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

from Hazumi,KEK

Is there any symmetry behind?

Nobel Prize Matrix

2

At first sight it looks chaotic, but ...

Flake Symmetry(Flavor

Symmetry)ª›®œ•Œ QuickTime˛ ©M°ßBMP°®∏—¿£¡Yæπ®”¿Àµ¯¶ππœµe°C

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

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.

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

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

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

Frampton and Kephart, `o1,Frampton,Kephart+Rohm, `09

direct products

twisted products

32+13=45 groups

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

Discrete translational inv.+parity

From the geometry of a discrete dimension (dim. deconstruction)(Kubo, `05)

DN

Flavor group11

A4 From orbifolding extra dimensions

(Altarelli,Feruglio+Lin, `06)

with 120 degrees=> root vectors of SU(3)

Z2

In field theory:

12

Abe, K-S Choi, Kobayashi, Ohki, Sakai,`10Extended by

Orbifold symmetry x Abelian discrete symmetry

Non-abelian family symmetry

In string theory:

14

Ko,Kobayashi, park+Raby, `07;Kobayashi, Raby+Zhang, `05; Kobayashi, Nilles, Plöger, Raby+ Ratz,`07Abe et al, `09

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

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.

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

HPQCD, arXiv:1004.4285 [hep-lat]

and P.R.L.104: 132003, 2010.

Precise quark masses

Q6

using HPQCD mq with 2 sigma

UTfit

Q6 sum rule (Vacuum I)

Input:

Araki and JK, IJMod.A24, 5831 (2009)

UTfit

Q6

using HPQCD mq with 2 sigma

Q6 sum rule (Vacuum I)

Input:

Araki and JK, IJMod.A24, 5831 (2009)

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

Input:

Q6

The Majorana phases are not independent.

1. 1 Tree-level FCNC

Mondragon x2, Peinado,Phys.Rev.D76:076003,2007

Mondragon x2, Pained,Phys.Rev.D76:076003,2007

mixing Kifune, JK and Lenz, Phys.Rev.D77:076010,2008

cos βMH = 1.5 TeV(red)

=0.5 TeV (black)

cos βMH = 1.5 TeV(red)

=0.5 TeV (black)

(ratio of two Higgs masses)

1.2 Tree-level CP

Flavor symmetry with spontaneous CP

Babu+Meng, `09

Mismatch between flavorsSoft mass insertions

2. FCNC and CP in the SUSY sector

Hall, Kostelecky and Raby

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

2+1 family structure

real

EDMs

phase alignment

Soft-SUSY- breaking mass insertions:

with spontaneous CP

(complex VEV from the SM singlet sector)

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

Quark sectorQ6

34

Kobayashi, JK+Terao,`03;Itou,Kajiyama+JK,`05

Flavor symmetry with spontaneous CPsuppress FCNCs and CP too much!!

Can one get a large CP in the B mixing?0

B mixing

Lenz-Nierste parameterization of NP

Master equations for observables

0

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

III. Loop effects to JK and Lenz, Phys.Rev.D82:075001,2010

+ + ...

quadratic and logarithmic cancel.

softness flavor symmetry

large susy breaking

However, large finite terms.

small and large

FCNCEDM, b -> s+gammaMass of extra Higgions extra

Higgbosons

tree

one-loop

SMLenz+Nierste, `07CKMfitter

CDF :

UTfit

D0 :CKMfitter :

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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