Flavor-Symmetry based Flavor Violation in Supersymmetry Jisuke Kubo (kanazawa Univ.) at NCTS LHC Topical Program 1 based on: Babu and JK, PRD71, (2005); Itou, Kajiyama and JK, NPB743, 74 (2006); Kifune, JK and Lenz, PRD77, (2008); Araki and JK, IJMod.A24, 5831 (2009); Kawashima, JK and Lenz, PLB681,60 (2009); JK and Lenz, PRD82, (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)

The 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: 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 orders from Frampton and Kephart 8

Recent models Frampton and Kephart, `o1, Frampton,Kephart+Rohm, `09 direct products twisted products 32+13=45 groups 9

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) DNDN Flavor group 11

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,`10 Extended 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,`07 Abe 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, (2005); and to appear. The SM singlet sector breaks Q6 x Z4 x CP spontaneously.

Accidental permutation symmetries of V Higgs..... 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: [hep-lat] and P.R.L.104: , 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 β M H = 1.5 TeV(red) =0.5 TeV (black)

cos β M H = 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 flavors Soft 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 terms Q6 33 Kobayashi, JK+Terao,`03; Itou,Kajiyama+JK,`05

Quark sector Q6 34 Kobayashi, JK+Terao,`03; Itou,Kajiyama+JK,`05

Flavor symmetry with spontaneous CP suppress 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, quadratic and logarithmiccancel. softness flavor symmetry

large susy breaking However, large finite terms. small and large FCNC EDM, b -> s+gamma Mass of extra Higgions extra Higgbosons tree one-loop

SM Lenz+Nierste, `07 CKMfitter 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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