Amand Faessler, 22. Oct. 20041 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen...

Amand Faessler, 22. Oct. 2004

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Double Beta Decayand

Neutrino MassesAmand Faessler

Tuebingen

Accuracy of the Nuclear Matrix Elements.

It determines the Error of the Majorana Neutrino Mass extracted


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Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

P

P

n n

Left

Leftν

Phase Space

106 x 2νββ


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GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:


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P P

νν

n n

e-

e-

L/R l/r


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l/r

P

ν

P

l/r

n n

light ν

heavy N

Neutrinos


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Supersymmetry

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

---

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron


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Theoretical Description:Simkovic, Rodin, Pacearescu, Haug,

Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel, Stoica, Suhonen, Civitarese, Tomoda et al.

0+

0+

0+

1+

2-

k

k

ke1

e2PP

ν Ek

Ein n

0νββ


10


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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


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M0ν (QRPA)

O. Civitarese, J. Suhonen, NPA 729 (2003) 867

Nucleus their(QRPA, 1.254) our(QRPA, 1.25)

76Ge 3.33 2.68(0.12) 100Mo 2.97 1.30(0.10) 130Te 3.49 1.56(0.47) 136Xe 4.64 0.90(0.20)

A different procedure of fixing gpp to single beta decays. What is their g(pp) with error? How well is the 2-neutrino decay reproduced?

Higher order terms of nucleon Current included differently with Gaussian form

factors based on a special quark model ( Kadkhikar, Suhonen, Faessler, Nucl. Phys. A29(1991)727). Does neglect pseudoscalar coupling (see eq. (19a)), which is an effect of 30%.

We: Higher order currents from Towner and Hardy.

What is the basis and the dependence on the size of the basis?

We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!


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M0ν (R-QRPA; 1.25)

S. Stoica, H.V. Klapdor-Kleingrothaus, NPA 694 (2001) 269

The same procedure of fixing g(pp)

Higher order terms of nucleon current not considered

Nucleus l.m.s s.m.s our

76Ge 1.87 (l=12) 3.74 (s=9) 2.40(.12)

100Mo 3.40 4.36 1.20(.15)

130Te 3.00 4.55 1.46(.46)

136Xe 1.02 1.57 0.85(.23)

Model space dependence ?

Disagreement also between his tables and figures for R-QRPA and S-QRPA!


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Neutrino-Masses from the 0ν

and Neutrino Oscillations

Solar Neutrinos (CL, Ga, Kamiokande, SNO)Atmospheric ν (Super-Kamiokande)Reactor ν (Chooz; KamLand)

with CP-Invariance:


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Reactor Neutrinos (Chooz):

CP


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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


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(Bild)


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Summary:Accuracy of Neutrino

Masses from 0

Fit the g(pp) by in front of the particle-particle NN matrixelement include exp. Error of .

Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets (small about 2 shells, intermediate 3 shells and large 5 shells) the

Use QRPA and R-QRPA (Pauli principle)

Use: g(A) = 1.25 and 1.00

Error of matrixelement 20 to 40 % (96Zr larger; largest errors from experim. values of T(1/2, 2))


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Summary:Results from

<m()>(GeExp. Klapdor) 0.47 [eV]

<M(heavy >[GeV]

<M(heavy Vector B)> > 5600 [GeV]

SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4)

Mainz-Troisk: m(2.2 [eV]

Astro Physics (SDSS): Sum{ m() } < 1 to 2 [eV]

Klapdor et al. from Ge76 with R-QRPA (no error of theory included):

0.15 to 0.72 [eV], if confirmed.

The Theory Groups must check their Results against each other.

THE END


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Summary:Accuracy of Neutrino

Masses by the Double Beta Decay

Dirac versus Majorana NeutrinosGrand Unified Theories (GUT‘s), R-Parity violatingSupersymmetry

→Majorana-Neutrino = Antineutrinos

<m(eV; ‘ < 1.1*10**(-4)

Direct measurement in the Tritium Beta Decay in Mainz and Troisk

Klapdor et al.: <mββ> = 0.1 – 0.9 [eV] ; R-QRPA: 0.15 – 0.72 [eV]

n n

nn

PP

P P

d

d

d

d

u u

u

u u

u


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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


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ν-Mass-Matrix by Mixing with:

Diagrams on the Tree level:

Majorana Neutrinos:


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Loop Diagrams:

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

X

X

Majorana

Neutrino


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

(7x7) Mass-Matrix:

X

X

Block

Diagonalis.


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7 x 7 Neutrino-Massmatrix:

Basis: Eliminate Neutralinos in 2. Order:

separabel

{ Mass Eigenstate

Vector in

flavor space

for 2 independent

and possible


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Super-K:


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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:


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

U(1) charge conserved!

1,2,3 = families


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gPP fixed to 2νββ; M(0) [MeV**(-1)]

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


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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


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Amand Faessler, 22. Oct. 20041 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen...

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Transcript of Amand Faessler, 22. Oct. 20041 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen...