Modeling and Testing a Composite Higgs Andrea Wulzer Based on: - PowerPoint PPT Presentation

Modeling and Testing a Composite Higgs Andrea Wulzer Based on: “The Discrete Composite Higgs model”, with G. Panico, and work in progress with G.Panico and A.Matsedonski

Introduction: Good reasons to advocate a light Higgs : 1. EWPT 2. We have (perhaps) almost seen one !

Introduction: Imagine the Higgs is Composite (Georgi, Kaplan) Hierarchy Problem is solved : Corrections to screened above \ 1 /l H m H is IR-saturated m H

Introduction: Postulate a New Strong Sector SILH Paradigm (or Prejudice) : (Giudice, Grojean, Pomarol, Rattazzi) One mass scale One coupling (Example: ) But if the Higgs is a Goldstone Higgs Decay Constant:

Models of Composite Higgs The non-linear sigma-model Composite Sector Elementary states U = Exp [ ih a T a /f ]

Models of Composite Higgs The non-linear sigma-model Perfect to study modified Higgs couplings (Giudice et al, Barbieri et al, Espinosa et al.) λ ≃ λ SM (1 + c ξ ) EWPT suggest :

Models of Composite Higgs The non-linear sigma-model Perfect to study modified Higgs couplings (Giudice et al, Barbieri et al, Espinosa et al.) λ ≃ λ SM (1 + c ξ ) EWPT suggest : However , it is not completely predictive framework : Higgs Potential is not IR-saturated

Models of Composite Higgs G.Panico, A.W.: arXiv:1106.2719 The Discrete Composite Higgs model Introduce resonances that protect the potential W/B U 1 U 2 � ρ ρ � ′ � � � � L π = f 2 + f 2 ( D µ U 1 ) t D µ U 1 ( D µ U 2 ) t D µ U 2 4 Tr 4 Tr Each U is a Goldstone matrix of coset SO(5) L × SO(5) R / SO(5) V .

Models of Composite Higgs G.Panico, A.W.: arXiv:1106.2719 The Discrete Composite Higgs model Introduce resonances that protect the potential W/B U 1 U 2 � ρ ρ { � ′ � � � � L π = f 2 + f 2 ( D µ U 1 ) t D µ U 1 ( D µ U 2 ) t D µ U 2 4 Tr 4 Tr Each U is a Goldstone matrix of coset SO(5) L × SO(5) R / SO(5) V . 10+10 scalar d.o.f reduced to 4 by gauging ,

Models of Composite Higgs The Discrete Composite Higgs model Higgs is Goldstone under three symmetry groups : W/B U 1 U 2 � ρ ρ � ′ Collective Breaking (Arkani-Hamed, Cohen, Georgi) EWSB effects only through the breaking of all groups

Models of Composite Higgs The Discrete Composite Higgs model Higgs Potential is now finite at one loop Careful analysis reveals stronger ( ) suppression Similar protection mechanism for S and T

Models of Composite Higgs The Discrete Composite Higgs model Fermionic sector : � ψ q L /t R ψ U 1 U 2 ∆ � m Top Partners: L ( U 1 ) IJ ψ J + t R ∆ I R ( U 1 ) IJ ψ J + ψ ψ K + i ∆ iI I ∆ J I ( U 2 ) JK � L mix = q L Partial compositeness (Kaplan 1991;)

The Higgs Potential Dominated by fermionic contribution Gives realistic EWSB only if : N c The Higgs quartic is of order V (4) ∼ 16 π 2 y 4 � h � 4 � g ρ � � m H ∼ 4 2 N c m t . 4 π

The Higgs Potential However .... Blind Scan Points with no light partners 4 4 � � � � m t ' � g Ρ f � � � � � � � � � � � 3 � � 3 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � m H � m t � � � � � � � � � � � � � � m H � m t � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 2 � �� � � � � � � � � � � � � � � � � � � � 2 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 0 0 0 2 4 6 8 0 2 4 6 8 g Ρ g Ρ The naive estimate fails if there are light top partners