1. 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

2. 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

3. 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

4. Amand Faessler, Messina
Why did Ettore Majorana invent the „Majorana Neutrino“?
: Ettore Majorana lives secluded in Rome (See talk of E. Recami)
1933 – 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, )
short list: 1. Gian Carlo Wick (Palermo => Turino, * )
2. Giulio Racah (Pisa => Israel. *1909, +1965)
3. Giovanni Gentile (junior,* ; Cagliari/Sardinia)
Father Minister of Mussolini (Castelveterano)
Amand Faessler, Messina

5. 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

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

7. 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“?

8. 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

9. Amand Faessler, Messina
GERDA 76Ge  76Se (Heidelb.+Muenchen+Tueb.) in Gran Sasso, Jan. 2018; Qbb = 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)
Amand Faessler, Messina

10. 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]

11. 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

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

13. 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

14. 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