Gauge-Higgs Unification and the LHC

Transcription

1 Gauge-Higgs Unification and the LHC

2 If the Higgs boson is 124 or 126 or? GeV with SM couplings, Explain SM Higgs. with non-sm couplings, is not seen at LHC, Higgs is stable. Higgs does not exist. 2

3 If the Higgs boson is 124 or 126 or? GeV with SM couplings, with non-sm couplings, is not seen at LHC, Higgs is stable. gauge-higgs Higgs does not exist. 3

4 Discovery of un-discovery of the Higgs boson 4

5 It s no surprise in gauge-higgs unification. 5

6 Gauge-Higgs Unification A M 4-dim. components A µ 4D gauge fields γ, W, Z extra-dim. component A y 4D Higgs fields H Aharonov-Bohm phase Symmetry breaking Hosotani mechanism 6

7 e iˆθ H (x) P exp ig C ˆθ H (x) =θ H + H(x) f H dya y θ H = Higgs f H θ H θ H +2π differs from SM. 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 YH, Oda, Ohnuma, Sakamura 2008 YH, Noda, Uekusa 2009 Planck brane brane fermions brane scalar Λ = 6 k 2 SO(5) U(1) g A g B quarks, leptons TeV brane y = 0 y = π R 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 8

9 1 P 0 = P 1 = SO(5) SO(4) SU(2) L SU(2) R W Z γ A µ Higgs A y φ 1 φ 2 φ 3 φ 4 brane scalar SO(4) U(1) SU(2) L U(1) = SU(2) L U(1) Y θ H =0 U(1) EM 9

10 parameters inputs RS: k, z L = e kl g A, g B fermions α w, sin 2 θ W m Z quark/lepton masses One free parameter z L 10

11 Planck scale input m KK TeV scale output Weak scale m W input m KK = πke kl π kl m W kl = for z L = Symmetry breaking 11

12 in SM f H sin ˆθ H v + H L eff gf H sin ˆθ H W µ W µ cos 2 θ W Z µ Z µ y f f H sin ˆθ H ψ f ψ f ˆθ H = θ H + H f H f H = 2 kl m KK πg WWH ZZH Yukawa = SM cos θ H 12

13 YH, Oda, Ohnuma, Sakamura 2008 YH, Noda, Uekusa 2009 Planck brane SO(5) U(1) TeV brane ˆΦ (0, 1 2 ) ˆΦ = 0 Anomaly cancelation 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 TL B L t L b t L R 2 3 vector rep ν τ τ L L 1X L L 1Y τ L UL D L X L Y 1 b L R 1 3 ( 1 2, 1 ) (0, 0) 2 R L Ψ(x, y) =P 0 γ 5 Ψ(x, y) Ψ(x, πr y) =P 1 γ 5 Ψ(x, πr + y) L 2X L L 2Y L L 3X L L 3Y L ντ R 0 13

14 V eff (θ H )/m 4 KK U gauge total fermions z L = θ /π H θ H = π 2 SU(2) L U(1) U(1) EM m H = 135 GeV (z L = ) 14

15 θ H = π 2 YH, Ko, Tanaka, 2009 YH, Tanaka, Uekusa, 2010 θ H + H f H = π 2 + H f H π 2 H f H H : all other SM particles : + 15

16 SO(5) : SO(4) SU(2) L SU(2) R SO(5)/SO(4) { T α } = { T a L, T a R, T â, Tˆ4 } P H : SU(2) L SU(2) R T ˆ4 T ˆ4 Agashe, Contino, Da Rold, Pomarol 2006 T parameter Zb b 16

17 Where is SU(2) x U(1) L in SO(5) x U(1)? Y SO(5) U(1) X SO(4) U(1) X SU(2) L SU(2) R U(1) X ˆΦ = 0 SU(2) L U(1) = SU(2) L U(1) Y θ H =0 U(1) EM 17

18 SO(5) { T a L, Ta R, ˆT a, ˆT 4 } { I a L, Ia R, Îa, Î 4 } SU(2) L SU(2) R SU(2) L SU(2) R I a L I a R = 1 ± cos θ H 2 T a L + 1 cos θ H 2 T a R sin θ H 2 ˆT a Note: T a L + T a R = Ia L + Ia R : custodial SU(2) V W ± Z γ couples to I 1 c φ Q X + s φ I 3 L ± ii2 L R, s φ = t W c W I 3 L s W Q Y = Q EM = I 3 L + I3 R + Q X = T 3 L + T 3 R + Q X Higgs Î 4 = ˆT 4 YH, Sakamura 2007 Contino, Marzocca, Pappadopulo, Rattazzi 2011 Hatanaka, YH, Shimotani 18

19 W ± µ Z µ γ µ Z µ W 1 µ, W2 µ W 3 µ Bµ X Wµ 3 SU(2) L U(1) X SU(2) R Furthermore W (n) µ (x) C(z; λ (n) W )I+ L (θ H) sin θ H 2 [Ŝ(z; λ (n) W ) C(z; λ(n) W )] ˆT + All KK modes participate. 19

20 Collider signatures θ H = 1 2 π ν, ν background Cheung, Song, , Alves, YH, Tanaka, Uekusa,

21 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 YH, Tanaka, Uekusa,

22 KK Z (1) & γ (1) Z (1) γ (1) z L m Γ in GeV z L m Γ in GeV 10 strong couplings at TeV 22

23 q q Z (1), γ (1) e + e σ (pb/20gev)!"#!$# z L = 10 5 z L = z L = 10 5 z L = σ (pb/20gev) z L = 10 15!%#!&# z L = SM '( Z (1) z L m Γ m ee (GeV) in GeV m ee (GeV) γ (1) z L >

24 Ω H h 2 Relic abundance YH, Ko, Tanaka, semi-analytic micromegas WMAP H h Higgs mass (GeV) m H m H = GeV z L m H 72 GeV

25 z L > m H = 135 GeV m H = GeV z L 10 5 compatible with m H = GeV z l > 10 15? Yes Hatanaka, YH, 2011 m H = GeV 25

26 V eff = ± 1 2 d 4 p (2π) 4 n ln p 2 + m n (θ H ) U gauge total fermions θ /π H non-susy W, Z, Higgs mn t mn W, Z, Higgs m n = m 2 n + Λ2 gh m n = t m 2 n + Λ2 stop 26

27 m h = 120 GeV m h 120GeV z L = z L = Λ stop = GeV Λ gh > 1 TeV stopgev m h = m h 75GeV GeV m h = 70 GeV m h 70GeV Phase transition stop mass GeV 200 for m h = GeV No EWSB gh GeV GeV for m h 120 GeV 27

28 If the Higgs boson is 124 or 126 or? GeV with non-sm couplings, or is not seen at LHC (as Higgs is stable), gauge-higgs (extra dimensions). 28