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

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

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 1920-1927

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。

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

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

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

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):

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

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

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.

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:1411.4791).

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.

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!

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

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/0305195 The structure of the well? Role of Majorana phases?

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

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

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

The threshold or throat Part B EXTREMUM ×

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

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, 1612.08538) Predictions, thanks to the - reflection symmetry: consistent with current data!

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

Coupling-rod diagram Part C NH NH NH IH external intersect contained or IH Z.Z.X., Y.L. Zhou, arXiv:1404.7001

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:

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

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.

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

SUSY? Part C Example (A): R-parity violation Example (B): R-parity conservation H.V. Klapdor, hep-ex/9901021

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:1504.05820) It is hard to tell much

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.

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.

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

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

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:1307.4738)

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):   

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

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

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.