Search for the Cosmic Neutrino Background and the

Nuclear Beta Decay.

Amand FaesslerUniversity of Tuebingen

Germany

Publication: 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 electrons are captured by the protons and He4 nuclei and the

universe gets neutral. Photons move freely. Today: ~550 Photons /cm3 (~340 Neutrinos/cm3)

Planck Satellite Temperature FluctuationsComic Microwave Background (Release March 21. 2013)

e(f) = (8ph/c3) f3df/[exp(hf/kBT)-1][Energy/Volume]

Neutrino Decoupling and Cosmic Neutrino Background

For massless-massive Neutrinos:

Estimate of Neutrino Decoupling

Universe Expansion rate: H=(da/dt)/a; a ~ 1/T; (today, Planck) H = 67km/(sec*Mpc)

~ n Interaction rate: G= ne-e+<svrelative>

Neutrino Decoupling

G/H = ( kB T/ 1MeV)3 ~ 1

T(Neutrinos)decoupl ~ 1MeV ~ 1010 Kelvin;

today: Tn = 1.95 K

Time after Big Bang: 1 Second

(Energy=Mass)-Density of the Universe

log r

a(t)~1/T

Radiation dominated: r ~ 1/a4 ~ =Stefan-Boltzmann

Matter dominated: r ~ 1/a3 ~ T3

Dark Energy

1/Temp1 MeV1secn dec.

1 eV3x104y today

3000 K300 000 yg dec.

8x109 y g 2.7255 Kn 1.95 K

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

Q = 18.562 keV

mn 2>0 mn2 <0 Electron Energy

Eur. Phys. J. C40 (2005) 447

Search for Cosmic Neutrino Background CnB by Beta decay: Tritium

Kurie-Plot of Beta and induced Beta Decay: n(CB) + 3H(1/2+) 3He (1/2+) + e-

Electron Energy

2xNeutrino Masses

Emitted electron

Q = 18.562 keV

Infinite good resolution

Resolution Mainz: 4 eV mn < 2.3 eV

Resolution KATRIN: 0.93 eV mn < 0.2 eV 90% C. L.

Fit parameters: mn

2 and Q value meVAdditional fit: only

intensity of CnB

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

Kurie-Plot

Electron Energy

2xNeutrino Masses

Emitted electron

Resolution KATRIN: 0.93 eV mn < 0.2 eV 90% C.L.

Fit parameters: mn

2 and Q value meVAdditional fit: only

intensity of CnB

Two Problems1. 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

Gravitational Clustering of NeutrinosR.Lazauskas,P. Vogel and C.Volpe, J. Phys.g. 35 (2008) 025001;

Light neutrinos: Gravitate only on 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 (30 kpc to 1 Mpc)

nn/<nn> = nb/<nb> ~ 106 ; (R = 30 kpc)Nncapture(KATRIN) = 1.7x10-6 nn/<nn> (year-1)= 1.7 [counts per year]

Effective Tritium Source: 20 microgram 2 milligramNncapture(KATRIN*) = 1.7x10-4 nn/<nn> (year-1)= 170 [counts peryear];

See also: B. Monreal, J. A. Formaggio, Phys. Rev. D80 (2009) 051301 „Relativistic cyclotron radiation detection of tritium decay electrons“

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

2xNeutrino Masses

Emitted electron

Kurie-Plot

Electron Energy

Summary 21. Average Density: nne = 56 [ Electron-Neutrinos/cm-3] Katrin: 1 Count in 590 000 Years Gravitational Clustering of Neutrinos nn/<nn> < 106

1.7 counts per year (2 milligram 3H 170 per year)2. Measure only an upper limit of nn

THE END