PhysicsFlavor in Symmetry Broken 3S
Hirotaka Sugawara JSPS Office inHirotaka Sugawara, JSPS Office in Washington DC
W k b i d i h T hi kiWork being done with Toshiaki Kaneko, KEK, Japan
Long time ago I made a proposal together with S Pakvasa toLong time ago、I made a proposal together with S.Pakvasa, to understand flavor physics based on non-Abelian discrete symmetry such as .3Sy y
S.Pakvasa and H.Sugawara, Phys.Lett.B73,61(1978); B82,105(1979)B82,105(1979)
Recently, many attempts are being made to understand, at least in the leptonic part of flavor physics based on all kinds of nonin the leptonic part of flavor physics based on all kinds of non-Abelian discrete symmetries.
We still do not kno :We still do not know:
(1) What is the right symmetry?
(2) How is it broken?
(3) What is the origin of the symmetry?(3) What is the origin of the symmetry?
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illsymmetry w theoforigin theingunderstand The (2)dynamics.flavor
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Then
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32131 327
with
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21
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211 , mmmmmmsmmms
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usly.simultaneochangedbemust andofphase ,,d
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⎟⎟⎞
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*
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4
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5 iiiiii
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3
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iii
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Parameter Experimental CalculateParameter Experimental Calculateλ (Cabibbo) 0.2252 0.225195
A 0.8116 0.811834ρ 0.139 0.136225η 0.341 0.343641
Lepton caseLepton case
(1)neutrino sector
Assume large Majorana masses of right handed neutrino but zero majorana masses of left handed neutrino
)(0
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xxxxxxxxi
azM χν
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- We can diagonalize this by an orthogonal matrix
111
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solution.bimaximal-trithetocorrespondnot doesThis
We have to study the charged lepton matrix to get the mixing matrix.
The fact that the neutrino part is by itself gives good experimental fit
means that we must get identity matrix from the charged lepton sector.
Charged lepton family members are all s(3) singlet rather than singlet doublet. All the quarks and neutrinos are singlet-doublet.
scscc 1313121312 ⎟⎞
⎜⎛
ccsssc-scssscssccsccs-U
231323131223122313122312
231323131223122313122312⎟⎟⎟
⎠⎜⎜⎜
⎝ −−−−=
ccss
: smallfor get weccssscscss
13
231323131223122313122312 ⎠⎝s
cc
κθ3
sin 132 =
κθ435.0tan 12
2 +=
κθ 221tan 232 +=
132sin θ
0.025
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐≈0.02
3
122tan θ
132
122 sin
435.0tan θθ +=
0.550.5
Kamland data taken from M.C.Gonzalez-Garcia etal.arXiv:1001.4524v3,page9
The most important question is “Why S(3)?”
There are two kinds of symmetry in nature:
(1)Guage symmetry which is good at high energy(short distance).
(2)Non-gauge symmetry such as baryon number conservation,
CP invariance, parity etc.. These are good only in lower energy region(long distance.distance.
For example,
Baryon number conservation gets vilated when quarks and lepton go into a y g q p gsame multiplet. This makes sense at high energy.
CP is violated when 3rd generation quarks gets into the same multiplet as the other two generationsthe other two generations.
S(3) must belong to this category.
One possibility
)72,3()27,3()1,8()78,1(248638
+++→
×→ ESUE
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