Introduction : Extra dimensions. Y. Hosotani, PPP2011, YITP, 8 March 2011, - 2

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2 Introduction : Extra dimensions Y. Hosotani, PPP2011, YITP, 8 March 2011, - 2

3 Success in LHC Y. Hosotani, PPP2011, YITP, 8 March 2011, - 3

4 M 4 S 1 φ(x, y) = φ n (x) e i(n+α)y/r m 2 n = (n + α)2 R 2 KK towers M 4 K S 1 /Z 2 M 4 S 2 M 4 (S 1 /Z 2 ), RS warped space φ a (x, y) =P ab 0 φb (x, y), P 2 0 =1 Ψ(x, y) =γ 5 P 0 Ψ(x, y) Y. Hosotani, PPP2011, YITP, 8 March 2011, - 4

5 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 5

6 Gauge-Higgs Unification in 5 dimensions 4-dim. components Aµ extra-dim. component Ay Hosotani 1983, 1989 Davies, McLachlan 1988, 1989 Hatanaka, Inami, Lim, 1998 Higgs boson as an AB phase in extra dim eiθ H (x) P exp ig θ H (x) = θh + dyay C H(x) fh Y. Hosotani, PPP2011, YITP, 8 March 2011, - 6

7 SO(5) U(1) EW sym breaking H parity & stable Higgs Dark matter precision measurements Higgs production KK Z production KK gluon... Y. Hosotani, PPP2011, YITP, 8 March 2011, - 7

8 SO(5) U(1) ds 2 = e 2k y dx µ dx µ + dy 2 0 y L = πr Agashe, Contino, Pomarol 2005 Hosotani, Sakamura 2006 Medina, Shah, Wagner 2007 Planck brane Λ = 6 k 2 SO(5) U(1) TeV brane Aµ A y Aµ A y Orbifold BC (x, y) = P 0 Aµ A y (x, πr y) = P 1 Aµ A y (x, y)p 0 (x, πr + y)p 1 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 8

9 P 0 = P 1 = W Z γ A µ SO(5) SO(4) SU(2) L SU(2) R Higgs A y φ 1 φ 2 φ 3 φ 4 φ1 + iφ Φ = 2 φ 4 iφ 3 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 9

10 Matter content YH, Noda, Uekusa 2009 (YH, Oda, Ohnuma, Sakamura 2008) SO(5) U (1) Planck brane Quarks Brane scalar Φ (0, 1 ) 2 Leptons TL BL t L b L t 2 R 3 T R B R U R D R X R Y R ( 12, 0) L 2XR L 2Y R L 3XR L 3Y R L 1XR L 1Y R vector rep UL D L X L Y L br 1 3 TeV brane Ψ(x, y) = P0 γ 5 Ψ(x, y) L2X L (0, 0) L 2Y L L3X L ντ L L3Y L τ L ν τr 0 L1XL L1Y L τr 1 ( 12, 12 ) Y. Hosotani, PPP2011, YITP, 8 March 2011, - 10

11 Matter content YH, Noda, Uekusa 2009 TeV brane Planck brane Φ = 0 1 (0, 2 ) SM spectrum TL BL t L b L t 2 R 3 T R B R U R D R X R Y R ( 12, 0) L 2XR L 2Y R L 3XR L 3Y R L 1XR L 1Y R Anomaly cancellation UL D L X L Y L br 1 3 L2X L (0, 0) L 2Y L L3X L ντ L L3Y L τ L ν τr 0 L1XL L1Y L τr 1 ( 12, 12 ) Y. Hosotani, PPP2011, YITP, 8 March 2011, - 11

12 Effective interactions AB phase θ H = θh + H fh fh YH 1983, Oda-Weiler 2005 Leff Veff (θ H ) mw (θ H ) 2 2 mkk = kl πg Falkowski 2007 Wµ W µ mf (θ H ) ψ f ψf 1 2 mz (θ H )2 Zµ Z µ Sakamura-YH 2006, 2007 YH-Kobayashi 2008 θh θh + 2π Y. Hosotani, PPP2011, YITP, 8 March 2011, - 12

13 Gauge-Higgs m W (ˆθ H ) 1 2 gf H sin ˆθ H m Z (ˆθ H ) 1 2 cos θ W gf H sin ˆθ H m f (ˆθ H ) y f f H sin ˆθ H periodic nonlinear SM 1 g(v + H) 2 1 g(v + H) 2 cos θ W y f (v + H) ˆθ H = θ H + H f H WWH ZZH Yukawa WWHH ZZHH = SM cos θ H = SM cos 2θ H Y. Hosotani, PPP2011, YITP, 8 March 2011, - 13

14 Energy density/m 4 KK U 2 gauge total θ /π H U total gauge θ /π H - 6 fermions z L = fermions z L = m H : 70 GeV 135 GeV θ H = π 2 LEP2 bound is evaded. Y. Hosotani, PPP2011, YITP, 8 March 2011, - 14

15 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 15

16 Proof (2) SO(5) : YH, Tanaka, Uekusa, SO(4) SU (2)L SU (2)R { Tα } = { T al, T ar, T a, T 4 } { T ar, T al, T a, T 4 } Algebra is invariant under { T α } = SO(5)/SO(4) T α = ΩH T α Ω 1 H PH : ΩH = SU (2)L SU (2)R 1 1 T 4 T 4 Agashe, Contino, Da Rold, Pomarol 2006 T parameter Zbb Y. Hosotani, PPP2011, YITP, 8 March 2011, - 16

17 At θ H = π 2 A M Ω H A M Ω 1 P H -inv P H Y. Hosotani, PPP2011, YITP, 8 March 2011, - 17

18 P H = + W (n),z (n), γ (n), gluon (n),q (n), (n), H (n),w (n),z (n),q (n), (n), P H Y. Hosotani, PPP2011, YITP, 8 March 2011, - 18

19 Y. Hosotani, Kobe PPP2011, Workshop, YITP, 48 January March 2011,

20 Ω H h 2 Relic abundance semi-analytic micromegas WMAP H h Higgs mass (GeV) m H z L m H 70 GeV m H 72 GeV T f 3 GeV HH b b 34% WW 61% Y. Hosotani, PPP2011, YITP, 8 March 2011, - 20

21 Production: Z Z W Z W g g W t H H Z H H H H W Cheung, Song, Alves, ν, ν background hard at LHC, possible at ILC Y. Hosotani, PPP2011, YITP, 8 March 2011, - 21

22 YH, Tanaka, Uekusa, in preparation e + e ZHH Σ fb z L = 10 5 z L = Z L s Z T major background e + e Zν ν Polarized e ± s = 750 GeV,zL = 10 15,M mis > 250 GeV, cos θ < 0.6 L>2.0 ab 1 for 5σ Y. Hosotani, PPP2011, YITP, 8 March 2011, - 22

23 e + e Z,q q No. data SM z L : z L : z L : 10 5 sin 2 θ W χ 2 (AF B) χ 2 (Z decay) z L Y. Hosotani, PPP2011, YITP, 8 March 2011, - 23

24 Observe extra dimension KK modes YH, Tanaka, Uekusa, in preparation Y. Hosotani, PPP2011, YITP, 8 March 2011, - 24

25 mass z L : z L : 10 5 m KK mass Σ d θ H/π Z (1) gluon (1) u (1) Σ s θ H/π t (1) in GeV Y. Hosotani, PPP2011, YITP, 8 March 2011, - 25

26 KK Z (1) z L m Γ in GeV Large couplings for right-handed quarks and lepton 10 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 26

27 p p Z e + e σ(pb/bin) z L = 10 5 σ(pb/bin) z L = m = 653 GeV, Γ = 101 GeV m = 1130 GeV, Γ = 415 GeV σ =1.8 pb σ =0.06 pb z L Y. Hosotani, PPP2011, YITP, 8 March 2011, - 27

28 q q Z (1) e + e qg qz (1) jet + e + e σ(pb/bin) z L = σ(pb/bin) z L = m = 1130 GeV, Γ = 415 GeV m = 1130 GeV, Γ = 415 GeV σ =1.9 pb σ =1.0 pb Y. Hosotani, PPP2011, YITP, 8 March 2011, - 28

29 KK gluon (1) Strong couplings for right-handed quarks Couplings/g s u R c R t R In naive perturbation theory Γ 13 m Y. Hosotani, PPP2011, YITP, 8 March 2011, - 29

30 z L Z (1) m 1130 GeV, Γ 415 GeV m H 70 GeV z L 10 5 Y. Hosotani, PPP2011, YITP, 8 March 2011, - 30