Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka...
Transcript of Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka...
![Page 1: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/1.jpg)
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
![Page 2: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/2.jpg)
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?
![Page 3: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/3.jpg)
isbreakingitsofwayspecificithsymmetry wS(1): thatshow we work,continuing In this
d iflsector lepton andsector quark both with cosistent
isbreakingitsofway specificith symmetry wS(1) 3
illsymmetry w theoforigin theingunderstand The (2)dynamics.flavor
broken.is symmetry gauge way on then restrictio strong a give
![Page 4: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/4.jpg)
S of ABC 3
)}2,3,1(),3,2,1(),1,3(),3,2(),2,1(,1{:3S
++ ψψψψψψ ,,:function wave 321
=++ αψψψ
3:singlet 321
⎞⎛⎟⎞
⎜⎛ −ψψ
3
21
⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎟⎟⎟
⎜⎜⎜
+β
ψψψ 22:doublet ⎟
⎠⎜⎝⎟
⎟⎠
⎜⎜⎝
−+ γψψψ6
2 321
⎠⎝
![Page 5: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/5.jpg)
iHihliHi
3 :issinglet SisHiggswhen termmassor coupling Higgs
++R
3
)(ag
γγββαα b LRLRL
⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛
−−−−
+⎟⎟⎞
⎜⎜⎛
=1
)121112
111111
)(( ψψ
ψψψ ba
⎟⎟
⎠⎜⎜
⎝⎟⎟
⎠⎜⎜
⎝ −−−−+
⎟⎟
⎠⎜⎜
⎝
=
3
2321 )211121
3111111
3)(,,(
ψψψψψ
![Page 6: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/6.jpg)
matrixmixingfor thephaseArbitraryKMbroken? be scan How 3
violationCP matrixmixing for thephase-Arbitrary-KM
→matrix massmatrix mixing ←
brokenareSandCPbothmatrixmass thetophasespossible all Allow
→ brokenareSandCPboth 3→
![Page 7: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/7.jpg)
Then
⎞⎛ 131211 δδδ iii bb
Then
⎟⎟⎞
⎜⎜⎛ 131211
δδδ
δδδ
iii
iii bebeae
⎟⎟
⎜⎜= 232221 δδδ iii beaebeM
⎟⎠
⎜⎝
333231 δδδ iii aebebe ⎠⎝
![Page 8: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/8.jpg)
showsalgebrasimple :gfk
showsalgebrasimple
⎞⎛
:
hkfgfk
MM ⎟⎟⎞
⎜⎜⎛
∗
khhkfMM⎟⎟
⎠⎜⎜
⎝
=khg ⎟⎠
⎜⎝
realk :khkgkf ≤≤≤ Re,Re,Re
![Page 9: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/9.jpg)
:massesquarkthetoparameterstheofrelationThe
131
:massesquark the toparameterstheofrelation The
sk =
2222
1
13
Asshgf −≡−=++
3
21
123
Bhff h
Asshgf ≡=++
32131 327
with
Bsssshgffgh −≡+−=+
21
23
23
22
22
212
23
22
211 , mmmmmmsmmms
with++=++=
23
22
213 mmms =
![Page 10: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/10.jpg)
The phase convention and the number of variables
( k )(quark sector)Th l hThere are only two phases one can adjust j
:currentweak ,,
d
diL
uiL ψγψ μ
usly.simultaneochangedbemust andofphase ,,d
iLu
iL ψψ
![Page 11: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/11.jpg)
12214parametersofnumber)dandu (27,,,
==×−−−hgfk
46(masses)sobservableofnumber 122-14parametersofnumber
+===
( )
We can p t either p q ark or do n q ark f h realWe can put either up-quark or down quark f, h real but not both.
![Page 12: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/12.jpg)
Up quark f,h real caseUp quark f,h real case
⎟⎟⎞
⎜⎜⎛ ×− −101305.09999.011 4
*
i
⎟⎟
⎠⎜⎜
⎝ ×+=
− 19999.0101305.09999.09999.011)(
4
*
iMM u
⎟⎟⎟⎞
⎜⎜⎜⎛
+−++
= 07300.09965.0102453.09994.009677.09935.002453.09994.01
)( * iiii
MM d⎟⎠
⎜⎝ −+ 107300.09965.009677.09935.0 ii
⎟⎞
⎜⎛ ×−++ −105025057740032790517301913060120 5 iii
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−×−−−−×++
= −
5773.08048.01380.0102513.05774.003280.02875.01913.07392.0105025.05774.003279.05173.01913.06012.0
5 iiiiii
Uu
⎟⎟⎞
⎜⎜⎛
+−−−+++
=
⎠⎝
042080576001236016580391806857005607.05746.01932.05864.03792.03763.0
5773.08048.01380.0
iiiiii
U⎟⎟
⎠⎜⎜
⎝ −+=5772.07589.03014.0
04208.05760.01236.01658.03918.06857.0 iiiUd
![Page 13: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/13.jpg)
⎟⎞
⎜⎛ − 003269000129302252097430 i
matrixMixing
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
×−−−×−−
−
−
9991.0107367.00404.0003182.0008012.004117.09735.0101381.02251.0
003269.0001293.02252.09743.0
3
3
iii
i
⎠⎝ × 9991.0107367.00404.0003182.0008012.0 ii
Parameter Experimental CalculateParameter Experimental Calculateλ (Cabibbo) 0.2252 0.225195
A 0.8116 0.811834ρ 0.139 0.136225η 0.341 0.343641
![Page 14: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/14.jpg)
Lepton caseLepton case
(1)neutrino sector
Assume large Majorana masses of right handed neutrino but zero majorana masses of left handed neutrino
)(0
))(,( ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
MMM
CM CR
LMTD
DTC
RTL ν
νννν
0
)(
)(
11⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛⎟⎟⎞
⎜⎜⎛
=⎠⎝⎠⎝
VVM
MMD
TMM
R
λ
)()( ,
)(
2112
22
−==
⎟⎟⎠
⎜⎜⎝
=⎟⎟⎠
⎜⎜⎝⎟⎟⎠
⎜⎜⎝
VMVMVVM
VVMMMTDD
MTD
λλ
λ
0)()(
get, we, smallFor
111 =− −
VVVMMM TDMD λ
λ
02 ≈V
![Page 15: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/15.jpg)
⎟⎞
⎜⎛1
D
cc
⎟⎟⎟
⎜⎜⎜
= 1νD ccmM
⎞⎛
⎟⎠
⎜⎝ 1cc
⎟⎟⎞
⎜⎜⎛ 1 21
δδ
δδ ηηii
ii
M
ee
⎟⎟
⎜⎜= 1 31
δδ
δδ ηηii
iiM eeaM⎟⎠
⎜⎝ 132 δδ ηη ii ee
![Page 16: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/16.jpg)
ie ii i )1)(1( δχη δ ⋅⋅⋅++−=
ii i
i
))(1())((
χδχη++≈
i i
i
1))((
δχ
+≡complex
i
i
i
:1
δδ+
complexi :δ
![Page 17: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/17.jpg)
])()(
121112
[21212
⎟⎟⎞
⎜⎜⎛
++−
+⎟⎟⎞
⎜⎜⎛−
= xxxxxxxx
imM χεν ])(
)(211
121[
3232
3131⎟⎟
⎠⎜⎜
⎝ +−+−+
⎟⎟
⎠⎜⎜
⎝ −−−=
xxxxxxxxi
azM χν
“Real” part and “imaginary” part of the matrix commute with each other.
- We can diagonalize this by an orthogonal matrix
![Page 18: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/18.jpg)
111
222
ε
qqqqqqzc
−−−+=
+=
1 321321
η δii eq
qqqqqqzi=
+=
21 δδδη
iiii
i
xq
−+= ++
part.imaginary without definedares' Hereδ
![Page 19: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/19.jpg)
0xxx:casehierarchy Normal (1) 133221 =++ xxx
1,11
1,2(2
13
2
32
32
ν ⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛
⎟⎟⎞
⎜⎜⎛
+−+
= xx
xxxx
U
secodthe3eeigen valuantocorresponscolumnfirstThe
)(,
13,(
32
33
32
321
χ
ν⎟⎟
⎠⎜⎜
⎝⎟⎟
⎠⎜⎜
⎝ +−⎟⎟
⎠⎜⎜
⎝⎟⎟
⎠⎜⎜
⎝ − xxN
xxN
bi i lild0hW).2i(x-3 toone third thezeroand eeigen valu column to
secodthe,3eeigen valuan tocorresponscolumn first The
321χχ
++ xx
notation)ordinary in ( xTherefore,case.bimaximal-triexactly tocorrespond0that xseeWe
132
2
θ=
case. bimaximal- tri thefromdeviation theindicates
![Page 20: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/20.jpg)
x:hierarchy Inverted (2) 321
⎞⎛
== xx
31
21
61
⎟⎟⎟⎞
⎜⎜⎜⎛
123
12
16
1ν
⎟⎟⎟⎟
⎜⎜⎜⎜
−=U
3i3i ldldhdfiTh3
1032
⎟⎟
⎠⎜⎜
⎝−
e.eigen valu zero column to third theand 3ix-3eeigen valutocorrespondcolumnssecond theandfirst The iχ
solution.bimaximal-trithetocorrespondnot doesThis
![Page 21: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/21.jpg)
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.
![Page 22: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/22.jpg)
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 +=
![Page 23: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/23.jpg)
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
![Page 24: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/24.jpg)
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.
![Page 25: Broken S3 Symmetry in Flavor Physics · 3 Symmetry in Flavor Physics Hirotaka Sugawara JSPSHirotaka Sugawara, JSPS Office inOffice in Washington DC W k b i d i h T hi kiWork being](https://reader033.fdocuments.in/reader033/viewer/2022060416/5f13fd96833d27198801d10a/html5/thumbnails/25.jpg)
One possibility
)72,3()27,3()1,8()78,1(248638
+++→
×→ ESUE
:phases"for except "unbroken remain may S following Theenergy.high at broken be will This
group.flavor theas thisuse
i
3
3
3
SUSUWe
Tiππ
.
)3(31
e(1,2)
811
22i- 1
−+=
=
etc
IT
eTi
λλ
:Questionmodel. standard down tobroken
is group unfied grand how sconstraint strong give willThisSUn rather tha Uusing are fact weIn 33
:matrix mass tolead willmultiplets Higgs ofsort (2)What singlets? belepton chargedCan (1)
n?observatioour with consistent is which model a make topossibleit IsQ
⎞⎛ gfk?
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=∗
khghkfgfk
MM