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Majorana Nature of Massive  ’s and 02 Decays

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

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Majorana Nature of Massive  ’s and 02 Decays

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  1. Majorana Nature of Massive ’s and 02 Decays Zhi-zhong Xing (IHEP & UCAS, Beijing) “Majorana returns” —— Frank Wilczek Nature Physics 2009 Majorana neutrinos New form of matter Majorana zero mode 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:1703.01877, 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. Part A Beta decays before 1930 Energy crisis = New physics? 2-body decays What to do? J. Chadwick 1914/C. Ellis 1920-1927

  4. Part A Two ways out?  giving up sth  adding in sth Wolfgang Pauli (1930) Niels Bohr 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. Part A Solvay 1933 Pauli sold his neutrino proposal to Fermi in this congress. Paul Langevin

  6. 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. Part A 1935: 22 decays 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. Part A 1937: Majorana ★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. Part A 1939: 02 decays 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 22 background 02

  11. Part A Nuclear matrix elements 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. Part A Half-life 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:1411.4791).

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

  15. Part B The latest news NOA (arXiv:1703.03328, 9 March 2017): my bet

  16. Part B The effective mass The effectivemass 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/0305195 • The structure of the well? • Role of Majorana phases?

  17. Part B 3-d description sensitive insensitive Lower bound: blue; upper bound: light orange. 3 inputs of neutrino oscillation data (Xing, Zhao, Zhou, arXiv:1504.05820)

  18. Part B Contour of the bottom 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. Part B A bullet structure EXTREMUM = 0 ~ 1 meV Best-fit inputs of current data Xing, Zhao, arXiv:1612.08538

  20. Part B The threshold or throat EXTREMUM ×

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

  22. Part B Model building? 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, 1612.08538) 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. Part C Coupling-rod diagram NH NH external intersect contained NH or IH Z.Z.X., Y.L. Zhou, arXiv:1404.7001

  25. Part C Maximum + Minimum 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. Part C Occam’s razor 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. Part C What new physics? 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. Part C SUSY? Example (A): R-parity violation Example (B): R-parity conservation H.V. Klapdor,hep-ex/9901021

  30. Part C Possible effects New physics effects: Lower bound: blue; upper bound: light orange. Clearer sensitivities to mass and phase parameters (Xing, Zhao, Zhou, arXiv:1504.05820) It is hard to tell much

  31. Part D YES or NO? 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. Part D Electromagnetic properties Without electric charges, neutrinos have electromagnetic interactions with the photon via quantum loops. Given the SM interactions, a massive Diracneutrino can only have a tiny magnetic dipole moment: A massive Majorananeutrino can nothave 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. 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. Part D Nonrelativistic CB 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 Relic neutrino capture on -decaying nuclei Mean momentum today At least 2 ’s cold today Non-relativistic ’s! 1962 (Irvine & Humphreys, 83) no energy threshold on incident ’smono-energetic outgoing electrons

  35. Part D Towards a real experiment? 已有二十余篇论文讨论该可能性 prototype PTOLEMYPrinceton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield (Betts et al, arXiv:1307.4738) ★CB capture rate D = Dirac M = Majorana ★ first experiment ★100 g of tritium ★graphene target ★planned energy resolution 0.15 eV PTOLEMY

  36. Part D oscillations? 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. Part D Remarks 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! Theories 02 Bottom-up Top-down Experiments

  38. Part D More LNV processes 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. Part D Concluding remark 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.

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