21th. December 2007 Seminar Univ. of Toyama. D6 Family Sym. and CDM at LHC J. Kubo, Y. Kajiyama (Phys. Rev. D )

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1 21th. December 2007 Seminar Univ. of Toyama D6 Family Sym. and CDM at LHC J. Kubo, Y. Kajiyama (Phys. Rev. D )

2 Plan to talk 1; 2; 2-1); canonical seesaw 2-2); radiative seesaw(ma model) 3; Textures Predictions 4; CDM µ eγ. 5; 4-1); 4-2); Dark Matter 4-3); Sunyaev-Zel dovich(sz) effect

3 1; 1);... ) up,down 2/3,-1/3 GUTs SO(10),E6 2); etc... 2)-1;gauge coupling 2)-2; mass parameter}»»»,, texture, etc...

4 3);...Canonical seesaw, Radiative seesaw,etc... 4); (Dark Matter) 4)-1; SUSY...MSSM, etc. 4)-2; non-susy...zee-like Model 5);... (SUSY), (S(3),S(4)...), (String,...),...

5 LEPTON SECTOR!Radiative seesaw mechanism,! Discrete symmetry...d6 (Cold Dark Matter)!non-SUSY...Zee-like Model(Ma model)!"#,$,

6 2; 2-1); Canonical Seesaw mechanism Minkowsky, T. Yanagida, M. Gell-Mann lepton number %

7 2-2); Radiative seesaw mechanism Extra Higgs loop-level Neutrino Mass A.Zee,Phy.lett.(1980) Z -parity Odd Phys. Rev. D67, (2003) hep-ph/ ;M.Krauss, S. Nasri,M,Trodden Phys.Rev. D73 (2006) hep-ph/ ;e.ma SUSY Ma Model... Extra Higgs

8 Ma Model SU(2)L!U(1)Y!Z2 assignment Yukawa Lagrangian <%>=v,<&>=0 Re& Im& Majorana mass term Higgs Potential Neutrino mass

9 <<, k

10 3; Textures Predictions charged-lepton sector real part...6! M e = m 2 m 2 m 5 m 2 m 2 m 5 m 4 m 4 0 imaginary part...2 (Neutrino mass neutrino sector matrix % mns M ν = 2(ρ 2 ) (ρ 2 ) 2 2ρ 2 ρ 4 0 2ρ 2 ρ 4 2(ρ 4 ) 2 + (ρ 3 ) 2 e 2iφ phase) hep-ph/ ;j.kubo,mondragon...

11 ! Inverted Hierarchy (m(1, m(2> m(3) Maximal Mixing(sin'atm=1/" )!! m(2,min= f(tan'sol,)m32, )m12,%(=0) =0.038~0.067eV U e3 ~0.0034< ! 2 <mee>min~ )m23 sin2'sol(%(=0) =0.034~0.069eV

12 (Input parameters...7para.) 2 sin'sol= 0.23~0.38 sin'atm= 0.34~ )m32= (1.3~3.0)!10 ev )m12= (6.2~9.1)!10 ev mev, " MeV, * MeV 2 <m ee > [ev] sin! " 2 sin'sol= )m32= !10 ev !10 ev !10 ev 2 2 m 2 21 = ev ev 2, respective

13 Lepton Flavor violations Mh1,2~120GeV A.,M. Mondragon and e.peinado(s3-flavour symmetry as realized in lepton violating processes) Dihedral Group

14 2 D6 Dihedral Group R N = cos θ N sin θ N sin θ N cos θ N P = , P =, θ N = 2π N i 0 0 i 2N D 1,1 1,1 N Doublet N/2-1(even), (N-1)/2(odd) Singlet 4(even) 2(odd) x P RN 2 2 y

15 D 6 model ( x1 x 2 ) } {{ } 2 ( y1 y 2 ) } {{ } 2 = ( xi (σ 3 ) IJ y J ) } x I (σ 1 ) IJ y J {{ } 2 x I y }{{} I x I (iσ 2 ) IJ y J }{{} 1 1 ( a1 a 2 ) } {{ } 2 ( b1 b 2 ) } {{ } 2 = ( ai ( σ 3 ) IJ b J ) } a I (σ 1 ) IJ b J {{ } 2 a I b }{{} I a I (iσ 2 ) IJ b J }{{} 1 1 ( x1 x 2 ) } {{ } 2 ( a1 a 2 ) } {{ } 2 = ( x I a I ) } x I (iσ 2 ) IJ a J {{ } 2 x I (σ 1 ) IJ a J }{{} x I (σ 3 ) IJa J }{{} = 1, 1 1 = 1, 1 1 = = 1, 1 1 = 1, 1 1 = 1

16 D Assignment (Matter Assignment) L S n S e c S L I n I e c I SU(2) L U(1) Y (2, 1/2) (1, 0) (1, 1) (2, 1/2) (1, 0) (1, 1) (Higgs Assignment) D Ẑ Z SU(2) L U(1) Y φ S φ I η S η I (2, 1/2) (2, 1/2) (2, 1/2) (2, 1/2) D Ẑ Z *Quark Sector...(D6,Z 2,Z2)~(1,+,+) tree-level FCNC

17 Yukawa Lagrangian! %1-%2,&1-&2!

18 D 6 Ẑ2 Z 2, Higgs Potential Local Minimum # (µφ 1) 2, (µ φ 2) 2 > 0, (µ η 1) 2, (µ η 2) 2 < 0 V (φ, η) = V 1 [φ; µ φ 1, µ φ 2, λ φ 1,..., λ φ 7] + V 1 [η; µ η 1, µ η 2, λ η 1,..., λ η 7] + V 2 [φ, η], V 1 [φ; µ 1, µ 2, λ 1,..., λ 7 ] = µ 2 1(φ I φ I) µ 2 2(φ S φ S) + V 3 [(φ φ), (φ φ); λ 1, λ 2, λ 3 ] +λ 4 (φ S φ S)(φ I φ I) + λ 5 (φ S φ I)(φ I φ S) + [λ 6 (φ S φ I) 2 + h.c.] + λ 7 (φ S φ S) 2, V 2 [φ, η] = V 3 [(φ φ), (η η); κ 1, κ 2, κ 3 ] +κ 4 (φ S φ S)(η I η I) + κ 5 (φ I φ I)(η S η S) + κ 6 (φ S φ S)(η S η S) +V 3 [(φ η), (η φ); κ{ 7, κ 8, κ 9 ] +κ 10 (φ S η I)(η I φ S) + κ 11 (φ I η S)(η S φ I) + κ 12 (φ S η S)(η S φ S) + { V 3 [(φ η), (φ η); κ 13, κ 14, κ 15 ] } +κ 16 (φ S η I)(φ S η I) + κ 17 (φ I η S)(φ I η S) + κ 18 (φ S η S)(φ S η S) + h.c., V 3 [(A B), (C D); κ 1, κ 2, κ 3 ] I,J,K,L...(1,2) %1<->%2 &1<->&2 = κ 1 (A I B I)(C J D J) + κ 2 (A I (iσ 2) IJ B J )(C K (iσ 2) IJ D L ) +κ 3 [ (A I (σ 1) IJ B J )(C K (σ 1) IJ D L ) + (A I (σ 3) IJ B J )(C K (σ 3) IJ D L ) ] }

19 Higgs Masses (η1, 0 η2, 0 ηs) 0 L Mη = a=+,,s + ( m RI a A B 0 B A C [ φ ± = 1 2 (φ 1 ± φ 2 ), η ± = 1 2 (η 1 ± η 2 ). m 2 aη a (+) η a ( ) ] ) 2 η (0) a χ(0) a η1 0 η2 0 ηs 0, Ẑ 2 ± = (η+, 0 η, 0 ηs) 0 ( m R a ) 2 η (0) a η (0) a (a=+,-,s) ( ) m I 2 a χ (0) a χ (0) a η (0) a = cos γ aˆη a + sin γ a ˆχ a, χ (0) a = sin γ aˆη a + cos γ a ˆχ a, (a = ±, S), A + B B A C η+ 0 η 0 ηs 0

20 m η a... ˆη a m χ a,... ˆχ a m 2 a = (m η a) 2 (m χ a) 2 = [(m R a )2 (m I a )2 )] cos 2γ a 2(m RI a )2 sin 2γ a, = f(v D, v S, κ 13, κ 14, κ 15, κ 16, κ 17, κ 18, γ a ) Lepton Number

21 Neutrino Sector (M ν ) ij = (Y νa ) ik (Yνa ) jk Γa (M k ) &(+),+(+) a=±,s k=1,2,s Y ν+ = 1 ( Y ν1 + Y ν2 ) = 1 h 2 h 2 0 h 2 h h 4 h 4 0 (L Y N &(-),+(-) Y (L Y ν = 1 ( Y ν1 Y ν2 ) = h 2 h 2 0 h 2 h 2 0 h 4 h 4 0 (L N Y- &(S),+(S) Y- (L Y νs = h 3 (L YS N YS (L

22 Γ a (M k ) = M [ ] k (m η 8π exp( i2γ a /M k ) 2 ln(m η a/m k ) 2 a) 2 1 (m η (mχ a/m k ) 2 ln(m χ a/m k ) 2 a/m k ) 2 1 (m χ a/m k ) 2 M k 8π 2 exp( i2γ a) m 2 a Neutrino Mass Matrix 1 (m η a /M k) 2 + ln(m η a /M k) 2 (1 (m η a/m k ) 2 ) 2. M ν = G + (M 1 )h G + (M 1 )h 2 2 G (M 1 )h 2 h 4 0 G (M 1 )h 2 h 4 G + (M 1 )h ΓS (M S )h 2 3 G ± (M 1 ) = Γ + (M 1 ) ± Γ (M 1 ) (ρ 2 )2 = G + (M 1 )h 2 2 = (ρ 2) 2 e 2ip 2 (ρ 4 )2 = (G (M 1 )) 2 4G + (M 1 ) h2 4 = (ρ 4) 2 e 2ip 4 (ρ 3) 2 = (G+ (M 1 )) 2 (G (M 1 )) 2 /2 h 2 G Γ S (M S )h 2 3 = (ρ 3 ) 2 e 2ip 3 (M 1 )

23 M M ν = diag.(e ip 2, e ip 2, e ip 2 )M ν diag.(e ip 2, e ip 2, e ip 2 ) M P = P M ν P = M ν = exp i(p 2 p 4 ) 2(ρ 2 ) (ρ 2 ) 2 2ρ 2 ρ 4 0 2ρ 2 ρ 4 2(ρ 4 ) 2 + (ρ 3 ) 2 exp i2ϕ 3

24 4; CDM

25 µ eγ. 4-1); Yukawa Lagrangian Y + Y Y S L Y ν = Y ij + e Lin j η (+) + Yij e Lin j η (+) Y S ij e Li n j η (+) S Y ± = U T el (Y ν1 ± Y ν2 )/ 2, Y S = U T el Y ν3, (h 4 2ɛ e h 2 )/ 2 h 4 / 2 0 h 2 + ɛ e h 4 ɛ e h 4 0, 0 h 2 0 h 4 / 2 ( h 4 2ɛ e h 2 )/ 2 0 ɛ e h 4 h 2 ɛ e h 4 0 h h ɛ e h " + h.c., & (±) $, ( 2ɛ e = m e /m µ 2 sin θ )

26 B(µ eγ) = 3α 64πG 2 F X 4 X GeV 2 2 < X 2 h 4h 2 2 [ F2 (M 2 1 /m2 + ) m 2 + F 2(M 2 1 /m2 ) m 2 ] + h 2 3 m e F 2 (M3 2/m2 S ), m µ m 2 S F 2 (x) = 1 6x + 3x2 + 2x 3 6x 2 ln x 6(1 x) 4. x<1 xi=mi/ i 1/12(x=1)<F(x)<1/6(x=0) E.Ma,M.Raidal (hep-ph/ ) -) Cancellation Mechanism,) Suppression Mechanism

27 ! I CDM ( +- -)/ +<( +/500GeV)!10 +=500GeV -> -=500±5GeV Potential -> +- - = 0(.)V Fine Tuning

28 ! s CDM Y S &s L LHC 0 0 h ɛ e h , ( 2ɛ e = m e /m µ 2 sin θ ). ( ) ms>o(300)gev,f2~1/12,h3~0.93

29 el + &S ns

30 4-2); Dark Matter Ns CDM n S e L, ν τ n S e L, ν τ η S + η S n S ē L, ν τ n S ē L, ν τ! ns Annihilation Diagram

31 K.Griest,Phys.Rev(1988) vσ = a + bv , a = 0, b = h 3 4 r 2 (1 2r + 2r 2 ) 24πM 2 S r = M 2 S/(m 2 s + M 2 S) / ; Relativistic Cross Section v ; S Relativistic Velocity S Relic Density Ω d h 2 = Y s 0 M S 24πM 2 S K.Griest,M.Kamionkowski,M.S.Turne r,phys.rev(1990) ; Y 1 = 0.264g 1/2 M pl M S (3b/x 2 f ) x f = ln M pl(6b/x f )c(2 + c)m S (g x f ) 1/2

32 Y# ; Asymptotic Value 3 s0=2970/cm ; Entropy Density 19 Mpl=1.22!10 GeV ; Planck E xf ; feeze-out Temperature Ms/T 1/2 =10 ; feeze-out Temperature c=1/2 Massless [ ] b 0.12 = x (GeV ) 2 f Ω d h 2 [ M S GeV = x 1/2 f e x f 0.12 Ω d h 2 ]

33 [ ] Ms ms [ ] M S [GeV] $dh =0.13 $dh =0.12 $dh = h 3 = m S [GeV]

34 $dh =0.12 ms~750gev h 3 = M S [GeV] m S [GeV]

35 (" e,$ CDM ) $dh =0.12 ~300GeV B(" e,$)<1.2!10^(-11) ~750GeV ~750GeV 600 M S [GeV] ~230GeV m S [GeV] h <1.5

36 4-3); Sunyaev-Zel dovich(sz) effect el &s 10^(-5)~10^(-7)s CMB &s 30GeV< m& <750GeV(for h3~1,m&~mel>>mns). el + &S ns

37 5;! Predictive Neutrino Texture radiative seesaw mechanism! " e,$ CDM Fermionic s CDM! CDM CDM s... &s GeV<Ns<750GeV 300GeV<Ns<750GeV