Amand Faessler, Tuebingen Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen 1. Solution of the Solar Neutrino Problem by SNO. 2. Neutrino

Amand Faessler, Tuebingen

Double Beta Decayand

Neutrino Masses

Amand FaesslerTuebingen

1. Solution of the Solar Neutrino Problem by SNO.

2. Neutrino Masses and the Neutrinoless Double

Beta Decay: Dirac versus Majorana Neutrinos

3. Neutrino Masses and Supersymmetry


(1) Solar Neutrino Problem

Reaction Network:

Oscillations:Fewer νe on Earth detected

than produced in the Sun.

Oscillations depend on:


Sudburry Neutrino Observatory

Creighton Mine Ontario / Canada(Zink Mine)


THE SNO CHERENKOV DETECTOR WITH HEAVY WATER

9456 Photomultipliers Ø 20 cm 55 % of 4π

Cherenkow radiation of e-

Trigger ≥ 23 PMT

Eν (Threshold) = 6.75 MeV

Ø 17 m; view from below


Cherenkov - Detectors:

(ES) Elastic Neutrino Scattering:

e- forward scatteringS-KAMIOKANDE + SNO

e- (fast)

νe

W+

νe

e- (fast)

e- e-

νx

νx

Z0+

6 : 1:1:1


Charged Current (CC):

e- backwardSNO

e-

νe

W+

P

P

Deuteron

(p + n)


(NC) Neutral Current:

n-capture in salt NaCl (n, γ)

νx

νx

Z0

P n

Deuteron SNO


Assuming only Electron Neutrinos:(ES) 2.35*106 [Φ](CC) 1.76*106 [Φ](NC) 5.09*106 [Φ]

Including Muon and Tauon ν:

Φ(νe) = 1.76*106 (CC)

Φ(νμ+ντ) = 3.41*106 (CC+ES)

Φ(νe+νμ+ντ) = 5.09*106 (NC)

Φ(ν-Bahcall) = 5.14*106


ν1, ν2, ν3 Mass States

νe, νμ, ντ Flavor States

Theta(1,2) = 32.6 degrees Solar + KamLandTheta(1,3) < 13 degrees ChoozTheta(2,3) = 45 degrees S-Kamiokande


(Bild)


(2) Neutrinoless Double Beta Decay

The Double Beta Decay:

0+

0+

0+

β-

1+

2-

β-

e- e-

E>2me


2νββ-Decay (in SM allowed)

Thesis Maria Goeppert-Mayer1935 Goettingen

P P

n n


Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

P

P

n n

Left

Leftν

Phase Space

106 x 2νββ


GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:


P P

νν

n n

e-

e-

L/R l/r


l/r

P

ν

P

l/r

n n

light ν

heavy N

Neutrinos


Theoretical Description:

Simkovic, Rodin, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel et al.

0+

0+

0+

1+

2-

k

k

ke1

e2PP

ν Ek

Ein n

0νββ



Supersymmetry

Bosons ↔ Fermions--------------------------------------------------------------------

---

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron


Majorana;


The best choice:

Quasi-Particle-

(a) Quasi-Boson-Approx.:

(b) Particle Number non-conserv.(important near closed shells)

(c) Unharmonicities(d) Proton-Neutron Pairing

Pairing



Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe

150Nd

T1/2 (exp)[years]

>9.51021

>1.91025

>1.41022

>1.01021

>5.51022

>7.01022

>8.61022

>1.41022

>5.81022

>7.01023

>1.71021

Ref.: You Klap-dor

Elli-ott

Arn. Ejiri Dane-vich

Ales.

Ales. Ber. Staudt

Klimenk.

<m>[eV] <22.

<0.47

<8.7

<40.

<2.8 <3.8 <17.

<3.2 <27. <3.8

<7.2

η~m(p)/M(

<200.

<0.79

<15.

<79.

<6.0 <7.0 <27.

<4.9 <38. <3.5

<13.

λ‘(111)[10-4] <8.9

<1.1 <5.0

<9.4

<2.8 <3.4 <5.8

<2.4 <6.8 <2.1

<3.8

Only for Majorana ν possible.


gPP fixed to 2νββ

Each point: (3 basis sets) x (3 forces) = 9 values




Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments

from R-QRPA; m) = )


Neutrino-Masses for the Double 0νβ-Decay and Neutrino Oscillations

Solar NeutrinosAtmospheric νReactor ν (Chooz; KamLand)

with CP-Invariance:


Solar Neutrinos (+KamLand):

(KamLand)

Atmospheric Neutrinos: (Super-Kamiok.)


Reactor Neutrinos (Chooz):

CP


OSCILLATIONS AND DOUBLE BETA DECAY

Hierarchies: mν

Normal

m3

m2

m1

m1<<m2<<m3

Inverted m2

m1

m3

m3<<m1<<m2

Bilenky, Faessler, Simkovic P. R. D 70(2004)33003


Normal:

Inverted:


(Bild)




Summary:Neutrinos Oscillations, Neutrino

Masses andthe Double beta Decay

1. Solution of the Solar Neutrino Problem by theSudburry-Neutrino-Observatory (SNO):

Elastic Scattering (S-KAMIOKANDE):

Heavy Water (SNO: Charged Currents):

νx

νx

Z0

e-

e-

e-

e-νc

νc

W+

νc

d d

e-

W+

P P

Pn

n

n

P

P

νx

νx

Z0


2. Neutrinoless Double Beta Decay

Dirac versus Majorana NeutrinosGrand Unified Theories (GUT‘s),R-Parity violating Supersymmetry →Majorana-Neutrinos = Antineutrinos

Direct measurement in the Tritium Beta Decay in Mainz

and Troisk

n n

nn

PP

P P

ddd

d

u u

u

u u

u


3. Neutrino Masses and Supersymmetry

R-Parity violating Supersymmetry mixes Neutrinos with Neutrinalinos (Photinos, Zinos, Higgsinos) and Tau-Susytau-Loops, Bottom-Susybottom-Loops → Majorana-Neutrinos (Faessler, Haug, Vergados: Phys. Rev. D )

m(neutrino1) = ~0 – 0.02 [eV] m(neutrino2) = 0.002 – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV]

0-Neutrino Double Beta decay <mββ> = 0.009 - 0.045 [eV]

ββ Experiment: <mββ> < 0.47 [eV]

Klapdor et al.: <mββ> = 0.1 – 0.9 [eV]

Tritium (Otten, Weinheimer, Lobashow) <m> < 2.2 [eV]

THE END


ν-Mass-Matrix by Mixing with:

Diagrams on the Tree level:

Majorana Neutrinos:


Loop Diagrams:

Figure 0.1: quark-squark 1-loop contribution to mv

X

X

Majorana

Neutrino


Figure 0.2: lepton-slepton 1-loop contribution to mv

(7x7) Mass-Matrix:

X

X

Block

Diagonalis.


7 x 7 Neutrino-Massmatrix:

Basis: Eliminate Neutralinos in 2. Order:

separabel

{ Mass Eigenstate

Vector in

flavor space

for 2 independent

and possible


Super-K:


Horizontal U(1) Symmetry

U(1) FieldU(1) chargeR-Parity breaking terms must be without U(1) charge change (U(1) charge

conservat.)Symmetry Breaking:


How to calculate λ‘i33 (and λi33) from λ‘333?

U(1) charge conserved!

1,2,3 = families

Documents

Amand Faessler, Tuebingen Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen 1. Solution of the Solar Neutrino Problem by SNO. 2. Neutrino