s3 group mixing

21
2 1 3 1 6 1 2 1 3 1 6 1 0 3 1 3 2 3 2 1 e U MIXING MAL TRI/BIMAXI OF STATUS ph/0308282 - hep Ma E. ph/0301092 - hep 87 (2003) 560 PLB Zee A. He, X. ph/0204049 - hep 85 (2002) B533 PLB Xing Z. ) ph/9904297 - hep 79 (1999) 458 PLB HPS also (see ph/0202074 - hep 167 (2002) 530 PLB HPS 2003 Dec 5 - 3 II, - NOVE UK , RAL SCOTT, W. ) ( ELY APPROXIMAT LEAST AT

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S3 GROUP MIXING. (TRI-. MAX. MIXING). GENERALISES TBM:. SYMMETRIC S3 GROUP:. NAT. REP. S3 GROUP MATRIX:. (FLAVOUR BASIS). NAT. REP. CIRC. RETRO-CIRC. TRI-. MAX. MIXING. = S3 GROUP MIXING. S3 GROUP MIXING. (TRI-. MAX. MIXING). GENERALISES TBM:. CYCLIC C3 GROUP:. - PowerPoint PPT Presentation

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Page 1: S3  GROUP  MIXING

2

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MIXINGMALTRI/BIMAXI OF STATUS

ph/0308282-hep Ma E.

ph/0301092-hep 87 (2003) 560 PLBZee A. He,X.

ph/0204049-hep 85 (2002) B533 PLBXing Z.

)ph/9904297-hep 79 (1999) 458 PLB HPSalso (see

ph/0202074-hep 167 (2002) 530 PLBHPS

2003 Dec5-3 II,-NOVE

UK, RALSCOTT, W.

)

(

ELYAPPROXIMAT

LEASTAT

Page 2: S3  GROUP  MIXING

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TBM OF SYMMETRIES

VIOLATION-CP ZERO 1)

N'`REFLECTIO 2)

VEC.- ETRIMAX. ONE 3)

)!!( HOPEFULLYEAPPROXIMAT

ph/0305309-hepoura Grimus/Lav

ph/0210197-hep

219 (2002) 647 PLBHS

ph/0302025-hep 76 (2003) 537 PLBHS

ph/0203209-hep

163 (2002) 535 PLBHS

} ).'(` CPMAX

Page 3: S3  GROUP  MIXING

0309004/

...

exnucl

aletAhmedNS

????. (2003) ?? ett.Phys.Rev.L

0204008/

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exnucl

aletAhmadRQ

011301 (2002) 89 ett.Phys.Rev.L

OD2 Pure SaltOD2

46.043.0

44.043.0

09.009.0

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NC

CC

29.027.0

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09.010.0

07.007.0

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CC

036.0034.0

032.0031.0346.0

/

NCCC

028.0028.0

022.0022.0347.0

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NCCC

spectrum)-Bd undistorte assuming given thoseare here quoted (Results 8

ResultsSNO

03.035.0/ NCCC )

(

errorssystematicinncorrelatio

ignoresaveragenaivemy

Page 4: S3  GROUP  MIXING

Solar Datadist. spect. B and . systs corr. ignoring -Salt NoSalt of

average naivemy is 03.035.0/point SNO8

NCCC

ph/9601346-hep 111 (1996) 374 PLBalso see ;ph/0202074-hep 167 (2002) 530 PLBHPS

Page 5: S3  GROUP  MIXING

ph/9601346-hep 111. (1996) 374 PLB HPS3 Fig.

' BATHTUB9/53/19/5 ̀ THE

MIX.TRIMAX.IN DICTEDPRE ! ! ! !

Page 6: S3  GROUP  MIXING

/ KAMLANDVERDE- / PALOCHOOZ : ESPREACTORS

95)( eeP09.061.0

KAMLANDex/0212021-hep

al.et EguchiK.

Page 7: S3  GROUP  MIXING

*31*

*31*

*31*

2||U

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S3 GROUP MIXING

(TRI- MAX. MIXING)

GENERALISES TBM:

Page 8: S3  GROUP  MIXING

SYMMETRIC S3 GROUP:

001

100

010

)123(P

010

001

100

)321(P

100

010

001

I

NAT. REP.

100

001

010

)12(P

010

100

001

)23(P

001

010

100

)31(P

Page 9: S3  GROUP  MIXING

S3 GROUP MATRIX:

abb

bab

bba

NAT. REP.

)321()123(2 PbbPaIM

RETRO-CIRC.

TRI-

CIRC.

)12()31()23( zPyPxP

zxy

xyz

yzx

MAX. MIXING

(FLAVOUR BASIS)

'`

33

SQUARESMAGIC

ORTHOGONAL

= S3 GROUP MIXING

Page 10: S3  GROUP  MIXING

*31*

*31*

*31*

2||U

321

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S3 GROUP MIXING (TRI- MAX. MIXING)

GENERALISES TBM:

Page 11: S3  GROUP  MIXING

CYCLIC C3 GROUP:

001

100

010

)123(P

010

001

100

)321(P

100

010

001

I

NAT. REP.

Page 12: S3  GROUP  MIXING

C3 GROUP MATRIX:

abb

bab

bba

NAT. REP.

)321()123(2 PbbPaIM

CIRCULANT

TRIMAX. MIXING

Page 13: S3  GROUP  MIXING

TRI-MAXIMAL MIXING:

33

1

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1

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1 2 3

U

“ We are probably far from this…. . but not very far…”

N. Cabibbo:

Lepton-Photon 2001

HPS PLB 349 (1995) 357N. Cabibbo PL 72B (1978) 222.

(cf. C3 CHARACTER TABLE)

Page 14: S3  GROUP  MIXING

: TABLE . MULTIPLCLASS S3

3

2

1

c

c

c

2133

3212

321

22

22/

cccc

cccc

ccc

321 ccc

NORMALISED

3

)31()23()12(

2

)321()123(:: 321

ccIc

: OPERATORS CLASS S3

Page 15: S3  GROUP  MIXING

S3 CLASS ALGEBRA:

200

02/11

010

2c

021

200

100

3c

100

010

001

1c

NAT. REP.

Page 16: S3  GROUP  MIXING

S3 CLASS MATRIX:

qprr

rqpq

rqp

22

22/

NAT. REP.

3212 rcqcpcM l

TRI-BI-MAX. MIXING

v MASS BASIS)(

Page 17: S3  GROUP  MIXING

MIXINGCLASS S3

:IDENTIFY

222

22222

3

2

6

32362

e

e

mmm

p

mmr

mmmq

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).3.( TABLECHARACTERGROUPSTHEcf

(= TRI-BI-MAX. MIXING)

Page 18: S3  GROUP  MIXING

NAT. REP. S3

010

100

001

)()2( PC

111

111

111

)()()( ePPeP

100

010

001

)1( IC

OPERATOREXCHANGE

MATRIXMASSDEMOCRATIC

OPERATORIDENTITY)1,'`( MMUTATIVITY

)3,0,'`( DDEMOCRACY

321 SSS

CLASS OPERATORS:

)1,'`( IIDENTITY

Page 19: S3  GROUP  MIXING

CLAS-MATRIX:

usutu

utusu

uuuts

NAT. REP. S3

)3()2()1(2 CuCtCsM

TRI-BI-MAX. MIXING

( FLAVOUR BASIS )321 SSS

):'(` 2iiii uDtMsImFORMULAMASS

Page 20: S3  GROUP  MIXING

MIXING32 SS

:IDENTIFY

322

21

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21 mm

umm

tmm

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!!!. AGAINBIMAXTRI

Page 21: S3  GROUP  MIXING

SUMMARY

DATATHEWITH CONSISTENTTBM )1SYMMETRIES THREE TBM HAS )2

MIXING'GROUP `S3 )3

MIXING'CLASS `S3 )4

MIXING'S3 `S2 )5

) BASIS FLAVOUR(

) BASIS FLAVOUR(

) BASISMASS- (

*31*

*31*

*31*

) SNO ESP.(

CP, ZERO ( ) TRIMAX. ,REFLECTION 2

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TBM

TBM

TBM

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