KATRIN and the Cosmic Neutrino Background

Amand FaesslerUniversity 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 FluctuationsComic Microwave Background (March 21. 2013)

6

Curvature of the Univers

flat

xx x

1 1 1

WMAP 2002 :

1.00 0.02

We know the size of the hot spots.

The Universe is flat. The

density has the critical

value: W = 1.00+-

0.02

We can only see till the

sphere of the the last photon-electron

scattering:~14 x1012 light years

Black body radiation.

Temperature adjusted

(pdg 2012):T=2.7255(6) K

Experiment

Microwave Background Radiation

T = 2.7255(6) Kelvin

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).

WBaryon = rBaryon/rcritical = 0.02h-2 = 0.04

nB = 0.22 m-3

eB = 210 MeV/m-3

h = 0.71h2 = 0.5

Hubble-Konstant=H = 100 h [km/(sec Mpc)]

WBh2 = 0.02

Planck‘s Black Body Radiation

Decoupling of Photons and Neutrinos from Matter

„Re“-combination of Electrons with Protons and a-Particles (1 g 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{8 p G rtotal /3} = \sqrt{8 p r/(3 MPlanck2)} =

= O(T2) [1/time]

G ~ T3 <GF2 p2 c=1> = T3 GF

2 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

T(Photons)decoupling = 3000 Kelvin; heute: 2.7255 K Time(Photons)decoupling = 300 000 years

Below T = 1 MeV:

(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 MeV1sec n

dec.

1 eV3x104y heute

3000 K300 000 y

g dec.

8x109 y Tg = 2.7255 KTn = 1.95 K

Hamburg, March 3. 2008.

Tranformation from Mass to Flavor Eigenstates

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

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.

nrelic

DGZK=50Mpc

NeutrinoE = 4x1022 eVEnergy Momentum

conservation:n1(GZK,4x1022 eV)

+ n2(CB) Z0(4x1022eV)burst 10p0, 2 nucleons, 17 p+-

Anihilation of Relic Neutrinos with extreme High Energy Neutrinos > 1022 eV

Z0

Above GZK

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

Permanent Magnet

SuperconductingMagnet

Cylinder shaped

One half n

absorbing,the other

sterile. Balanced.

The system rotates 90 degrees.

Thomas Müller pointed this out to me.

A. Ringwald: arXiv:hep-ph/031157v1; 2003.

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-

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

Search for Cosmic Neutrino Background CnB by Beta decay: 187Re

Kurie-Plot of beta and induced beta Decay: n(CB) + 187

75Re112(5/2+) 18776Os111(1/2-) + e-

Electron Energy

2xNeutrino Masses

Emitted electron

Q = 2.460 keV

Infinite good resolution

MARE-Genova: DE ~ 11 eV mn ~ 2 eV 90% C.L. Milano-Bicocca:DE ~24 eV mn ~ 3-4 eV

Fit parameters: mn

2 and Q value meVAdditional 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-MoleculesNncapture(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-MoleculesNncapture(KATRIN) = 1.7x10-6 nn/<nn>(year-1)Every 590 000 years a counts.(For nn= <nn>)

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 Dark Matter and Neutrinos in Galaxies

Was kompensiert die Zentrifugalkraft?

Dunkle Materie

?Faktum

erwartet

Gravitational Clustering of NeutrinosA. Ringwald, Y. Wong: arXiv:hep-ph/0408241; solved Vlasov eq. for n; Dark Matter from Navarro et al. Ap J490 (1997) 493

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.

Virial Mass:Mvir = 5v2R/G;v = velocity in sight

Gravitational Clustering of NeutrinosR.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)+187

76Os(1/2)- + e-

MARE Genova and Milano

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)

Main Contribution: n s(1/2); e- p(3/2)

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).

2xNeutrino Masses

Emitted electron

Resolution KATRIN: .93 eV mn < 0.2 eV 90% C.L.

Fit parameters: mn

2 and Q value meVAdditional fit: only

intensity of CnB

Kurie-Plot

Electron Energy

Summary 21. 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

ENDE