Flavor-Symmetry based Flavor Violation in Supersymmetry Jisuke Kubo (kanazawa Univ.) at NCTS LHC...
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![Page 1: Flavor-Symmetry based Flavor Violation in Supersymmetry Jisuke Kubo (kanazawa Univ.) at NCTS LHC Topical Program 1 based on: Babu and JK, PRD71, 056006.](https://reader030.fdocuments.in/reader030/viewer/2022032702/56649cdb5503460f949a58f1/html5/thumbnails/1.jpg)
Flavor-Symmetry basedFlavor Violation
in Supersymmetry
Jisuke Kubo (kanazawa Univ.)
at NCTS LHC Topical Program
1
based on: Babu and JK, PRD71, 056006 (2005); Itou, Kajiyama and JK, NPB743, 74 (2006);Kifune, JK and Lenz, PRD77, 076010 (2008); Araki and JK, IJMod.A24, 5831 (2009); Kawashima, JK and Lenz, PLB681,60 (2009);JK and Lenz, PRD82,075001 (2010)
Text
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from Hazumi,KEK
Is there any symmetry behind?
Nobel Prize Matrix
2
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At first sight it looks chaotic, but ...
Flake Symmetry(Flavor
Symmetry)ª›®œ•Œ QuickTime˛ ©M°ßBMP°®∏—¿£¡Yæπ®”¿Àµ¯¶ππœµe°C
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ª›®œ•Œ QuickTime˛ ©M°ßBMP°®∏—¿£¡Yæπ®”¿Àµ¯¶ππœµe°CThe symmetry group of
is D6 , one of the finite groups.
Nakaya, 1936 (中谷宇吉郎)
the first who made snow crystal in a
laboratory
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Tri-bimax. mixing ?
Harrison, Perkins+Scott, `02;Perkins+Scott, `02, Xing, `02
Exp:
Schwetz, arXiv:0808.2016
What about the
A family symmetry may be realized at low energy.
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I Non-abelian finite group
III Flavor-Symmetry based FACNC and CP
II Where do non-abelian discrete family symmetries come from?
IV Conclusion
PLAN
6
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The classification of the finite groups has been completed; 1981 Gorenstein, 1995 Aschbacher+Smith more than 100 years later than the case of the continues group.
g= order of a finite group = # of the group elements
7
I Non-abelian finite group
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1. No non-abelian finite group exists for prime g.2. For smaller g (<31) there exist only three types:
3. The smallest non-abelian finite group is S3=D3.
a) Permutation groups
b) Dihedral groups and Binary dihedral (Dicyclic) groups
c) Twisted products like
Non-abelian Finite groups of lower ordersfrom Frampton and Kephart
8
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Frampton and Kephart, `o1,Frampton,Kephart+Rohm, `09
direct products
twisted products
32+13=45 groups
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II Where do discrete family symmetries come from?
*It is simply there!
*It comes from the geometry of extra dimensions.
*It comes from SSB of a non-abelian continuous G.
10
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Discrete translational inv.+parity
From the geometry of a discrete dimension (dim. deconstruction)(Kubo, `05)
DN
Flavor group11
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A4 From orbifolding extra dimensions
(Altarelli,Feruglio+Lin, `06)
with 120 degrees=> root vectors of SU(3)
Z2
In field theory:
12
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Abe, K-S Choi, Kobayashi, Ohki, Sakai,`10Extended by
Orbifold symmetry x Abelian discrete symmetry
Non-abelian family symmetry
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In string theory:
14
Ko,Kobayashi, park+Raby, `07;Kobayashi, Raby+Zhang, `05; Kobayashi, Nilles, Plöger, Raby+ Ratz,`07Abe et al, `09
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III Flavor-Symmetry based FCNC and CP
Two Sources:
1. Multi Higgs Structure Higgs Family
Tree-level FCNC and CP
2. SUSY sector
Loop-level FCNC and CP SUSY breaking
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A concrete SUSY model based on Q6 x Z4 x CP
2+1=3 structure except U
SM singlet
Each sector, except U, forms a family with parents + one child
SM non-singlet
Babu and JK, PRD71, 056006 (2005); and to appear.
The SM singlet sector breaks Q6 x Z4 x CP spontaneously.
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Accidental permutation symmetries of VHiggs
.....
Vacuum I:
Vacuum II:
.....
Two minima are physically different.
9 theory parameters for 6 quark masses and 4 CKM parameters.
One sum rule among them
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HPQCD, arXiv:1004.4285 [hep-lat]
and P.R.L.104: 132003, 2010.
Precise quark masses
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Q6
using HPQCD mq with 2 sigma
UTfit
Q6 sum rule (Vacuum I)
Input:
Araki and JK, IJMod.A24, 5831 (2009)
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UTfit
Q6
using HPQCD mq with 2 sigma
Q6 sum rule (Vacuum I)
Input:
Araki and JK, IJMod.A24, 5831 (2009)
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Dirac phase
Violation of symmetry
Lepton sector:
The flavor and CP symmetry allows 6 + 1=7 theory parameters for 3+3 masses and 1+2
phases.
JK, Mondragonx2,Rodriguez, `03; JK,`04
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Input:
Q6
The Majorana phases are not independent.
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1. 1 Tree-level FCNC
Mondragon x2, Peinado,Phys.Rev.D76:076003,2007
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Mondragon x2, Pained,Phys.Rev.D76:076003,2007
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mixing Kifune, JK and Lenz, Phys.Rev.D77:076010,2008
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cos βMH = 1.5 TeV(red)
=0.5 TeV (black)
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cos βMH = 1.5 TeV(red)
=0.5 TeV (black)
(ratio of two Higgs masses)
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1.2 Tree-level CP
Flavor symmetry with spontaneous CP
Babu+Meng, `09
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Mismatch between flavorsSoft mass insertions
2. FCNC and CP in the SUSY sector
Hall, Kostelecky and Raby
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Introduce to constrain the Yukawa sector, and simultaneously to soften the SUSY flavor problem.
low-energy family symmetry
(Dine,Leigh+Kagan,`93; Pouliot+Seiberg,`93; Kaplan+Schmalz,`94;Hall+Murayama, `95; Carone, Hall+Murayama, `96; Babu+Barr,`96;Babu+Mohapatra,`99; Chen+Mahanthappa`02; Babu, Kobayashi+Kubo, `03;Hamaguchi,Kakizaki+Yamaguchi, `03; Ross, Velasco-Sevilla+Vives, `03; King+Ross,`03; Maekawa+Yamashita, `04; Ross, Velasco-Sevilla+Vives, `04;.................................)
Susy Flavor Problem
31
Combine spontaneous CP violation to suppress CP , Babu+JK,`05
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2+1 family structure
real
EDMs
phase alignment
Soft-SUSY- breaking mass insertions:
with spontaneous CP
(complex VEV from the SM singlet sector)
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Lepton sector
(Gbbiani et al, Abel, Khalil + Lebedev, Endo, Kakizaki +Yamaguchi, Hisano + Shimizu; Hisano..............)
FCNCs induced by the soft termsQ6
33
Kobayashi, JK+Terao,`03;Itou,Kajiyama+JK,`05
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Quark sectorQ6
34
Kobayashi, JK+Terao,`03;Itou,Kajiyama+JK,`05
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Flavor symmetry with spontaneous CPsuppress FCNCs and CP too much!!
Can one get a large CP in the B mixing?0
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B mixing
Lenz-Nierste parameterization of NP
Master equations for observables
0
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Kawashima, JK and Lenz, PLB681,60 (2009)
I : Tree-level Higgs contribution
II: Contributions from the soft mass insertions
I+II
Yukawa couplings for neutral Higgses are real even for the mass eigen states.
is real, and
EDMs
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III. Loop effects to JK and Lenz, Phys.Rev.D82:075001,2010
+ + ...
quadratic and logarithmic cancel.
softness flavor symmetry
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large susy breaking
However, large finite terms.
small and large
FCNCEDM, b -> s+gammaMass of extra Higgions extra
Higgbosons
tree
one-loop
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SMLenz+Nierste, `07CKMfitter
CDF :
UTfit
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D0 :CKMfitter :
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Flavor symmetry with spontaneous CP can nicely suppress FCNCs and CP in SUSY models.
: small to suppress EDMs: large to suppress FCNC
Large SUSY breaking in the extra Higgs sector
Large loop effects to large CP in the B mixing
Conclusion
Built-in mechanism to keep CP small in the first two generations, but to enhance CP for the third generation.
*
*
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謝謝
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