Why did Ettore Majorana invent the Majorana Neutrino

Why did Ettore Majorana invent the „Majorana Neutrino“ and is the Neutrino really „Majorana“? Amand Faessler University of Tuebingen, GERMANY Messina 3 -6 October 2018

1930 Beta-Spectrum 1930 Beta-Decay: Z Z Z+1 + e Z+1 Wolfgang Pauli: On December 4 th. 1930: Letter from Zuerich to Tuebingen: Sehr geehrte radioaktiven Damen und Herren, Dear radioactive Ladies and Gentelmen, Z (, N) Z+1 (, N-1) + e- + nc Electron Energy Pauli: „The Neutrino can not be measured. “ Amand Faessler, Messina

Detection of the Neutrinos: • 1956 Reines and Cowan : Electron-Neutrinos • 1962 Steinberger : Myon-Neutrinos • 2000 DONAT Collaboration : Tau-Neutrinos • 1995 on: Neutrino Oscillations Neutrinos have a mass • Helicity not good for massive Neutrinos. HELICITY≠ vneutrino left handed CHIRALITY Vanti-n right handed Amand Faessler, Messina Spin

Why did Ettore Majorana invent the „Majorana Neutrino“? 1933 -1937: Ettore Majorana lives secluded in Rome (See talk of E. Recami) 1933 – 1937 lived practically alone in an appartment of the Majorana family in Rome, curtains closed and only his physics friends send him somtimes a hair cutter. He publishes no paper. 1937 competition for three theoretical chairs short list: (Chairman of committee: Enriquo Fermi *1901, +1954 ) 1. Gian Carlo Wick (Palermo => Turino, *1909 +1992) 2. Giulio Racah (Pisa => Israel. *1909, +1965) 3. Giovanni Gentile (junior, *1906 +1942; Cagliari/Sardinia) Father Minister of Mussolini (Castelveterano) Amand Faessler, Messina

Ettore Majorana (See talk of Erasmo Recami) Surprising application for a chairs by Ettore Majorana: „Chiara fama“ (due to the undoubtable good reputation) → Naples For the competition has to write an scientific article: „La Teorica simmetrica dell‘ electrone e del positrone“ Nuovo Cimento , Vol. 14, 1937, pp. 171 – 184. Electron different from Positron (Dirac Particle), but Ettore Majorana: Neutrino can be identical with antineutrino: Majorana Neutrino Amand Faessler, Messina

Ettore Majorana in Naples Oct. 1937 Script of the Lecture 25. 1. XVI Copy from Aldo Covello 25. Januar 1938 in Napels 26. March 1938 disappeared without a trace Ship: Napels→ Palermo → Napels ? ? Amand Faessler, Messina

Can one distinguish experimentally between Dirac and Majorana Neutrinos? Nucleus: Z+1, A Electron Proton P Antineutrino Spin parallel n P n neutron Nucleus: Z, A Thesis: Maria Goeppert. Mayer 1935 Goettingen: Two-Neutrino Double-Beta Decay. How can we proof, that the Neutrino is „Majorana“?

Neutrinoless Double Beta-Decay (Lepton Number and Helicity ) forbidden in the Standard Model. P P Left Energy difference 76 Ge 76 Se: Q = 2038 ke. V Phase Space ν Left n 106 x 2νββ n Se Only possible for massive Majorana Neutrinos. Amand Faessler, Messina

GERDA 76 Ge 76 Se (Heidelb. +Muenchen+Tueb. ) in Gran Sasso, Jan. 2018; Qbb = 2038 ke. V Sum of Energy of the two Electrons [ke. V] 90 % Confidence Limit: T 0 n ½ > 8 x 1025 [years]; Background: 10 -3 counts/(ke. V*kg*year) GERDA Collaboration: Agostini et al. Phys. Rev. Lett. 120 (2018) 132503 Amand Faessler, Messina

CUORE 130 Te 130 Xe (Status 2018, Milano, Roma Sapienza, Zaragoza) in Gran Sasso; Qbb = 2528 ke. V 60 Co 2528 ke. V Sum of Energies of the two electrons [ke. V] 90 % Confidence Limit : T 0 n 1/2 > 2. 7 x 1024 [years]

Majorana Fermions in Solid State Physics S. R. Elliott and M. Franz: Rev. Mod. Phys. 87 (2015) 137 Supra(vk)2 conductor: 1 Electron Occupation (vk)2 =1 -(u-k)2 Fermi Surface Fermi-Energy vk 2 = u-k 2 = 1/2 Sharp „Fermi Surface“ Diffuse „Fermi Surface„ u 2 + v 2 = 1 Electron Energy Quasi-Particle: a+k = uk c+k + vk c-k ; ak = uk c-k + vk c+k Quasi-Particle = Quasi-Hole near/at the Fermi Surface Amand Faessler, Messina

New Commutative Properties: Winding Number A Novel Quantum-Mechanical Behavior Bosons Fermions Majorana (topologic, chiral) Fermions Non-Abelian Anyions Amand Faessler, Messina

Quantum Computer more stable qubits due to topological (chiral) winding number. • q-bits = q; Binary code. • |0> [= q = 0] winding number zero ; • |1> [= q = 1] winding number 1 q = a |0> + b |1>; 2 a + 2 b =1 Quanten–Computer: |q 6 q 5 q 4 q 3 q 2 q 1> all numbers from 0 to 63 Amand Faessler, Messina

Summary of the „Majorana Neutrinos“ • Dirac-Neutrinos: Neutrino different from Antineutrino • Majorana-Neutrino: Neutrino = Antineutrino • Neutrino Oscillations Neutrinos have a mass (helicity ? ? ? ) (Grand Unified Theories) require as a rule Majorana Neutrinos. • Neutrinoless Double Beta Decay only possible for massive Majorana Neutrinos. Not yet found. • Neutrinoless Double Beta Decay allows to determine the mass of the Majorana Neutrino with the matrix element. • Majorana Fermions in supraconducting solids. Hope: Topolocical Winding Number more stable q-bits? Amand Faessler, Messina The END