University of Tuebingen, 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

Amand Faessler, Messina 1930 Beta-Spectrum : 1930 Beta-Decay Z Z  Z+1 + e- Z+1 Wolfgang Pauli: On December 4th. 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. vneutrino left handed Spin HELICITY≠CHIRALITY Vanti-n right handed Spin Amand Faessler, Messina

Amand Faessler, Messina 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 (Chairman of committee: Enriquo Fermi *1901, +1954 ) short list: 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 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 Thesis: Maria Goeppert- Mayer1935 Goettingen: Two-Neutrino Double-Beta Decay. Proton P P Electron Antineutrino Spin parallel n n neutron Nucleus: Z, A How can we proof, that the Neutrino is „Majorana“?

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

Amand Faessler, Messina GERDA 76Ge  76Se (Heidelb.+Muenchen+Tueb.) in Gran Sasso, Jan. 2018; Qbb = 2038 keV 2038 keV Sum of Energy of the two Electrons [keV] 90 % Confidence Limit: T0n ½ > 8x1025 [years]; Background: 10-3 counts/(keV*kg*year) GERDA Collaboration: Agostini et al. Phys. Rev. Lett. 120 (2018) 132503 Amand Faessler, Messina

CUORE 130Te  130Xe (Status 2018, Milano, Roma Sapienza, Zaragoza) in Gran Sasso; Qbb = 2528 keV 60Co 2528 keV Sum of Energies of the two electrons [keV] 90 % Confidence Limit : T0n1/2 > 2.7x1024 [years]

Amand Faessler, Messina Majorana Fermions in Solid State Physics S. R. Elliott and M. Franz: Rev. Mod. Phys. 87 (2015) 137 Fermi Surface Fermi-Energy vk2 = u-k2 = 1/2 Supra- conductor: (vk)2 Sharp „Fermi Surface“ Diffuse „Fermi Surface„ u2 + v2 = 1 1 Electron Occupation (vk)2 =1-(u-k)2 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

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>; a2 + b2 = 1 Quanten–Computer: |q6 q5 q4 q3 q2 q1>  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? The END Amand Faessler, Messina