the 3 3 neutrino mixing scheme electromagnetic dipole...
TRANSCRIPT
![Page 1: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/1.jpg)
the 3+3 Neutrino Mixing Scheme&
Electromagnetic Dipole Moments
Zhi-zhong Xing【IHEP, Beijing】
@ Behind the Neutrino Mass, ICTP, 17-21/9/2012
Motivation for sterile neutrino physics
A description of the 66 mixing matrix
CP violation from non-unitarity effects
Seesaw-induced enhancement of EDM
Xing, 1110.0083 (PRD); Xing, Zhou, 1201.2543 (PLB)
![Page 2: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/2.jpg)
1What’s Behind Mass?
Dependent on mass ratios Dependent on simple numbers
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 (Fritzsch ansatz) Example (Discrete symmetries)
PREDICTIONS
Flavor Symmetry
Texture zeros Element correlations GUT relations
![Page 3: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/3.jpg)
2
1st generation: 2nd generation: 3rd generation:
Way 1: Constant + Perturbation
13 23 129 7 .
Xing,
arXiv:1011.2954
Cabibbo (78)
Wolfenstein (78)
Democratic (96)
Bimaximal (97/98)
Tri-bimaximal (02)
Golden-ratio (07)
shift
![Page 4: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/4.jpg)
3Way 2: Texture Zeros The flavor mixing angles are simple functions of 4 lepton mass ratios.
22 33
1977
1977,78
Texture zeros
S. Weinberg H. Fritzsch
Texture zeros of a fermion mass matrix dynamically mean that some matrix elements are strongly suppressed (in comparison with those weakly suppressed or unsuppressed elements) and may stem from a flavor symmetry (e.g., the Froggatt-Nielsen mechanism 1979)
The charged-lepton sector
12 23 1334 40 9
~ , ~ , ~ So the neutrino sector plays a primary role. e.g. the Fritzsch texture works (Xing 2002)
![Page 5: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/5.jpg)
4Lessons from Chemistry
Linus Pauling: The best way …. But so far we have had ….
Guiding principle
Flavor structures
Flavor properties
Good idea?
![Page 6: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/6.jpg)
Neutrinos
sub-eV
active neutrinos sub-eV
sterile neutrinos keV
sterile neutrinos
TeV
Majorananeutrinos
EeV
Majorana neutrinosclassical seesaws + GUTs
Sterile Neutrino PhysicsThe white paper arXiv:1204.5379
![Page 7: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/7.jpg)
Weinberg’s 3rd law of progress in theoretical physics (83):
You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you will be sorry ..…………………………………….. What could be better?
Fertile Soil Sterile Land
FLAVOR
DESERT
Really nothing in?
sub-eV
keV
≥ TeV
HOT DM
MATTER
WARM DM
![Page 8: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/8.jpg)
7How Many?
Observational hints (really true? harmless in cosmology?)
Theoretical motivation (seesaw + leptogenesis scenarios)
Or just for fun? “3” is a strange and interesting number!
![Page 9: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/9.jpg)
8Then Nontrivial…
The generic (3+3) flavor mixing scheme can be simplified to the (3+2) or (3+1) flavor mixing scheme, but
by forgetting the heavy neutrino(s) when discussing light neutrino oscillation phenomenology. The reason is
---- the heavy sterile neutrino(s) can result in the indirect
---- the light sterile neutrino(s) will give rise to the direct
violation of unitarity of the standard 3×3 active neutrino mixing matrix! They are distinguishable in -oscillations.
3 3
3
1
3 3
3
2 2
2
11 3
![Page 10: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/10.jpg)
9Flavor Mixing
active flavor
sterile flavor
mass
state
![Page 11: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/11.jpg)
10Why a Full Parametrization?
Seesaw
LeptogenesisLepton flaovr violation
Lepton number violation
12
23
13
1m
2m
3m
Is this a donkey?
No, an elephant!
![Page 12: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/12.jpg)
11A Possible Way
sterile part active partinterplay
Full parametrization:
15 rotation angles 15 phase phases
(Xing, 1110.0083)
![Page 13: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/13.jpg)
![Page 14: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/14.jpg)
13Unitarity
sterile part
active part
unitarity:
Relations between flavor and mass eigenstates:
![Page 15: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/15.jpg)
14A Blue-Collar Job (1)
Exact results in a triangular pattern (9 angles + 9 phases)
They describe small departures of and from unitarity. 0V 0U
![Page 16: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/16.jpg)
15A Blue-Collar Job (2)
Exact results which also depend on 9 angles and 9 phases.
They describe the interplay between active and sterile ’s.
![Page 17: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/17.jpg)
16Non-unitarity Mixing?Example A: light sterile neutrinos ---- some preliminary hints with ??
Example B: heavy Majorana neutrinos ---- popular seesaw scenarios.
Example C: whole tower of KK states ---- in extra dimension models.
The scheme of Minimal Unitarity Violation (Antusch et al 06): ---- Only 3 light neutrino species are considered; ---- Sources of non-unitarity are allowed only in those terms of the SM Lagrangian which involve neutrinos.
Constraint on the 3×3 -mixing matrix V ---- data on -oscillations, W and Z decays, the LFV modes and leptonic universality tests (Antusch et al 06).
Unitarity of the neutrino mixing matrix: good or bad at the 1% level.
![Page 18: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/18.jpg)
17Approximation9 active-sterile mixing angles are constrained to be at most of O(0.1).
Standard weak charged-current interactions:
![Page 19: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/19.jpg)
18Application (1)In the assumption of 3 light sterile neutrinos, the effective masses of the tritium beta decay / neutrinoless double-beta decay get modified.
The tritium decay:
The 02 decay:
Both and possible due to CP-violating phases.
![Page 20: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/20.jpg)
19Application (2)
Deformedunitarity triangles
New effects
of
CP violation
![Page 21: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/21.jpg)
20
Production + detection of a neutrino beam via CC weak interactions:
+ _
Neutrino Oscillations
Like the case of the non-standard interactions in initial + final states.
![Page 22: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/22.jpg)
21Direct/Indirect New EffectsNeutrino oscillation probability in vacuum (Antusch et al 06, Xing 08):
Unitary: universal Jarlskog invariant = 2 area of each unitarity triangle.
Non-unitary: 9 different Jarlskog invariants, and triangles polygons.
Jarlskog invariants of CP violation:
“Zero-distance” (near-detector) effect at L = 0 :
If (3+3) (3+2) or (3+1), both direct and indirect non-unitary effects occur.
![Page 23: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/23.jpg)
22Jarlskog’sIn the standard case:
In the presence of non-unitary effects:
CPV:
For heavy sterile ’s
![Page 24: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/24.jpg)
23CP ViolationCP-violating asymmetries:
Correlation:
Testing the unitarity of the PMNS matrix at low energies: a window to possible new physics at superhigh energies.
![Page 25: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/25.jpg)
24MSW Matter EffectsIllustration: 3 heavy Majorana neutrinos and constant matter density.
,,e ,,e
n,p,e n,p,e
Z
e
ee
e
W
e
ee
e
W
(Goswami, Ota 08; Luo 08; Xing 09)
Genuine CPV Matter effect
The same matter term appears in disappearance _ _ oscillation.
4~ 2.6 10 km
![Page 26: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/26.jpg)
25Dipole MomentsGiven the SM interaction, a massive Dirac neutrino can have a tiny magnetic dipole moment . 2010 B
A Majorana neutrino can not have the magnetic & electric dipole moments.
Both Dirac and Majorana neutrinos have transitiondipole moments:
— neutrino decays
— scattering with electrons
— interaction with external magnetic fields
— correlation to the origin of neutrino mass
EX bound: 1110 Ba few
No net contribution to the DMs
Xing, Zhou, 1201.2543
the canonical seesaw
![Page 27: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/27.jpg)
26Canonical SeesawThe canonical seesaw mechanism:
The basis transformation:
Physical masses:
Charged-current interactions:
Exact seesaw:
Comment (1): neutrino masses and mixing parameters are entangled;
Comment (2): the crucial question is where the seesaw mass scale is;
Comment (3): lower the seesaw scale and magnify non-unitarity of V.
![Page 28: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/28.jpg)
27SM Vacuum
e.g., Holthausen et al.; Masina, Notari; Elias-Miro et al.; Xing, Zhang, Zhou 12
TeV Scale?
Planck scale
QCD scale
Fermi scale
TeV / SUSY?
Seesaw scale?
GUT scale?
210~ MeV
210~ GeV
1910~ GeV
1610~ GeV
1210~ GeV
310~ GeV
The SM vacuum stability for a light Higgs
![Page 29: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/29.jpg)
28Lift the GIMAfter a careful treatment of infinities + non-unitary effects, we obtain
Non-unitary effects:
The same as Shrock’s result (82) but contains non-unitary effects.
Lift the GIM suppression:
conventional termnew term / non-unitary effect
The 1st term is the seesaw-induced effect which may be comparable with or even larger than the 2nd term.
![Page 30: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/30.jpg)
29Parameters
12
13
23
34
9
45
2 5 2
12
2 3 2
23
7.6 10 eV
2.5 10 eV
m
m
Input parameters:
In addition,
1 2 3
1 2 3
min{ , , } 5 meV
, , (1) TeV
m m m
M M M O
Seesaw + unitarity
Current constraints (Antusch et al. 06)
Arbitrary CP phases to satisfy:
![Page 31: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/31.jpg)
30Conventional CaseComment (a): almost degenerate 3 heavy neutrinos to assure that the radiative correction to the masses of 3 light neutrinos are sufficiently small (Pilaftsis 1992); e.g., smaller than 0.5 meV .
Comment (b): to present numerical results in a convenient way, let us define a parameter to measure the strength of unitarity violation of V:
The conventional case (0 non-unitary effects)
15 meVm
35 meVm
EX bound: 1110 Ba few
![Page 32: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/32.jpg)
Enhanced electromagnetic DMs:
![Page 33: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/33.jpg)
Enhanced decay rates: (too small to have impact on the CIB)
![Page 34: the 3 3 Neutrino Mixing Scheme Electromagnetic Dipole Momentsusers.ictp.it/~smr2366/talks/Xing-Bene2012.pdf · 2012-09-20 · the 3+3 Neutrino Mixing Scheme Electromagnetic Dipole](https://reader033.vdocuments.net/reader033/viewer/2022050205/5f5829e38f4b5308e86a4102/html5/thumbnails/34.jpg)
33
1) Do we feel happy/painful/sorry to add sterile neutrinos into the SM (Weinberg’s theorem)?
2) How many species of sterile neutrinos should be taken into account for this or that purpose?
3) If all the current experimental and observational hints disappear, will the sterile neutrino physics still survive?
5) How about the flavor structures of charged and neutral fermions, including the extra species? (Flavor Theory) ….
THANK YOU FOR YOUR ATTENTION!
Summary: Open Questions
4) How strong is the correlation between electromagnetic properties of neutrinos and the origin of their masses?
R. Feynman