1. Majorana Nature of Massive ’s and 02 Decays
Zhi-zhong Xing (IHEP & UCAS, Beijing)
“Majorana returns”
—— Frank Wilczek
Nature Physics 2009
Majorana zero mode
Majorana neutrinos
New form of matter
中科大交叉学科理论研究中心，2017年03月10日

2. Recent effects in China
arXiv: , 7 March 2017
复旦大学2017年6月28日至30日 (上海交通大学PANDAX-3)
International Workshop on Neutrinoless Double Beta Decay Physics

3. Beta decays before 1930 What to do? Energy crisis = New physics ?
Part A
Beta decays before 1930
2-body
decays
Energy crisis = New physics ?
What to do?
J. Chadwick 1914/C. Ellis

4. Two ways out?  giving up sth  adding in sth Part A
Niels Bohr
Wolfgang Pauli (1930)
Dears, what attitude do you take towards new physics ????
近来的几条乌龙: 中微子超光速、BICEPII引力波、750GeV玻色子。

5. Solvay 1933
Part A
Pauli sold his neutrino proposal to Fermi in this congress.
Paul Langevin

6. Fermi’s theory ★ Pauli’s idea: neutrinos
Part A
Fermi’s theory
Enrico Fermi assumed a new force for  decay by combining 3 new concepts:
I will be remembered for this paper.
Fermi in Italian Alps, Christmas 1933
★ Pauli’s idea: neutrinos
★ Dirac’s idea: creation of particles
★ Heisenberg’s idea: isospin symmetry

7. 1935: 22 decays
Part A
22 decay: certain even-even nuclei have an opportunity to decay to the 2nd nearest neighbors via 2 simultaneous  decays (equivalent to the decays of two neutrons).
necessary conditions:
arsenic
germanium
selenium
1935

8. 1937: Majorana ★ Theory of the Symmetry of Electrons and Positrons
Part A
★ Theory of the Symmetry of Electrons and Positrons
Ettore Majorana Nuovo Cim. 14 (1937) 171
1938年：自杀；逃往阿根廷，并在那里隐姓埋名地生活了二十几年；遁入空门；遭到绑架或杀害，以阻止他加入制造原子弹的项目；沦为乞丐；..…
Enrico Fermi (1938):

9. Part A
If this is the case, …
22
22
02
02

10. 1939: 02 decays
Part A
A 02 decay can happen if massive ’s have the Majorana nature (Wendell Furry 1939)
germanium
selenium
Lepton number violation
CP-conserving process
exchange
background
22
02

11. Nuclear matrix elements
Part A
Unfortunately, nuclear matrix elements can be calculated only based on some models which describe many-body interactions of nucleons in nuclei. Since different models focus on different aspects of nuclear physics, large uncertainties (a factor of 2 or 3) are unavoidable.

12. Half-life
Part A
Comparing the 90% C.L. experimental lower limits on the half-life of a 0-decaying nuclide with the corresponding range of theoretical prediction, given a value of 0.1 eV for the effective Majorana neutrino mass term (Bilenky and Giunti, arXiv: ).

13. The reverse is also true Motivation of this talk
Part A
Schechter-Valle THEOREM (1982): if a 02 decay occurs, there must be an effective Majorana mass term.
Bruno Pontecorvo’s Prediction
Motivation of this talk
to look at the effective 02 mass in a geometric way;
to show the effects of Majorana phases in a 3-d graph;
to look into the well in the normal mass ordering case;
to explain why we have to go beyond the 02 decays.

14. Oscillation data Part B
F. Capozzi et al (2014) —— the standard parametrization:
Favored by
Super-K
T2K
NOA
at 2 level.
It should be taken seriously!

15. The latest news
Part B
NOA (arXiv: , 9 March 2017):
my bet

16. The effective mass Part B The effective mass
Vissani Graph
Maury Goodman asks:
An intelligent design?
How possible to fall into the well?
A dark well = catastrophe?
Vanishing 02 mass?
Xing, hep-ph/
The structure of the well?
Role of Majorana phases?

17. 3-d description Part B insensitive sensitive
Lower bound: blue; upper bound: light orange. 3 inputs of neutrino oscillation data (Xing, Zhao, Zhou, arXiv: )

18. Contour of the bottom Part B
Let us understand the champagne-bottle profile of the effective 02 mass term in the normal hierarchy case:
Contour
Bottom of the Well:
not an exact ellipse
The dark well in the normal hierarchy

19. A bullet structure Part B EXTREMUM = 0 ~ 1 meV
Best-fit inputs of current data
Xing, Zhao, arXiv:

20. The threshold or throat
Part B
EXTREMUM ×

21. To fall into the well Part B The three-dimensional parameter space of
Take it easy!
It is difficult to fall into the well!
Vissani Graph

22. Model building? Part B Why the relationship is reasonable?
Remember in the quark sector as done by
S. Weinberg
H. Fritzsch
F. Wilczek + A. Zee
1977
The effective Majorana neutrino mass matrix (Xing, Zhao, )
Predictions, thanks to the - reflection symmetry:
consistent with current data!

23. Part B A generic Majorana neutrino mass term reads as follows:
Under - reflection, the mass term is
Invariance of this transformation:

24. Coupling-rod diagram Part C NH NH NH IH external intersect containedor IH
Z.Z.X., Y.L. Zhou, arXiv:

25. Maximum + Minimum Part C Maximum in either hierarchy:
The above diagrams allow us to obtain the maximum/minimum limit:
Maximum in either hierarchy:
Minimum in normal hierarchy (1) :
Minimum in normal hierarchy (2):
Minimum in inverted hierarchy:

26. Occam’s razor Part C Fewer facial parameters
Entities must not be multiplied beyond necessity.
Numerical illustration
ZZX, Y.L. Zhou, 2015

27. Part C
New physics
In the presence of a kind of new physics, we denote:
2 very simple configurations are illustrated on the left-hand side:
In the above Occam’s razor case, a pentagon can be simplified to a quadrangle.

28. What new physics?
Part C
Type (A): NP directly related to extra species of neutrinos.
Example 1: heavy Majorana neutrinos from type-I seesaw
In most cases the heavy contribution is negligible
Example 2: light sterile neutrinos from LSND etc
In this case the new contribution might be constructive or destructive
Type (B): NP has little to do with the neutrino mass issue.
SUSY, Left-right, and some others that I don’t understand

29. SUSY? Part C Example (A): R-parity violation Example (B):
R-parity conservation
H.V. Klapdor, hep-ex/

30. Possible effects Part C New physics effects:
Lower bound: blue; upper bound: light orange. Clearer sensitivities to mass and phase parameters (Xing, Zhao, Zhou, arXiv: )
It is hard to
tell much

31. YES or NO? YES or I don’t know! Part D
QUESTION: are massive neutrinos the Majorana particles?
One might be able to answer YES through a measurement of the 02 decay or other LNV processes someday, but how to answer with NO?
YES or
I don’t know!
The same question: how to distinguish between Dirac and Majorana neutrinos in a realistic experiment?
Answer 1: The 02 decay is currently the only possibility.
Answer 2: In principle their dipole moments are different.
Answer 3: They show different behavior if nonrelativistic.

32. Electromagnetic properties
Part D
Electromagnetic properties
Without electric charges, neutrinos have electromagnetic interactions with the photon via quantum loops.
Given the SM interactions, a massive Dirac neutrino can only have a tiny magnetic dipole moment:
A massive Majorana neutrino can not have magnetic & electric dipole moments, as its antiparticle is itself.
Proof: Dirac neutrino’s electromagnetic vertex can be parametrized as
Majorana neutrinos
intrinsic property of Majorana ’s.

33. Transition dipole moments
Part D
Transition dipole moments
Both Dirac & Majorana neutrinos can have transition dipole moments (of a size comparable with _) that may give rise to neutrino decays, scattering with electrons, interactions with external magnetic field & contributions to  masses. (Data: < a few  10^-11 Bohr magneton).
neutrino decays
scattering

34. Nonrelativistic CB Part D
When T ~ 1 MeV after the Big Bang, the neutrinos became decoupled from thermal plasma, formed a  background in the Universe. Today the relic neutrinos are nonrelativistic.
Temperature today
Mean momentum today
At least 2 ’s cold today
Non-relativistic ’s!
Relic neutrino capture on -decaying nuclei
no energy threshold on incident ’s mono-energetic outgoing electrons
(Irvine & Humphreys, 83)
1962

35. Towards a real experiment?
Part D
已有二十余篇论文讨论该可能性
PTOLEMY
prototype
★ first experiment
★ 100 g of tritium
★ graphene target
★ planned energy resolution 0.15 eV
★ CB capture rate
D = Dirac
M = Majorana
PTOLEMY Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield (Betts et al, arXiv: )

36. oscillations?    Part D
Comparison: neutrino-neutrino and neutrino-antineutrino oscillation experiments.
neutrino  neutrino
neutrino  antineutrino
Feasible and successful today! Unfeasible, a hope tomorrow?
Sensitivity to CP-violating phase(s):   

37. Remarks Bottom-up Top-down Part D Theories Experiments
Without information on the nature of massive neutrinos (Majorana or not) and all the CP-violating phases, one will have no way to establish a full theory of  masses and flavor mixing. Give 02 a chance!
Experiments
Theories
Bottom-up
Top-down
02

38. More LNV processes Part D
To identify the Majorana nature, CP-violating phases and new physics it is imperative to observe the 02 decays and other lepton-number-violating processes (e.g., neutrino-antineutrino oscillations, the relic neutrino background, doubly-charged Higgs decays). None is realistic

39. Concluding remark Part D
All of us expect the massive neutrinos to be the Majorana particles. If this expectation comes true someday thanks to the 02 decay, then we will be required to have some right/good ideas to probe the Majorana phases.
C.S. Wu: It is easy to do the right thing once you have the right ideas.
L.C. Pauling: The best way to have a good idea is to have a lot of ideas.