=(WeakM(K=ME), ),
integral_type=FourParticleIntegral,
kind=kind)
]
def decay_charged_pion(meson=None, lepton=None, neutrino=None, kind=None):
CKM = particles.quarks.CKM[(1, 1)]
return [
CrossGeneratingInteraction(
name="Charged pion decay into neutrino and charged lepton",
particles=((meson, ), (lepton, neutrino)),
antiparticles=antiparticles,
Ms=(ThreeParticleM(
K=2 * (CONST.G_F * meson.decay_constant * CKM)**2 *
lepton.mass**4 * (((meson.mass / lepton.mass)**2 - 1))), ),
integral_type=ThreeParticleIntegral,
kind=kind)
for antiparticles in [((False, ),
(False, True)), ((True, ), (True, False))]
]
def leptons_leptons_NC(lepton1=None,
lepton2=None,
g_L=CONST.g_R - 0.5,
kind=None):
return CrossGeneratingInteraction(
name="Neutral current lepton-lepton interactions",
particles=((lepton1, lepton2), (lepton1, lepton2)),
antiparticles=((False, False), (False, False)),
Ms=(
WeakM(K1=4 * (g_L**4 + CONST.g_R**4), order=(0, 1, 2, 3)),
WeakM(K1=4 * 2 * g_L**2 * CONST.g_R**2, order=(0, 3, 1, 2)),
WeakM(K2=4 * -g_L * CONST.g_R * (g_L**2 + CONST.g_R**2),
order=(0, 2, 1, 3)),
),
integral_type=FourParticleIntegral,
kind=kind)
def neutral_scalar_meson(theta=1., sterile=None, active=None, meson=None, kind=None):
""" \begin{align}
N \to \nu + meson
\end{align}
"""
return [CrossGeneratingInteraction(
name="Sterile neutrino decay to neutral scalar meson and neutrino",
particles=((sterile, ), (active, meson)),
antiparticles=antiparticles,
Ms=(
ThreeParticleM(K=(CONST.G_F * theta * meson.decay_constant)**2
* sterile.mass**4 * np.abs(1 - (meson.mass / sterile.mass)**2)), ),
integral_type=ThreeParticleIntegral,
kind=kind
) for antiparticles in [
((False, ), (False, False)),
((True, ), (True, False))
]]
def sterile_quark_charged(theta=1., sterile=None, lepton=None, up=None, down=None, kind=None):
""" \begin{align}
N_S + l^+ &\to u + \overline{d}
\end{align}
"""
CKM = SM_particles.quarks.CKM[(up.family, down.family)]
return CrossGeneratingInteraction(
name="Sterile-quarks charged channel interaction",
particles=((sterile, lepton), (up, down)),
antiparticles=((False, True), (False, True)),
Ms=(
SterileM(theta=theta, K1=4. * CKM**2, order=(0, 3, 1, 2)),
),
integral_type=FourParticleIntegral,
kind=kind
)
def sterile_active_to_leptons_CC(theta=1., sterile=None,
active=None, lepton1=None, lepton2=None, kind=None):
""" \begin{align}
N_S + \overline{\nu_{\alpha}} \to l1^+ + l2^-
\end{align}
"""
return [CrossGeneratingInteraction(
name="Charged current sterile-lepton interactions",
particles=particles,
antiparticles=((False, True), (True, False)),
Ms=(
SterileM(theta=theta, K1=4., order=(0, 2, 1, 3)),
),
integral_type=FourParticleIntegral,
kind=kind
) for particles in [
((sterile, active), (lepton2, lepton1)),
((active, sterile), (lepton1, lepton2))
]]
def neutrino_scattering(neutrino_a, neutrino_b, kind=None):
""" \begin{align}
\nu_\alpha + \nu_\beta &\to \nu_\alpha + \nu_\beta
\end{align}
\begin{equation}
|\mathcal{M}|^2 = 32 G_F^2 (p_0 \cdot p_1) (p_2 \cdot p_3)
\end{equation}
"""
return CrossGeneratingInteraction(name="Neutrino species scattering",
particles=((neutrino_a, neutrino_b),
(neutrino_a, neutrino_b)),
antiparticles=((False, False),
(False, False)),
washout_temperature=0 * UNITS.MeV,
Ms=(WeakM(K1=1.,
order=(0, 1, 2, 3)), ),
integral_type=FourParticleIntegral,
kind=kind)
def sterile_active_to_leptons_NC(theta=1., g_L=CONST.g_R+0.5, sterile=None,
active=None, lepton=None, kind=None):
""" \begin{align}
N_S + \overline{\nu_{\alpha}} \to l^+ + l^-
\end{align}
"""
return [CrossGeneratingInteraction(
name="Neutral current sterile-lepton interactions",
particles=((sterile, active), (lepton, lepton)),
antiparticles=antiparticles,
Ms=(
SterileM(theta=theta, K1=4. * g_L**2, order=(0, 2, 1, 3)),
SterileM(theta=theta, K1=4. * CONST.g_R**2, order=(0, 3, 1, 2)),
SterileM(theta=theta, K2=4. * CONST.g_R * g_L, order=(2, 3, 0, 1))
),
integral_type=FourParticleIntegral,
kind=kind
) for antiparticles in
[((False, True), (True, False)),
((True, False), (False, True))
]]
def sterile_active_scattering(theta=1., sterile=None, active_a=None,
active_b=None, kind=None):
""" \begin{align}
N_S + \nu_{\beta} &\to \nu_{\alpha} + \nu_{\beta}
\end{align}
"""
# SOMETHING IS CLEARLY NOT RIGHT
K1 = 2. if active_a == active_b else 1
return [CrossGeneratingInteraction(
name="Sterile-active neutrino scattering",
particles=particles,
antiparticles=((False, False), (False, False)),
Ms=Ms,
integral_type=FourParticleIntegral,
kind=kind
) for particles, Ms in zip(
[((sterile, active_b), (active_a, active_b)),
((active_a, active_b), (sterile, active_b))],
[(SterileM(theta=theta, K1=K1, order=(0, 1, 2, 3)), ),
(SterileM(theta=theta, K1=K1, order=(2, 3, 0, 1)), )]
)]
def charged_vector_meson(theta=1., sterile=None, lepton=None, meson=None, kind=None):
""" \begin{align}
N \to l + meson
\end{align}
"""
CKM = SM_particles.quarks.CKM[(1, 1)]
# Only charged rho for now
return [CrossGeneratingInteraction(
name="Sterile neutrino decay to charged vector meson and lepton",
particles=((sterile, ), (lepton, meson)),
antiparticles=antiparticles,
Ms=(ThreeParticleM(
K=2 * (CONST.G_F * theta * meson.decay_constant * CKM)**2 * sterile.mass**4 * (
(1 - (lepton.mass / sterile.mass)**2)**2 + (meson.mass / sterile.mass)**2
* (1 + (lepton.mass / sterile.mass)**2) - 2 * (meson.mass / sterile.mass)**4
)
),),
integral_type=ThreeParticleIntegral,
kind=kind
) for antiparticles in [
((False, ), (False, True)),
((True, ), (True, False))
]]
from library.SM import particles as SMP
from interactions import CrossGeneratingInteraction
from interactions.four_particle import FourParticleM, FourParticleIntegral
from particles import Particle
from evolution import Universe
from common import CONST, UNITS, Params
params = Params(T=2 * UNITS.MeV, dy=0.025)
photon = Particle(**SMP.photon)
neutrino = Particle(**SMP.leptons.neutrino_e)
neutrino_scattering = CrossGeneratingInteraction(
particles=((neutrino, neutrino), (neutrino, neutrino)),
antiparticles=((False, True), (False, True)),
Ms=(FourParticleM(K1=64 * CONST.G_F**2, order=(0, 1, 2, 3)), ),
integral_type=FourParticleIntegral)
universe = Universe(params=params)
universe.PARALLELIZE = False
universe.add_particles([photon, neutrino])
universe.interactions += [neutrino_scattering]
import numpy
addition = numpy.vectorize(lambda x: 0.1 * numpy.exp(-(x / UNITS.MeV - 3)**2),
otypes=[numpy.float_])
neutrino._distribution += addition(neutrino.grid.TEMPLATE)
# def check(p=[]):
# return neutrino_scattering.F_B(in_p=p[:2], out_p=p[2:]) * (1 - neutrino.distribution(p[0])) \
# - neutrino_scattering.F_A(in_p=p[:2], out_p=p[2:]) * neutrino.distribution(p[0])