KATRIN and the Cosmic
Neutrino Background
Amand Faessler
University of Tuebingen
Germany
Amand Faessler, Rastislav Hodak,
Sergey Kovalenko, Fedor Simkovic:
arXiv: 1304.5632 [nucl-th] 20. April 2013.
Cosmic Microwave
Background Radiation
(Photons in the Maximum 2 mm)
Decoupling of the photons from matter about
300 000 years after the Big Bang,when the electron
are captured by the protons and He4 nuclei and the
universe gets neutral. Photons move freely.
Penzias and Wilson;
Bell Telephon
Nobel Price 1978
Planck Satellite Temperature Fluctuations
Comic Microwave Background (March 21. 2013)
We know the
size of the
hot spots.
Curvature of the
Univers
flat
x
x
 1
 1
x
WMAP 2002 :
  1.00  0.02
 1
6
The Universe is
flat. The
density has
the critical
value:
 = 1.00+-0.02
We can only
see till the
sphere of the
the last
photonelectron
scattering:
~14 x1012
light years
Microwave Background Radiation
Experiment
T = 2.7255(6) Kelvin
Black body
radiation.
Temperature
adjusted
(pdg 2012):
T=2.7255(6) K
The relative number
abundance of the light
nuclei formed in the
big bang allows to
determine the
absolute baryon
density and relative to
the critical density (flat
universe).
Baryon = rBaryon/rcritical
= 0.02h-2 = 0.04
nB = 0.22 m-3
eB = 210 MeV/m-3
h = 0.71
h2 = 0.5
Hubble-Konstant=
H = 100 h [km/(sec Mpc)]
Bh2 = 0.02
Planck‘s Black Body Radiation
Decoupling of Photons
and Neutrinos from Matter
„Re“-combination of Electrons with Protons and a-Particles
(1g out of 1.7x109 from upper tail)  3000 Kelvin;
300 000 years after Big Bang;
e- + p  neutral Hydrogen-Atom
2e- + a  neutral Helium-Atom
Photons move freely since 14x1012 years.
Last sphere of scattering: Radius = 14x1012 light years.
Today Tg = 2.7255(6) Kelvin independent of the direction.
Neutrino Decoupling and
Cosmic Neutrino Background
For massless-massive Neutrinos:
Estimate of Neutrino Decoupling
Universe Expansion rate: H=(da/dt)/a
~ n Interaction rate: G ne-e+<svrelative>
H = \sqrt{8p G rtotal /3} = \sqrt{8 p r/(3 MPlanck2)} =
= O(T2) [1/time]
G ~ T3 <GF2 p2 c=1> = T3 GF2 T2 = GF2 T5 [Energy = 1/time]
hbar = h/(2p) = c = 1
Neutrino Decoupling
G/H = ( kB T/ 1MeV)3 ~ 1
T(Neutrinos)decoupl ~ 1MeV ~ 1010 Kelvin; Today: 1.95 K
Time after Big Bang: 1 Second
Below T = 1 MeV:
T(Photons)decoupling = 3000 Kelvin; heute: 2.7255 K
Time(Photons)decoupling = 300 000 years
(Energy=Mass)-Density of the Universe
log r
Radiation dominated: r ~ 1/a4 ~ 𝑇4=Stefan-Boltzmann
Matter dominated: r ~ 1/a3 ~ T3
Dark Energy
a(t)~1/T
1 MeV 1 eV
3000 K
1sec 3x104y 300 000 y
n dec.
g dec.
8x109 y Tg = 2.7255 K
Tn = 1.95 K
1/Temp
heute
Tranformation from Mass
to Flavor Eigenstates
Hamburg, March 3. 2008.
Mass of the Electron Neutrino?
Tritium decay (Mainz + Troisk)
With:
Hamburg, March 3. 2008.
Measurement of the upper Limit of the
Neutrino Mass in Mainz: mn < 2.2 eV 95% C.L.
Kurie-Plot
Eur. Phys. J.
C40 (2005) 447
mn
2>0
mn2 <0
Q = 18.562 keV
Electron Energy
Negatives Squares of the
Measured Neutrino Masses
Ch. Kraus,
B. Bornschein, L.
Bornschein, J. Bonn,
B. Flatt, A. Kovalik,
B. Ostrick, E. W.
Otten, J. P. Schall,
Th. Thümmler,
Ch Weinheimer:
Eur. Phys. J. C40
(2005) 447-468.
Anihilation of Relic Neutrinos with extreme
High Energy Neutrinos > 1022 eV
Energy Momentum
conservation:
n1(GZK,4x1022 eV)
+ n2(CB)
Z0(4x1022eV)burst
10p0, 2 nucleons,
17 p+-
Neutrino
E = 4x1022 eV
nrelic
Z0
Above GZK
DGZK=50Mpc
Anihilation below
Greisen-Zatsepin-Kuzmin
Radius of 50 Mpc
Cosmic Radiation from
Z-Burst expected at 1021 -1022eV
Free magnetic floating cylinder
with half n absorbing material
The system
rotates 90
degrees.
Permanent
Magnet
Superconducting
Magnet
Thomas Müller pointed
this out to me.
A. Ringwald: arXiv:hepph/031157v1; 2003.
One half
n absorbing,
the other
sterile.
Balanced.
Cylinder
shaped
Search for Cosmic Neutrino Background
CnB by Beta decay (KATRIN): Tritium
Kurie-Plot of Beta and induced Beta Decay:
n(CB) + 3H(1/2+)  3He (1/2+) + e-
Infinite good
resolution
Q = 18.562 keV
Resolution Mainz: 4 eV
 mn < 2.3 eV
Emitted
electron
Resolution KATRIN: 0.93 eV
 mn < 0.2 eV 90% C.L.
Fit parameters:
mn2 and Q value meV
Electron Energy
2xNeutrino
Masses
Additional fit: only
intensity of CnB
Search for Cosmic Neutrino
Background CnB by Beta decay: 187Re
Kurie-Plot of beta and induced beta Decay:
n(CB) + 18775Re112(5/2+)  18776Os111(1/2-) + e-
Infinite good
resolution
Q = 2.460 keV
MARE-Genova:
DE ~ 11 eV  mn ~ 2 eV 90% C.L.
Milano-Bicocca:
DE ~24 eV  mn ~ 3-4 eV
Fit parameters:
mn2 and Q value meV
Emitted
electron
Electron Energy
2xNeutrino
Masses
Additional fit: only
intensity of CnB
Tritium Beta Decay: 3H 3He+e-+nce
Neutrino Capture: n(relic) + 3H 3He + e-
20 mg(eff) of Tritium  2x1018 T2-Molecules:
Nncapture(KATRIN) = 1.7x10-6 nn/<nn> [year-1]
Every 590 000 years a count!! for <nn> = 56 cm-3
Kaboth, Formaggio, Monreal: Phys. Rev. D82 (2010) 062001
66 mg(eff) of Tritium 6.6x1018 T2-Molecules:
Nncapture(KATRIN) =5.5x10-6 nn/<nn> (year-1)
Every 180 000 years a count. (For nn = <nn>)
Faessler et al.: J. Phys. G38 (2011) 075202
50mg(eff) of Tritium  5x1018 T2-Molecules
Nncapture(KATRIN) = 4.2x10-6 nn/<nn>(year-1)
Every 240 000 years a counts.(For nn= <nn>)
Drexlin April 2013:
20mg(eff) of Tritium  2x1018 T2-Molecules
Nncapture(KATRIN) = 1.7x10-6 nn/<nn>(year-1)
Every 590 000 years a counts.(For nn= <nn>)
Two Problems
1. Number of Events with average Neutrino Density
of nne = 56 [ Electron-Neutrinos/cm-3]
Katrin: 1 Count in 590 000 Years
Gravitational Clustering of Neutrinos!!!???
2. Energy Resolution (KATRIN) DE ~ 0.93 eV
Kurie-Plot
Emitted
electron
Resolution KATRIN: 0.93 eV
 mn < 0.2 eV 90% C.L.
Fit parameters:
mn2 and Q value meV
Electron Energy
2xNeutrino
Masses
Additional fit: only
intensity of CnB
Gravitational Clustering of Dark
Matter and Neutrinos in Galaxies
Dunkle
Materie
?
Faktum
erwartet
Was kompensiert
die Zentrifugalkraft?
Gravitational Clustering of Neutrinos
A. Ringwald, Y. Wong: arXiv:hep-ph/0408241; solved Vlasov
eq. for n; Dark Matter from Navarro et al. Ap J490 (1997) 493
Virial Mass:
Mvir = 5v2R/G;
v = velocity in
sight
Circles: 1h-1 kpc; Pentagons: 10h-1 kpc; Squares: 100h-1 kpc; Triangles 1000h-1 kpc. h-1 = 1.4
The solar system is 8 kpc = 24 000 ly from the galactic center.
Gravitational Clustering of Neutrinos
R.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) 025001;
Light neutrinos: Gravitate only on Mpc (50 Mpc Galaxy Cluster) scale:
nn/<nn> ~ nb/<nb> ~ 103 – 104; <nb>= 0.22 10-6 cm-3
A. Ringwald and Y. Wong: Vlasov trajectory simulations
Clustering on Galactic Scale possible
nn/<nn> = nb/<nb> ~ 106 ; (R = 30 kpc)
Nncapture(KATRIN) = 1.7x10-6 nn/<nn> (year-1)
= 1.7 (170 for 2 milligram) [counts per year]
R. Wigmans, Astroparticle Physics 19 (2003) 379
discusses up to: nn/<nn> = 1013 but for us unrealistic.
n Capture: ne(relic) + 18775Re(5/2)+18776Os(1/2)- + eMARE Genova and Milano
Main Contribution: n  s(1/2);
e-  p(3/2)
760 grams of AgReO4  Nncapture(MARE) = 6.7x10-8 nn/<nn> [year-1]
For nn = <nn>: Every 15 Million years a count.
For: nn/<nn> = 106: Every 15 years a count. (KATRIN: 1.7 per year)
Summary 1
• The Cosmic Microwave Background allows to
study the Universe 300 000 year after the BB.
• The Cosmic Neutrino Background 1 sec after
the Big Bang (BB): Tn(today) = 1.95 Kelvin.
• Extremly difficult to detect: Small Cross
Section and low Density 56 n‘s/cm3 and low
Energies (1.95 Kelvin = 2x10-4 eV).
Summary 2
1. Average Density: nne = 56 [ Electron-Neutrinos/cm-3]
Katrin (20 mg eff. mass 3H): 1 Count in 590 000 Years
Gravitational Clustering of Neutrinos nn/<nn> < 106
 1.7 counts (2 milligram of 3H  170 counts) per year.
2. Measure only an upper limit of nn
Kurie-Plot
Emitted
electron
Resolution KATRIN: .93 eV
 mn < 0.2 eV 90% C.L.
Fit parameters:
mn2 and Q value meV
ENDE
Electron Energy
2xNeutrino
Masses
Additional fit: only
intensity of CnB