Neutrino Masses, Double Beta Decay, and Nuclear Structure in Astrophysics Research
This document explores the fascinating topics of neutrino properties, the see-saw model, and the mechanisms behind single and neutrinoless double beta decay. Developed during the Doctoral Training Program on "Neutrinos in Nuclear, Particle, and Astrophysics" at the ECT* in Trento, it highlights historical developments in neutrino research, including key discoveries and experimental milestones. Additionally, the theoretical frameworks such as the Quasi-Particle Random Phase Approximation (QRPA) and different competing mechanisms for neutrinoless decay are examined, with insights into their implications for understanding nuclear structure and astrophysics.
Neutrino Masses, Double Beta Decay, and Nuclear Structure in Astrophysics Research
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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 0nbb-Matrix element? 8. Competing Mechanisms for the 0nbb 9. The Heidelberg-Moscow data and the Neutrino Mass FAESSLER; Trento 2011
0. History of the Neutrinos • 1930 Pauli‘s invention of the neutrino • 1955 Reines and Cowen detection of the electron neutrino ne • 1962 Brookhaven; detection of muon neutrino nm • 2000 Fermi Lab; detection of tau neutrino nt • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay • 1986 Santa Barbara (Caldwell) detection of 2nbb. • 20xx Detection of 0nbb 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 ne • 1962 Brookhaven; detection of muon neutrino nm • 2000 Fermi Lab; detection of tau neutrino nt • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay • 1986 Santa Barbara detection of 2nbb decay • 20xx Detection of 0nbb decay ? FAESSLER; Trento 2011
Reines and Cowen at the Neutrino-Experiment (at Savannah River Reactor) Fissions of 23592 Uranium143 produces neutron rich fragments. Beta decay: n p + e- + nec FAESSLER; Trento 2011
History of the Neutrinos • 1930 Pauli‘s invention of the neutrino • 1955 Reines and Cowen detection of the electron neutrino ne • 1962 Brookhaven; detection of muon neutrino nm p- m- + ncm; ncm + p n + m+ (no: e+) • 2000 Fermi Lab; detection of tau neutrino nt • 1935 Göttingen, thesis of Maria Goeppert-Mayer theory of 2nbb decay • 1986 Santa Barbara: 2nbb decay by Caldwell • 20xx Detection of 0nbb decay ? FAESSLER; Trento 2011
1. Neutrino properties: What is the Mass of the Neutrino ? • mne Mass measurement in the single beta decay • nm and nt ? • Si mni from cosmology • mnefrom the neutrinoless double beta decay FAESSLER; Trento 2011
antineutrino For the Triton FAESSLER; Trento 2011 Te [keV] (Te - Q) [eV]
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 % (2.2 eV)2 0 mnb2 FAESSLER; Trento 2011
A dinosaur on trip KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe FAESSLER; Trento 2011
Mass of nm (Paul Scherrer Institut 1996): FAESSLER; Trento 2011
Mass of tau Neutrino ARGUS (DESY Hamburg) e+ + e- t+ + t-; mnt < 28 MeV by ALEPH mnt < 15 MeV together FAESSLER; Trento 2011
Neutrino Mass from Astrophysics: Density Distribution of Matter in the Universe (Power Spectrum of Matter Distribution) Hubble law: v = H0 *Distance = h*100 [km/(sec*Mpc)] *Distance [Mpc] = 71[km/(sec*Mpc)]*Distance [Mpc]; h=0.71; Hubble Constant: H0 = 71 [km/sec*Mpc] FAESSLER; Trento 2011
k = 2p/l [(h=0.71)/ Mpc] FAESSLER; Trento 2011
W0 = 1.0 WL= 0.66Wb= 0.04H0 = 72 ns = 0.94 Wn = 0 0.01 FAESSLER; Trento 2011
W0 = 1.0 WL= 0.66Wb= 0.04H0 = 72 ns = 0.94 Wn = 0.05 0.01 FAESSLER; Trento 2011
W0 = 1.0 WL= 0.66Wb= 0.04H0 = 72 ns = 0.94 Wn = 0.25 0.01 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
Page 1 FAESSLER; Trento 2011
2. The See-Saw Model Diagonalise the matrix: FAESSLER; Trento 2011
3. The Single Beta Decay p e nc p e -1/( MW2 )d(r12) W- 1/(q2 – MW2 ) n n n FAESSLER; Trento 2011
Page 17 FAESSLER; Trento 2011
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
Oνββ-Decay (forbidden in Standard Model) only formassive MajoranaNeutrinos ν = νc P P Left ν Phase Space 106x2νββ Left n n FAESSLER; Trento 2011
GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: FAESSLER; Trento 2011
P P ν e- e- ν L/R l/r 2*2*2 = 8 posibilities n n FAESSLER; Trento 2011
p p e- e- n n L/R l/r W n n P light ν heavy N Neutrinos P ν l/r n l/r 8x8x2 = 128 contributions n FAESSLER; Trento 2011
Theoretical Description of Nuclei: Vadim Rodin, Fedor Simkovic, Amand Faessler, Saleh Yousef, D.-L. Fang P k 0+ P e2 k 1+ e1 k 2- ν Ek n n Ei 0+ 0+ 0νββ 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 0nbb-Decay Tranformation from Mass to Flavor Eigenstates CP Time reversal CPT = I FAESSLER; Trento 2011
Page 25b FAESSLER; Trento 2011
2011 FAESSLER; Trento 2011
From Dirac to Majorana Neutrinos DIRAC NEUTRINOS: Majorana Neutrinos: FAESSLER; Trento 2011
Neutrino Masses • Single Beta Decay (Mainz, Troisk) • Double Beta Decay Majorana Mass (Tübingen): • Astophysics: S = m1 + m2 + m3 < 0.17 to 2.0 [eV] Depends on Cosmological models (Hannestad) < 2.2 [eV] < 0.27 [eV] FAESSLER; Trento 2011
Page 26 FAESSLER; Trento 2011
PMNS-Matrix Parameters 2011 Pontecorvo-Maki-Nakagawa-Sakata • Solar: • Atmospheric: • Reactor FAESSLER; Trento 2011
Results from Oscillations: No Hierarchy, no absolute Mass Scale (Bild) Fogli, Lisi, Marrone, Palazzo: Prog. Part. Nucl. Phys. 57(2006)742; Data 2011 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 0nbb-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 mbb versus lowest mass m1
Inverted Hierarchy: Double Beta Decay Majorana Mass mbb versus lowest mass m3 FAESSLER; Trento 2011
6. Different Methods for the 0nbb-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
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.). 128Te Not in QRPA 82Se Increasing Admixtures in the Ground State Amand Faessler, Tuebingen
