Holography and DEWSB at the LHC Veronica Sanz Boston University - PowerPoint PPT Presentation

Holography and DEWSB at the LHC Veronica Sanz Boston University with Johannes Hirn and Adam Martin (Yale) hep-ph/0712.3783 + work in progress

What we know: • Strong interactions are difficult! • Rescaled QCD models are ruled out: S parameter: f π v → W L , Z L π a → S > 0 , O (1) ρ , a 1 ρ T , a T → Peskin-Takeuchi’90 • EW scale strong interactions must be very different from QCD -- But then how do we calculate? • Many attempts have been made...

What’s been done: Very few collider studies! • 4D: Walking Technicolor (Lane) Full Collider Topcolor (Hill) Study Low-ScaleTC (LSTC) (Lane) (D)BESS (Casalbuoni et al) Low-N TC (Sannino) Deconstructed Higgsless (Chivukula) Parton ... Level • 5D: Higgsless (Csaki et al) Composite Higgs (Pomarol et al) ... Common feature: TeV scale spin- resonances ( ρ T , W KK ) 1

What’s been done: Very few collider studies! • 4D: Comprehensive Walking Technicolor (Lane) More Full Collider Topcolor (Hill) Collider studies Study Low-ScaleTC (LSTC) (Lane) (D)BESS (Casalbuoni et al) Low-N TC (Sannino) Deconstructed Higgsless (Chivukula) Parton ... Level • 5D: Higgsless (Csaki et al) Composite Higgs (Pomarol et al) ... Common feature: TeV scale spin- resonances ( ρ T , W KK ) 1

Moving beyond Models: Proposal • Most general has parameters L (SM + spin − 1) O (100) way too many for practical pheno! Need an organizing principle • Start by extending holographic techniques; Can we expose new + distinct features? • NOT a new model, RATHER an organizing scheme • Implement this scheme into matrix-element generator No models currently implemented!

Moving beyond Models: Proposal • Most general has parameters L (SM + spin − 1) O (100) way too many for practical pheno! Need an organizing principle a DEWSB equivalent of what mSUGRA is for MSSM • Start by extending holographic techniques; Can we expose new + distinct features? • NOT a new model, RATHER an organizing scheme • Implement this scheme into matrix-element generator No models currently implemented!

Moving beyond Models: Proposal • Most general has parameters L (SM + spin − 1) O (100) way too many for practical pheno! Need an organizing principle a DEWSB equivalent of what mSUGRA is for MSSM • Start by extending holographic techniques; Can we expose new + distinct features? Short answer: Yes • NOT a new model, RATHER an organizing scheme • Implement this scheme into matrix-element generator No models currently implemented!

Higgsless Basics: • AdS/CFT inspired 5D version of strong DEWSB • 5D interval ; containing z ∈ ( ℓ 0 , ℓ 1 ) gauge fields. SU (2) L ⊗ SU (2) R ℓ 2 • Bulk geometry usually: z 2 ( η µ ν dx µ dx ν − dz 2 ) 0 • BC break EWS KK tower of states; γ , W ± , Z 0 zero modes are W ± +Vector, Axial resonances (not quite!): n , Z n � ℓ 1 • Resonance couplings: dz ℓ 0 z φ A ( z ) φ B ( z ) φ C ( z ) g ABC ∝ ℓ 0

Higgsless cont. • small large N T C g 5 • Spectrum: tower of narrow, weakly interacting resonances (large ) N T C large coupling to comes from plugging W L , Z L in polarizations exchange of many resonances delays unitarity violation • BUT , 5D+bifundamental leads to QCD-like spectrum ; Small perturbations don’t help S > 0 , O (1) (Agashe et al ‘07) Limited Models can be made viable Phenomenology at the expense of = 0 g ffV ∼

Our scheme: Modifying Holography • How can we extend the Holographic framework to incorporate new features? • Effective warp factors: L = − 1 � dx ω V ( z ) F V,NM F NM + ω A ( z ) F A,MN F MN V A 2 g 2 5 � z ω V,A ( z ) = ℓ 0 � 4 � � o V,A o V , o A < 0 z exp 4 ℓ 1 (Hirn, Sanz ’06,’07)

Our scheme: Modifying Holography • How can we extend the Holographic framework to incorporate new features? • Effective warp factors: L = − 1 � dx ω V ( z ) F V,NM F NM + ω A ( z ) F A,MN F MN V A 2 g 2 5 � z ω V,A ( z ) = ℓ 0 � 4 � � o V,A o V , o A < 0 z exp 4 ℓ 1 (Hirn, Sanz ’06,’07) Positive definite Acts like condensate Deformed in IR - power of z o V,A Π V,A ∼ unimportant ( Q ℓ 1 ) 4

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial M M Dialing for fixed : o A o V m A 2 m A 2 m V 2 m V 2 Remember: m A 1 m A 1 Eigenstates are a W ± m V 1 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial M M Dialing for fixed : m V 2 o A o V m A 2 m A 2 m V 2 m V 1 Remember: m A 1 m A 1 Eigenstates are a W ± 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial M M Dialing for fixed : m V 2 o A o V m A 2 m A 2 Degenerate spectrum m V 2 m V 1 Remember: m A 1 m A 1 Eigenstates are a W ± 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V < 0 , o A = 0 o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial m V 2 M M Dialing for fixed : o A o V m A 2 m A 2 Degenerate spectrum m V 2 m V 1 Remember: m A 1 m A 1 Eigenstates are a W ± 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V < 0 , o A = 0 o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial m V 2 M M Dialing for fixed : o A o V m A 2 m A 2 m V 2 m V 1 Remember: m A 1 m A 1 Eigenstates are a W ± 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

Why this deformation? ω V,A = ℓ 0 z e o V,A z 4 / ℓ 4 1 • Allows us to vary the length of the dimension the vector feels relative to the axial m V 2 M M Dialing for fixed : o A o V m A 2 m A 2 m V 2 or Inverted spectrum m V 1 Remember: m A 1 m A 1 Eigenstates are a W ± 1 , 2 , Z 0 m V 1 1 , 2 mixture of V, A | ψ X ( z ) � = | V X ( z ) , A X ( z ) � o V ≪ 0 , o A = 0 o V = 0 , o A = 0 • Added only 2 new parameters, no new fields • Couplings , etc. will also vary with ℓ 1 , o V , o A g W 1 W Z

What do we gain? • Parameter space contains non-QCD like spectrum • WSRs and simple resonance models S ameloriated when de Rafael-Knecht ‘97 M W 1 ∼ = M W 2 Appelquist-Sannino ‘98 • Whenever ; unconventional triboson, 4- ω V � = ω A boson couplings 1 ν ] ( W + [ µ Z 0 ν ] ( Z 0 1 ν ] ) + g 3 ∂ [ ν Z 0 [1 ν W + 1 W Z = g 1 ∂ [ µ W − ν ] ) + g 2 ∂ [ µ W − ν ] ( W − ν ] ) g W − [ µ W − � ℓ 1 � ℓ 1 dz ω V ( V 1 A W + A Z ) · · · � = g 3 ⊃ dz ω A ( V 1 A W + A Z ) · · · g 1 ⊃ � = g 2 ℓ 0 ℓ 0 Same region degenerate (non-QCD) mixed photon coupling g W − 1 W + γ

What do we gain? New pheno. and a new twist on old pheno. • Parameter space contains non-QCD like spectrum • WSRs and simple resonance models S ameloriated when de Rafael-Knecht ‘97 M W 1 ∼ = M W 2 Appelquist-Sannino ‘98 • Whenever ; unconventional triboson, 4- ω V � = ω A boson couplings 1 ν ] ( W + [ µ Z 0 ν ] ( Z 0 1 ν ] ) + g 3 ∂ [ ν Z 0 [1 ν W + 1 W Z = g 1 ∂ [ µ W − ν ] ) + g 2 ∂ [ µ W − ν ] ( W − ν ] ) g W − [ µ W − � ℓ 1 � ℓ 1 dz ω V ( V 1 A W + A Z ) · · · � = g 3 ⊃ dz ω A ( V 1 A W + A Z ) · · · g 1 ⊃ � = g 2 ℓ 0 ℓ 0 Same region degenerate (non-QCD) mixed photon coupling g W − 1 W + γ

Exploring and : o V o A Along o A = 0 , o V < 0 Level repulsion Only vector Both resonances unitarizes Nonzero in W L W L → W L W L g W 1 , 2 W γ

What about SM fermions? • Coupling of fermions to the new resonances will determine the best production methods at the LHC • Full 5D treatment of fermions would re-introduce many parameters... For starters: one more parameter g ffV g ffW = g SM • We can study several models of fermion interactions = g ffV κ g ffW ideally delocalized ∼ = 0 g ffV mostly composite t R ≫ g t R t R V g ffV