Transcript C5: Neutrinos, Nuclear structure and Physics beyond the
Neutrino Masses, Double Beta Decay and Nuclear Structure
ECT*(Trento), Doctoral Training Program on “Neutrinos in Nuclear, Particle and Astrophysics”.
Amand Faessler, University of Tuebingen, www.uni-tuebingen.de/faessler/
CONTENTS: 0. History of the Neutrinos (Introduction) 1. Neutrino Properties 2. The See-Saw Model 3. The Single Beta Decay 4. The Neutrinoless Double Beta Decay 5. The Quasi-Particle Random Phase Approximation (QRPA) 6. Comparison of QRPA, Shell Model, Projected Hartree Fock Bogoliubov (PHBF), Interacting Boson Model 2 7. Can one measure with Charge Transfer Reactions the 0 nbb -Matrix element?
8. Competing Mechanisms for the 0 nbb 9. The Heidelberg-Moscow data and the Neutrino Mass FAESSLE
R;
Trento 2011
0
.
History of the Neutrinos
• 1930 Pauli‘s invention of the neutrino • 1955 Reines and Cowen detection of the electron neutrino n e • 1962 Brookhaven; detection of muon neutrino n m • 2000 Fermi Lab; detection of tau neutrino n t • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2 nbb decay • 1986 Santa Barbara (Caldwell) detection of 2 nbb .
• 20xx Detection of 0 nbb decay ?
FAESSLER; Trento 2011
Sehr geehrte radioaktiven Damen und Herren: Invention of the Neutrino in a letter from Zuerich to Tuebingen on December 4th, 1930: Conservation of Energy and Angular momentum.
FAESSLER; Trento 2011
History of the Neutrinos
• 1930 Pauli‘s invention of the neutrino • 1955 Reines and Cowen detection of the electron neutrino n e • 1962 Brookhaven; detection of muon neutrino n m • 2000 Fermi Lab; detection of tau neutrino n t • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2 nbb decay • 1986 Santa Barbara detection of 2 nbb • 20xx Detection of 0 nbb decay ?
decay FAESSLER; Trento 2011
Reines and Cowen at the Neutrino Experiment (at Savannah River Reactor) Fissions of 235 92 Uranium 143 rich fragments produces neutron . Beta decay: n p + e + n e c
History of the Neutrinos
• 1930 Pauli‘s invention of the neutrino • 1955 Reines and Cowen detection of the electron neutrino n e • 1962 Brookhaven; detection of muon neutrino n m p m + n c m ; n c m + p n + m + (no: e + ) • 2000 Fermi Lab; detection of tau neutrino n t • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2 nbb decay • 1986 Santa Barbara: 2 nbb decay by Caldwell • 20xx Detection of 0 nbb decay ?
FAESSLER; Trento 2011
1. Neutrino properties: What is the Mass of the Neutrino ?
m n e Mass measurement in the single beta decay n m and n t ?
S i m n i from cosmology m n e from the neutrinoless double beta decay FAESSLER; Trento 2011
T e [keV] (T e - Q) [eV] antineutrino For the Triton
Mass of the Electron Neutrino?
Tritium decay (Mainz + Troitsk)
With: FAESSLER; Trento 2011
Upper Limit of the Neutrino Mass:
< (2.2 eV)
2
; 95% conf. limit
5 % 95 % 0 (2.2 eV) 2 m nb 2 FAESSLER; Trento 2011
KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe FAESSLER; Trento 2011 A dinosaur on trip
Mass of
n m
(Paul Scherrer Institut 1996):
FAESSLER; Trento 2011
Mass of tau Neutrino ARGUS
(DESY Hamburg) e + + e t + + t ; m nt
Neutrino Mass from Astrophysics: Hubble law: v = H 0 *Distance = h *100 [km/(sec*Mpc)] *Distance [Mpc] = 71[km/(sec*Mpc)]*Distance [Mpc]; h=0.71
; Hubble Constant: H 0 = 71 [km/sec*Mpc] FAESSLER; Trento 2011
k = 2 p / l [(h=0.71)/ Mpc]
W 0 = 1.0 W L = 0.66 W b = 0.04
H 0 = 72 n s W n = 0.94 = 0 0.01
FAESSLER; Trento 2011
W 0 = 1.0 W L = 0.66 W b = 0.04
H 0 = 72 n s W n = 0.94 = 0.05
0.01
FAESSLER; Trento 2011
W 0 = 1.0 W L = 0.66 W b = 0.04
H 0 = 72 n s W n = 0.94 = 0.25
0.01
FAESSLER; Trento 2011
FAESSLER; Trento 2011
• WMAP = Wilkinson Microwave Anisotropy Probe.
• ACBAR = Arcminute Cosmology Bolometer Array Receiver (Berkeley) • CBI = Cosmic Background Imager (CALTEC) • 2dFGRS = 2 degree Field Galaxy Redshift Survey FAESSLER; Trento 2011
FAESSLER; Trento 2011
Page 1
2. The See-Saw Model
Diagonalise the matrix: FAESSLER; Trento 2011
p
3. The Single Beta Decay
e n c p e n W 1/(q 2 – M W 2 ) n FAESSLER; Trento 2011 -1/( M W 2 ) d (r 12 ) n
FAESSLER; Trento 2011 Page 17
4. Neutrino Mass from Neutrinoless Double Beta Decay • The neutrinoless Double Beta Decay is forbidden in the Standard Model. Allowed in GUT‘s and SUSY. It determines the absolute mass of Majorana Neutrinos. • Matrix elements as important as the data.
• Practically all Grand Unified Theories and Supersymmetry request massive Majorana Neutrinos FAESSLER; Trento 2011
O νββ -Decay (forbidden in Standard Model)
P Left n P ν Left n Phase Space 10 6 x 2 νββ
only for massive Majorana ν = ν c Neutrinos FAESSLER; Trento 2011
GRAND UNIFICATION
Left-right Symmetric Models SO(10) Majorana Mass: FAESSLER; Trento 2011
e P ν n P e ν L/R l/r n
2*2*2 = 8 posibilities FAESSLER; Trento 2011
e p n n p e L/R n
W
l/r n
l/r n P ν
FAESSLER; Trento 2011
P n l/r light ν heavy N Neutrinos
8x8x2 = 128 contributions
Theoretical Description of Nuclei: Vadim Rodin, Fedor Simkovic, Amand Faessler, Saleh Yousef, D.-L. Fang
0 + 0 k k k 0 + 1 + 2 νββ e 1 P ν n P n e 2 E k E i 0 +
FAESSLER; Trento 2011
Neutrinoless Double Beta Decay Probability FAESSLER; Trento 2011
5. The best choice: Quasi-Particle Random Phase Approximation (QRPA) and Shell Model
QRPA starts with Pairing:
FAESSLER; Trento 2011
Effective Majorana Neutrino-Mass for the 0 nbb Decay Tranformation from Mass to Flavor Eigenstates
CP
Time reversal
CPT = I
FAESSLER; Trento 2011
FAESSLER; Trento 2011
FAESSLER; Trento 2011 Page 25b
2011 FAESSLER; Trento 2011
From Dirac to Majorana Neutrinos DIRAC NEUTRINOS: Majorana Neutrinos : FAESSLER; Trento 2011
Neutrino Masses
• Single Beta Decay (Mainz, Troisk) < 2.2 [eV] • Double Beta Decay Majorana Mass (Tübingen): < 0.27 [eV] • Astophysics: S = m 1 + m 2 + m 3 < 0.17 to 2.0 [eV] Depends on Cosmological models (Hannestad) FAESSLER; Trento 2011
FAESSLER; Trento 2011 Page 26
FAESSLER; Trento 2011
• Solar: • Atmospheric: • Reactor FAESSLER; Trento 2011
Results from Oscillations:
No Hierarchy, no absolute Mass Scale
Fogli, Lisi, Marrone, Palazzo: Prog. Part. Nucl. Phys. 57(2006)742; Data 2011
(Bild) Sequence 1-2 fixed by oscillations in the sun and in vacuum. No oscillations 13 for solar neutrinos observed,
Effective Majorana Neutrino-Mass for the 0 nbb Decay Tranformation from Mass to Flavor Eigenstates
CP
Time reversal
CPT = I
CP = T= K FAESSLER; Trento 2011
Normal Hierarchy: Double Beta Decay Majorana Mass m bb versus lowest mass m 1
Inverted Hierarchy: Double Beta Decay Majorana Mass m bb versus lowest mass m 3 FAESSLER; Trento 2011
6. Different Methods for the 0 nbb -Matrix Elements for the Light Majorana Neutrino Exchange .
A. Escuderos, A. Faessler, V. Rodin, F. Simkovic, J. Phys. G37 (2010) 125108; arXiv: 1001.3519 [nucl-th] • Quasi-Particle Random Phase Approximation (QRPA; Tübingen).
• Shell Model (Strasbourg-Madrid).
• Angular Momentum Projected Hartee-Fock Bogoliubov (Tuebingen; P. K. Rath et al.).
• Interacting Boson Model (Barea and Iachello).
Amand Faessler, Tuebingen
Neutrinoless Double Beta Decay Probability FAESSLER; Trento 2011
a) QRPA all the Ring diagrams: Ground State (Exercise IV.5): 0, 4, 8, 12 , … quasi particles (seniority) b) The Shell Model Ground state: 0, 4, 6, 8, ….
Problem for SM: Size of the Single Particle Basis .
Amand Faessler, Tuebingen
Additive Contributions of 0, 4, 6, … Quasi-Particle States in the SM (Poves et al.).
128 Te Not in QRPA 82 Se Increasing Admixtures in the Ground State Amand Faessler, Tuebingen
Basis Size Effect for 82 Se 82 Kr on the Neutrinoless Double Beta Decay
.
4levels (Shell Model): 1p3/2, 0f5/2, 1p3/2, 0g9/2 4levels: Ikeda Sum rule 50 %; 5 levels: 60 % 6levels: 0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2 9levels:0f7/2, 1p3/2, 0f5/2, 1p3/2, 0g9/2, 0g7/2, 1d5/2, 2s1/2, 1d3/2 Amand Faessler, Tuebingen
GT Contrib. of different Angular Momenta Neutron Pairs to the 0 nbb Decay.
A Comparison QRPA (TUE) and Shell Model (Madrid) with the same Basis. Amand Faessler, Tuebingen 82 Se ; 2p 3/2 , 1f 5/2 , 2p 1/2 , 1g 9/2 130 Te; 1g 7/2 , 2d 5/2 , 2d 3/2 , 3s 1/2 ,1h 11/2
Contributions of different Angular Momentum and Parity Neutron Pairs to the Matrix Elements of 0 nbb Decay in QRPA for 76 Ge , 100 Mo and 130 Te. Amand Faessler, Tuebingen QRPA QRPA
Contribution of Higher Angular Momentum Pairs in Projected HFB.
HFB 0 bbn Only even Angular Momentum Pairs with Positive Parity can contribute. IBM: = 0 + and 2 + Pairs Amand Faessler, Tuebingen
IBM: Lowest Order Mapping (LO) . A p (j) and B p (j, j‘) by equating matrix elements in Fermion and Boson representation.(Tabulated by Barea and Iachello table XVII Phys. Rev. C79 (2009) 044301
Next to Lowest Order Mapping (NLO) Fermions Bosons 76 Ge 76 Se Lowest Order is enough
Neutrinoless Double Beta Decay Probability FAESSLER; Trento 2011
QRPA (TUE), Shell Model
IBM2
, PHFB, PHFB+GCM(
b
)
QRPA; RQRPA; 3 Basis Sets; g A =1.00 1.25; Bonn+Argonne; 2 Short Range Correlations Amand Faessler, Tuebingen
7. Can one measure with Charge Transfer Reactions the 0 nbb Fermi Matrix Element? (V. Rodin and A. Faessler, Phys.Rev. C80(2009)041302; Prog. Part. Nucl. Phys. 66 (2011) 441) Fermi and Gamow-Teller 0 nbb Transition Operator with Closure FAESSLER; Trento 2011
Fermi and Gamow-Teller 0 nbb Transition Operator with Closure 0 nbb Transition Matrix Element with Closure Relation: Amand Faessler, Tuebingen
Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS> Isotensor force needed: T T-2; Coulomb Interaction 0 + |DIAS> = |T, T-2> T 0 + |IAS> = |T, T-1 > T T |g.s.
i >=|0 i + > |g.s.
f >=|T-2,T-2> + e |DIAS>
Gamow Teller Strength not concentrated in one State broad Resonance.
Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0 Gamow-Teller: g A ( s*s ) |S=0> = - g A S=0 3 |S=0> Fermi (no spin dep.): g V |S=0> = 1 |S=0> Shell Model for Fermi ~ (1/5) of QRPA Amand Faessler, Tuebingen
Fermi 0
nbb
Transition Operator (Vadim Rodin)
Amand Faessler, Tuebingen
FAESSLER; Trento 2011 Page 38
Transition Matrix Elements for Fermi Transitions:
First Leg Second Leg 0 + T 0 + T |IAS> = |T, T-1> Exp. (d, 2 He): Frekers; Sakai; Zegers |g.s.
i > =|T, T> |g.s.
f > = |T-2,T-2> + e |DIAS>
8. How to find the Leading Mechanism for the o
nbb
?
• Light left handed Majorana n Exchange • Heavy left handed Majorana n Exchange • Heavy right handed Majorana n • SUSY Lepton Number Violating Mechanism.
Amand Faessler, Tuebingen
d
GUT: Light and Heavy left handed Majorana Neutrino
u
Exchange
W L n kM mass e U n ek=1,2,3 Page 41 e W L d u Amand Faessler, Tuebingen
Different Mechanisms for the 0 nbb FAESSLER; Trento 2011
Coefficients for the different Mechanisms FAESSLER; Trento 2011
SUSY: R-Parity Breaking Lepton Number-Violating Minimal Supersymmetric Model Super-fields: Amand Faessler, Tuebingen
Gluino Exchange; Strong Interaction; Gluinos couple to Quarks and SUSY-Quarks.
l ‘ ijk L L i Q L j D R k FAESSLER; Trento 2011
Transition Probability prop to Inverse Half Life; SUSY Contribution
l
‘
111
.
Dominance of Gluino echange in short range part assumed.
Similar expression for Dominance of Neutralino exchange. Amand Faessler, Tuebingen
Two leading non-interfering Mechanisms: Light Majorana and Heavy R Neutrino i = different nuclei, e.g. 76 Ge, 100 Mo, 130 Te; | h| 2 > 0 and our matrix element for g A = 1.25 Due to ratios only minimal changes for g Amand Faessler, Tuebingen A =1.00
Two interfering Mechanisms: Light Majorana and Heavy Left Neutrino Light Majorana-Neutrino and Gluino or Neutralino exchange .
Three different transitions needed, e.g. 76 Ge, 100 Mo, 130 Te, to determine the three parameters .
Amand Faessler, Tuebingen
9. HD claim for Detection of 0 n DBD
hep-ph/0512263
Klapdor and coworkers in Heidelberg claim, they have detected 0
nbb
of 76 Ge
Source = Detector
10.9 kg - ( 86% from 8% nat.) 76 Ge Gran Sasso Laboratory (Italy) Spectrum with 71.7 kg •y FAESSLER; Trento 2011
Neutrino Mass from
0nbb
Experiment Klapdor et al. 76 Ge Mod. Phys. Lett. A21,1547(2006) ; T(1/2; 0
nbb
) = (2.23 +0.44 -0.31) x 10 25 years; 6
s
•
Matrix Elements: QRPA Tuebingen
n
)> = 0.24 [eV] (exp+-0.02; theor+-0.01) [eV]
Amand Faessler, Tuebingen
1) Summary
Comparing four different approaches for the 0nbb matrix elements: a. Shell model only small basis; violates the Ikeda sum rule by 50 to 60%. b. Interacting boson Model: only s (0 + ) and d (2 + ) pairs.
c. Projected Hartee Fock Bogoliubov: Only 0 + pairs . d. QRPA large basis; fulfills Ikeda sum rule; realistic forces. Amand Faessler, Tuebingen
2) Summary
Search for the Leading Mechanism One Leading Mechanism: Determine the h 1 ( m n ?) in two systems. Is it the same? Two leading non-interfering mechanisms: Determine h 1 and h 2 in three systems Two interfering mechanisms: Determine h 1 , h 2 and the relative phase theta in three nuclei and
THE END
Amand Faessler, Tuebingen
7. Can one measure with Charge Transfer Reactions the 0 nbb Fermi Matrix Element? (V. Rodin and A. Faessler, Phys.Rev. C80(2009)041302; Prog. Part. Nucl. Phys. 66 (2011) 441) Fermi and Gamow-Teller 0 nbb Transition Operator with Closure FAESSLER; Trento 2011
Fermi and Gamow-Teller 0 nbb Transition Operator with Closure 0 nbb Transition Matrix Element with Closure Relation: Amand Faessler, Tuebingen
Fermi Strength concentrated in the Isobaric Analogue State |IAS> and Double Isobaric Analogue State |DIAS> Isotensor force needed: T T-2; Coulomb Interaction 0 + |DIAS> = |T, T-2> T 0 + |IAS> = |T, T-1 > T T |g.s.
i >=|0 i + > |g.s.
f >=|T-2,T-2> + e |DIAS>
Gamow Teller Strength not concentrated in one State broad Resonance.
Fermi Transition: narrow Gamow-Teller: Main Contrib. Neutron Pairs: T =1, L=0 Gamow-Teller: g A ( s*s ) |S=0> = - g A S=0 3 |S=0> Fermi (no spin dep.): g V |S=0> = 1 |S=0> Shell Model for Fermi ~ (1/5) of QRPA Amand Faessler, Tuebingen
Fermi 0
nbb
Transition Operator (Vadim Rodin)
Amand Faessler, Tuebingen
Transition Matrix Elements for Fermi Transitions:
First Leg Second Leg 0 + T 0 + T |IAS> = |T, T-1> Exp. (d, 2 He): Frekers; Sakai; Zegers |g.s.
i > =|T, T> |g.s.
f > = |T-2,T-2> + e |DIAS>