s3 group mixing
DESCRIPTION
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 PresentationTRANSCRIPT
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S3 GROUP MIXING
(TRI- MAX. MIXING)
GENERALISES TBM:
SYMMETRIC S3 GROUP:
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)123(P
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100
)321(P
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010
001
I
NAT. REP.
100
001
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010
100
001
)23(P
001
010
100
)31(P
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)
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33
SQUARESMAGIC
ORTHOGONAL
= S3 GROUP MIXING
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S3 GROUP MIXING (TRI- MAX. MIXING)
GENERALISES TBM:
CYCLIC C3 GROUP:
001
100
010
)123(P
010
001
100
)321(P
100
010
001
I
NAT. REP.
C3 GROUP MATRIX:
abb
bab
bba
NAT. REP.
)321()123(2 PbbPaIM
CIRCULANT
TRIMAX. MIXING
TRI-MAXIMAL MIXING:
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“ 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)
: TABLE . MULTIPLCLASS S3
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321 ccc
NORMALISED
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2
)321()123(:: 321
ccIc
: OPERATORS CLASS S3
S3 CLASS ALGEBRA:
200
02/11
010
2c
021
200
100
3c
100
010
001
1c
NAT. REP.
S3 CLASS MATRIX:
qprr
rqpq
rqp
22
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NAT. REP.
3212 rcqcpcM l
TRI-BI-MAX. MIXING
v MASS BASIS)(
MIXINGCLASS S3
:IDENTIFY
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(= TRI-BI-MAX. MIXING)
NAT. REP. S3
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MIXING32 SS
:IDENTIFY
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!!!. AGAINBIMAXTRI
SUMMARY
DATATHEWITH CONSISTENTTBM )1SYMMETRIES THREE TBM HAS )2
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MIXING'CLASS `S3 )4
MIXING'S3 `S2 )5
) BASIS FLAVOUR(
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