Boundary Conditions in AdS Life Without a Higgs

Transcription

1 Boundary Conditions in AdS Life Without a Higgs Csáki, Grojean, Murayama, Pilo, JT hep-ph/ Csáki, Grojean, Pilo, JT hep-ph/ Csáki, Grojean, Hubisz, Shirman, JT hep-ph/ Cacciapaglia, Csáki, Grojean, JT hep-ph/ , hep-ph/

2 Outline Motivation Gauge Theory on an Slice of AdS Unitarity of WW Scattering Life without a Higgs Models Conclusions

3 Hierarchy Problem SUSY Technicolor

4 Hierarchy Problem SUSY curved Extra Dimensions Technicolor flat RS bulk fermions small large little Higgs discrete

5 Klebanov-Strassler Klebanov, Strassler hep-th/ with a single wrapped D5 brane at the bottom of the duality cascade: SU(2) SU(2) L SU(2) R U(1) A 1 1 B 1 1 on part of moduli space SU(2) L SU(2) R SU(2) electroweak symmetry breaking! Luty, Grant, JT hep-ph/

6 Klebanov-Strassler Cartoon IR BC AdS

7 Can we break Electroweak Symmetry with AdS Boundary Conditions? how do we reduce the rank of the gauge group? is WW scattering unitary? why does MW 2 = cos θ W MZ 2? how do we get quark and lepton masses?? precision electroweak measurements???

8 Ground Rules extra dimensions branes AdS/CFT correspondence low-scale SUSY

9 Ground Rules extra dimensions branes AdS/CFT correspondence low-scale SUSY strong coupling

10 Ground Rules extra dimensions branes AdS/CFT correspondence low-scale SUSY strong coupling anthropic incantations

11 Gauge Theory on an Slice of AdS ds 2 = ( R z ) 2 (η µν dx µ dx ν dz 2 ) R z R Mixed Boundary Conditions z A µ (x, z) = g2 5 v2 2 A µ(x, z) Dirichlet and Neumann are special cases

12 KK Modes A a µ(x, z) = n ψa n(z)a µ (x)e ip nx, where p 2 n = M 2 n ( 2 z 1 z ) z + Mn 2 ψ a n (z) = 0, ψn a = Vb aψb g cubic g abc mnk = g 5 dz ( R z ) ψ a m (y)ψ b n(y)ψ c k (y) g 2 quartic g 2 abcd mnkl = g 2 5 dz ( R z ) ψ a m (y)ψ b n(y)ψ c k (y)ψd l (y)

13 Scattering Amplitude incoming: p µ = (E, 0, 0, ± E 2 Mn) 2 outgoing: k µ = (E, ± E 2 Mn 2 sin θ, 0, ± E 2 Mn 2 cos θ) longitudinal polarization: ɛ µ = ( p M, E p M p ) (4) E4 A = A Mn 4 (2) E2 + A Mn 2 + A (0) +...

14 WW Scattering via KK bosons

15 Cancellation E 4 term: g 2 nnnn k g2 nnk dy ψ 4 n (y) = k dy dz ψ 2 n(y)ψ 2 n(z)ψ k (y)ψ k (z) completeness of hermitian operator: k ψ k(y)ψ k (z) = δ(y z) k M 2 k E 2 term: 4g 2 nnnnm 2 n 3 k g2 nnk M 2 k ( dy ψ 2 n (y)ψ k (y) ) 2 = 4 3 M 2 n dy ψ 4 n (y) 2 3 [ψ3 nψ n] +2 k [ψ nψ nψ k ] dy ψ 2 n(y)ψ k (y) k [ψ2 nψ k ] dy ψ 2 n(y)ψ k (y) for Dirichlet or Neumann BC s the E 2 terms cancel

16 Finite VEV for small v: M 2 W = g2 v 2 4 z ψ(z) = g2 5 v2 2 ψ(z) R 2 R 2 for R = GeV 1, R = GeV 1

17 Decoupling the Higgs for v = 1 TeV ψ(z) z Higgs decouples from scattering as v

18 Towards a Realistic Model ds 2 = ( R z ) 2 (η µν dx µ dx ν dz 2 ) SU(2) L SU(2) R U(1) B L BC s: at z = R : SU(2) R U(1) B L U(1) Y at z = R : SU(2) L SU(2) R SU(2) z A L a µ = 0, A R 1,2 z ( g5 B µ + g 5 A R 3 µ µ = 0 A L a 5 = 0, A R a 5 = 0, B 5 = 0 ) = 0, g5 B µ g 5 A R 3 µ = 0 ( ) z A L a µ + A R µ a = 0, z B µ = 0 A L µ a A R µ a = 0, A + a 5 = 0, z A a 5 = 0, B 5 = 0 at z = R, F La ν5 + F Ra ν5 = 0

19 KK Modes B µ (x, z) = g 5 a 0 A µ (x) + A L µ 3 (x, z) = g 5 a 0 A µ (x) + A R 3 µ (x, z) = g 5 a 0 A µ (x) + k=1 ψ(b) k k=1 ψ(l3) k k=1 ψ(r3) k A L ± µ (x, z) = k=1 ψ(l±) k (z) W (k) ± µ (x), A R ± µ (x, z) = k=1 ψ(r±) k (z) W (k) ± ( ψ (A) k (z) = z a (A) k µ (x). (z) Z µ (k) (x), (z) Z µ (k) (x), (z) Z µ (k) (x), ) J 1 (M k z) + b (A) k Y 1 (M k z) M 2 W = 1 R 2 log( R R ) M 2 Z = g g2 5 g g2 5 1 R 2 log( R R )

20 SM Gauge Couplings g 5 g ( 5 a 0 Qγ µ + g 5 ψ1 L± (R)T ± W µ ± + g 5 ψ (L3) 1 (R)T 3 + g 5 ψ (B) 1 (R) Y 2 ) Z µ g 2 = e 2 = R R R g 2 5 ψ(l±) 1 (R) 2 dz R z (ψ(l±) 1 (R) 2 +ψ (R±) g 2 5 g2 5 a2 0 R R R dz ( R z )(2 g 2 5 +g2 5 )a2 0 = 2 g5 1 (R) 2 ) = R log(r /R) g 2 5 g2 5 (g g2 5 )R log(r /R) the Z couplings are also reproduced: g 2 cos θw 2 = g 2 5 ψ(l3) (R) 2 R R = g 2 = sin θ W = R dz ( R z )(ψ (L3) (R) 2 +ψ (R3) (R) 2 +ψ (B) (R) 2 ) g 2 5 g 2 R log(r 5 + g2 5 /R), g5 2+2 g2 5 g 2 5 g2 5 (g5 2+ g2 5 )R log(r /R), g 5 = g g g 5 2 g2 +g 2

21 Custodial Symmetry cos θw 2 = g2 5 + g2 5, g5 2+2 g2 5 M 2 W = 1 R 2 log( R R ) M 2 Z = g g2 5 g g2 5 1 R 2 log( R R ) Hence ρ = M 2 W M 2 Z cos2 θ W = 1

22 Anthropic Misunderstandings The universe must be such that life can be advanced enough to contemplate the universe and be primitive enough to contemplate the anthropic principle. what varies between different universes? Anthropic Chestnut: The Higgs VEV must be in a narrow range for complex chemistry to arise... unless we make other modifications in the theory, with a warped extra dimension an infinite range is allowed!

23 Precision Electroweak W µ B µ L eff = S 16π F 3µν L F µν QCD, technicolor S = O(1) RS with TeV fermions S = O( 30) Golden, Randall; Holdom, JT; Peskin, Takeuchi Csaki, Erlich JT, hep-ph/

24 Light Resonances, Small S Log R [GeV -1 ] 10-4 Log R [GeV -1 ] g SM g SM -.1 g SM -8 T g SM S c L c L

25 Perturbative Unitarity Λ NDA 24π3 g 2 5 R R 12π4 M 2 W g 2 M W ( = O 12π 4 R log(r /R) )

26 Fermion Boundary Conditions χ L,R = z 5 2 ψ L,R = z 5 2 S T ev = d 4 x ( R z [ ] A L,R J 1 2 L,R(m n z) + B L,R J +c 1 (m n z) 2 c L,R [ ] A L,R J 1 2 L,R(m n z) + B L,R J c 1 (m n z) 2 +c L,R ) 4 MD R [ ψ R χ L + χ L ψr + ψ L χ R + χ R ψl ] S P l = d 4 x i ξ σ µ µ ξ iησ µ µ η + f ( ηξ + ξ η ) +M R ( ψ R ξ + ξ ψ R ) Taking c L 0.4, c R 1 3, M D = 900, M t = 0, M b = and f = GeV gives m t 170 GeV m b 4.5 GeV

27 Fermion Wavefunctions ψ z 3/ t R b L t L b R z

28 Delocalized Higgs? AdS/CFT Correspondence: a localized Higgs O with d[o] = more realistic: d[o] to be finite Higgs profile in bulk, finite VEV walking technicolor limit d[o] = 2 Two Branes are Better than One? Two AdS 5 with a shared Planck brane and two TeV branes Dimopoulos, Kachru, Kaloper Lawrence, Silverstein hep-th/ different R and R for third generation third generation couples to a different CFT sector

29 Conclusions/Questions BC s can be used to break electroweak symmetry WW scattering can be unitarized without a Higgs models with custodial symmetry exist oblique corrections can be small can m t vs Zb b problem be fixed? can we do this analysis for Klebanov-Strassler?