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Neutrino-Antineutrino Oscillation
Zhi-zhong Xing, IHEP, Beijing

---- Lepton Flavor Mixing ----

@the 16th Lomonosov Conference on Elementary Particle Physics@ 22 -- 28/08/2013, Moscow


Centenary of Pontecorvo
Theory of the Symmetry of Electrons and Positrons
Ettore Majorana
Nuovo Cim. 14 (1937) 171
Are massive neutrinos and antineutrinos identical or different ---- a fundamental puzzling question in particle physics.

2

Mesonium and Anti-mesonium
Bruno Pontecorvo
Zh. Eksp. Teor. Fiz. 33 (1957) 549 Sov. Phys. JETP 6 (1957) 429
If the two-component neutrino theory turned out to be incorrect and if the conservation law of neutrino charge didn't apply, then neutrino -antineutrino transitions would in principle be possible to take place in vacuum.


Great Imagination

3

A lesson learnt from the meson-antimeson oscillations:

Neutrino and antineutrino are massive. The lepton number is not conserved. A single family without flavor mixing.
Pontecorvo's original idea for the neutrino-antineutrino transitions


Flavor Mixing: Road Behind/Ahead
Quark mixing:

12

23

13



new physics ? ~ 40 years !

Experimental time scales??

13° 2°

0.2° 65°

Lepton mixing: (in general, we consider three Majorana neutrinos)

P 23 12 13 9° // ? ? ? new physics ? ~ 100 years ?

45° 34°


A Crucial Question

5

Question: what can we do to determine all the CP-violating phases in the PMNS matrix if the massive 's are someday identified to be the Majorana particles via a convincing measurement of the 0 decay?

Lepton number violation

CP-conserving process

OR just Dirac? How to know? No direct way!


Theorist's Concern
Theories

6

Warning: without information on all the CP-violating phases, one will have no way to establish a full theory of masses and flavor mixing.

Bottom-up

Top-down

Experiments


What to do (conceptually)?

7

The best approach (in principle): neutrino antineutrino oscillations.

neutrino neutrino Feasible and successful today!

neutrino antineutrino Unfeasible, a hope tomorrow?









In this talk, let's see how much neutrino-antineutrino oscillations can teach us about the fundamental properties of Majorana particles.


References
J. Bahcall, H. Primakoff, PRD 18 (1978) 3463

8

L.N. Chang, N.P. Chang, PRL 45 (1980) 1540
J. Schechter, J.W.F. Valle, PRD 23 (1981) 1666 L.F. Li, F. Wilczek, PRD 25 (1982) 143

J. Bernabeu, P. Pascual, NPB 228 (1983) 21
J.D. Vergados, Phys. Rept. 133 (1986) 1 P. Langacker, J. Wang, PRD 58 (1998) 093004

The Majorana phenomenology



A. De Gouvea, B. Kayser, R.N. Mohapatra, PRD 67 (2003) 053004 D. Delepine, V.G. Macias, S. Khalil, G.L. Castro, PLB 693 (2010) 438 [On the Dirac case: C. Giunti, A. Studenikin, PAN 72 (2009) 2089] Z.Z. Xing, PRD 87 (2013) 053019 Z.Z. Xing, Y.L. Zhou, PRD 88 (2013) 033002 systematic 3-flavor

This talk


Neutrino Antineutrino
Neutrino-Antineutrino Oscillations:

9

mass Effective mass terms:

CP-conserving Jarlskog-like parameters:

CP-violating


Relations
The effective mass terms:

10

The sum rule (for arbitrary L):

The zero-distance effect (at L = 0):

The typical oscillation lengths:


CP Asymmetries
The CP-violating asymmetry: (to cancel the |K|/E factors) The explicit expressions:

11

sensitive to all 3 CP phases sensitive to the mass scale.

CP-/T-violating asymmetries in normal neutrino-neutrino oscillations:


Jarlskog-like Parameters
In the standard parametrization of U:

12

Nine-independent Jarlskog-like parameters: Each one depends on two CP-violating phases or phase combinations.


Pseudo-Dirac (==0)

13

input angles


green solid =0 red dashed = /4 blue dotted = /2 dashed-dotted = input angles

Pseudo-Dirac (==0)


green solid =0 red dashed = /4 blue dotted = /2 dashed-dotted = input angles

Pseudo-Dirac (==0)


Effective Mass Terms
To reconstruct the Majorana neutrino mass matrix, we have to know all the 3 CP phases and the absolute scale of neutrino masses.

16


NH = normal hierarchy the smallest mass: m1 IH = inverted hierarchy the smallest mass: m3 WMAP / PLANCK: m1+m2+m3 < 0.23 eV (95% C.L., 1303.5076)
input angles

Arbitrary values of 3 CP phases: , , .


Lessons for Model Building
Flavor Symmetry
Texture zeros Element correlations

18

GUT relations

They reduce the number of free parameters, and thus lead to predictions for 3 flavor mixing angles in terms of either the mass ratios or constant numbers.
Example (Continuous symmetries) Example (Discrete symmetries)

Dependent on mass ratios

Dependent on simple numbers

PREDICTIONS


Type-Two Seesaw

19

Salient features: 1) U is exactly unitary; 2) singly- or doubly-charged Higgs bosons can be produced at colliders independently of Yukawa couplings; 3) LNV processes are directly related with neutrino masses and flavor mixing parameters.

Typical LNV modes and their branching ratios:

Insensitive to 3 phases




Taking

. Other inputs are the same as taken before.


Taking

. Other inputs are the same as taken before.


Taking

. Other inputs are the same as taken before.


CP Violation
Normal mass hierarchy with m1 = 0

23



input angles


CP Violation
Normal mass hierarchy with m1 = 0

24



input angles


CP Violation
Normal mass hierarchy with m1 = 0

25



input angles


CP Violation
Inverted mass hierarchy with m3 = 0
blue solid lines = /2, - = 0 red dashed lines = 0, - = /4

26

insensitive to masses
input angles


CP Violation
Nearly degenerate mass hierarchy:
blue solid lines

27

red dashed lines

insensitive to masses
input CP-violating phases


CP Violation
Nearly degenerate mass hierarchy:
blue solid lines

28

red dashed lines

insensitive to masses
input CP-violating phases


CP Violation
Nearly degenerate mass hierarchy:
blue solid lines

29

red dashed lines

insensitive to masses
input CP-violating phases


Summary: YES or NO?

30

QUESTION: are massive neutrinos the Majorana particles?
One might be able to answer YES through a measurement of the 0 decay or other LNV processes someday, but how to answer with NO?

YES

or
I don't know!
If I don't know, then no way to know which mass model to be right?
If YES, then how to determine the two Majorana CP-violating phases?

An answer might not be available until the second centenary of Pontecorvo? (if so, be patient!)


SM + 's is left with CP-violating phases: way out?

md

M


W

mu
12

ms
1/5

12

mc
13

mb

13
23



q

OK!

SM


w




s

mt

4/5

me


l

23



m1
m2

NO!

m

m

M

H

m3