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Flavor-Symmetry based Flavor 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)

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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

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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 orders from Frampton and Kephart 8

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

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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) DNDN Flavor group 11

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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,`10 Extended 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,`07 Abe 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 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

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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 β M H = 1.5 TeV(red) =0.5 TeV (black)

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

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

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Flavor symmetry with spontaneous CP suppress 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 logarithmiccancel. softness flavor symmetry

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

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SM Lenz+Nierste, `07 CKMfitter 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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