Y. Hosotani, SI2010, 15 August 2010, - 2

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2 = Y. osotani, SI2010, 15 August 2010, - 2

3 Gauge-iggs Unification a la Kaluza-Klein osotani 1983, 1989 Davies, McLachlan 1988, 1989 atanaka, Inami, Lim, 1998 Gauge theory A M in higher dimensions 4-dim. components A µ 4D gauge fields γ, W, Z extra-dim. component A y 4D iggs fields Aharonov-Bohm phase Symmetry breaking Y. osotani, SI2010, 15 August 2010, - 3

4 ds 2 = e 2k y dx µ dx µ + dy 2 0 y L = πr Agashe, Contino, Pomarol 2005 osotani, Sakamura 2006 Medina, Shah, Wagner 2007 Planck brane Λ = 6 k 2 SO(5) U(1) TeV brane Aµ A y Aµ Aµ (x, y) = P 0 A y Aµ (x, πr y) = P 1 A y A y Orbifold BC : P 0, P 1 (x, y)p 0 (x, πr + y)p 1 Y. osotani, SI2010, 15 August 2010, - 4

5 P 0 = P 1 = W Z γ A µ SO(5) SO(4) SU(2) L SU(2) R iggs A y φ 1 φ 2 φ 3 φ 4 Φ = φ1 + iφ 2 φ 4 iφ 3 Y. osotani, SI2010, 15 August 2010, - 5

6 Y, Noda, Uekusa 2009 (Y, Oda, Ohnuma, Sakamura 2008) Planck brane SO(5) U(1) TeV brane Φ (0, 1 2 ) ˆT R ˆB R ÛR ˆD R ˆX R ŶR ( 1 2, 0) ˆL 2XR ˆL 2YR ˆL 3XR ˆL 3YR ˆL 1XR ˆL 1YR T B t b t 2 3 vector rep ν τ τ L 1X L 1Y τ U D X Y 1 b 1 3 ( 1 2, 1 ) (0, 0) 2 L 2X L 2Y L 3X L 3Y ν τ 0 Y. osotani, SI2010, 15 August 2010, - 6

7 Y, Noda, Uekusa 2009 (Y, Oda, Ohnuma, Sakamura 2008) Planck brane TeV brane ˆT R ˆB R ÛR ˆD R ˆX R ŶR ( 1 Φ (0, 1 2, 0) 2 ) ( 1 SM spectrum ˆL 2XR ˆL 2YR ˆL 3XR ˆL 3YR ˆL 1XR ˆL 1YR 4D anomaly cancellation in SU(2) L SU(2) R U(1) TL B L t L b t L R 2, ν τ τ L L 1X L L 1Y τ L UL D L X L Y 1 b L R 1 3 ) (0, 0) R L Ψ(x, y) =P 0 γ 5 Ψ(x, y) Ψ(x, πr y) L 2X L L 2Y L L 3X L L 3Y L ντ R = P 1 γ 5 Ψ(x, πr + y) 0 Y. osotani, SI2010, 15 August 2010, - 7

8 Planck brane Symmetry breaking SO(5) U(1) TeV brane orbifold BC SO(4) U(1) SU(2) L SU(2) R U(1) ˆΦ Planck brane SU(2) L U(1) Y Exotic fermions : masses O(m KK ) osotani mechanism top quark multiplet U(1) EM Y. osotani, SI2010, 15 August 2010, - 8

9 iggs field = fluctuations of an AB phase in the 5th dim eiθ P exp ig A45 y (x, y) = h0 (y) θ + Gauge inv (x) f dyay C θ Planck brane fictitious flux RS TeV brane θ θ + 2π Y. osotani, SI2010, 15 August 2010, - 9

10 Effective interactions ˆθ = θ + f f = 2 kl m KK πg L eff V eff (ˆθ ) Y 1983, Oda-Weiler 2005 m W (ˆθ ) 2 W µ W µ 1 2 m Z(ˆθ ) 2 Z µ Z µ Sakamura-Y 2006, 2007 m f (ˆθ ) ψ f ψ f Y-Kobayashi 2008 Y. osotani, SI2010, 15 August 2010, - 10

11 Gauge-iggs m W (ˆθ ) 1 2 gf sin ˆθ m Z (ˆθ ) 1 2 cos θ W gf sin ˆθ m f (ˆθ ) y f f sin ˆθ periodic nonlinear SM 1 g(v + ) 2 1 g(v + ) 2 cos θ W y f (v + ) ˆθ = θ + f WW ZZ Yukawa WW ZZ = SM cos θ = SM cos 2θ Y. osotani, SI2010, 15 August 2010, - 11

12 1 U Energy gauge Θ Π total top quark osotani mechanism 1983 m : 55 GeV 140 GeV θ = π 2 cos θ =0 LEP2 bound is evaded. Y. osotani, SI2010, 15 August 2010, - 12

13 -Parity & Absolute Stability Mirror reflection symmetry (x µ,y) (x µ, y) (A µ,a y ) (A µ, A y ), Ψ ±γ 5 Ψ invariant under ˆθ = θ + f ˆθ Enhanced gauge symmetry invariant under ˆθ ˆθ + π Y. osotani, SI2010, 15 August 2010, - 13

14 θ = π 2 π 2 + π f 2 π f 2 f Invariant under : all other SM particles : + Y. osotani, SI2010, 15 August 2010, - 14

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16 = b b = b n b b Z W g Z W t g Y. osotani, SI2010, 15 August 2010, - 16

17 Ω h 2 Relic abundance 0.2 semi-analytic micromegas WMAP h iggs mass (GeV) m 70 GeV m T f 3 GeV b b 34% WW 61% z L 10 5 Y. osotani, SI2010, 15 August 2010, - 17

18 !"#$! %! 5" %).& / 0 67!96 :33;(%/77<%=::5>?4(@A4B(A;%/77C%DE<FG :$="I%"""%/77J :K:=!:"55%/77E L:IMI67%/77C NK#5%542O'1%/77J NK#5%/77E%*+ 67!9/ NK#5%542O'1%DP33G :QR+.S+O%5+1(;S;T;SU 67!98 % many uncertainties 67!99 % / 67 8!"#$%&'((%)*+,-. / 0 arxiv: [astro-ph.co] 18 Dec 2009 Y. osotani, SI2010, 15 August 2010, - 18

19 Production: Z Z W W Z W Z W g g t K. Cheung, J. Song arxiv: hard at LC, possible at ILC Y. osotani, SI2010, 15 August 2010, - 19

20 KK Z couplings in g w z L #7 2#1;<= &6/(89 >&6&5&5 =#1;<= &68(// >&6/.-9 2#?@0A= >&6%-%( >%6&-, =#?@0A= >&68-.% >&65(,8 B#1;<= >&6,/%- &6&.-, C#1;<= >&6,/-& >&69858 B#?@0A= &6&.&5 &6(/8% C#?@0A= &6&.&/ &6/5-5 ;#1;<= >&685,/ &6&(,9 )2#1;<= >&685,/ &6&(,9 ;#?@0A= &68,8/ %6-8, )2#?@0A= &68,8% %6(/8 for z L 10 5 (10 15 ) m KK 836 (1, 466) GeV m 652 GeV (1, 129 GeV) Γ 95 GeV (372 GeV) p p Z e + e z L = Y. osotani, SI2010, 15 August 2010, - 20

21 In the Gauge-iggs unification m 70 GeV We might see extra dimensions! Y. osotani, SI2010, 15 August 2010, - 21