EFT for a Composite Goldstone Higgs Giuliano Panico IFAE Bacelona ‘HEFT 2015’ workshop Chicago – 5 November 2015
Introduction
Introduction In the quest for a fundamental description of the EW dynamics we have to cope with a serious obstruction: the Naturalness Problem The LHC will finally tell us if the EW symmetry breaking dynamics is “Natural” or fine-tuned. In this talk: focus on a class of Natural BSM theories, the composite Higgs scenarios ❖ general structure of the models ❖ description in the EFT framework ❖ impact of the LHC searches
Introduction: Composite Higgs in a nutshell In composite Higgs models the EW dynamics is linked to a new strongly-coupled sector [Georgi, Kaplan; . . . ; Contino, Nomura, Pomarol; Agashe, Contino, Pomarol; Contino, Da Rold, Pomarol; . . . ] [For reviews see: Contino, 1005.4269; G. P., Wulzer, 1506.01961] Main features: composite sector ❖ resonances at the TeV scale ρ, ψ • Fermionic resonances • Spin- 1 resonances h (KK-gluons and EW resonances) ❖ Higgs doublet as a composite Goldstone • symmetry structure ensures a mass gap between the resonances and the Higgs
Introduction: Composite Higgs in a nutshell elementary composite sector sector Elementary sector: ρ, ψ q L , u R , d R • SM states: gauge fields, W µ , B µ elementary fermions h The SM states are coupled to the composite dynamics • small (explicit) breaking of the Goldstone symmetry ➢ the Higgs gets a potential and a mass ➢ EW symmetry breaking is triggered
Introduction The top sector and the “ top partners ” control the generation of the Higgs potential and the stability of the Higgs mass top ∼ − y 2 h h h h 8 π 2 M 2 top δm 2 � + NP ψ � TeV 1 − loop ∼ h � top ➢ Light top partners are required to minimize the fine-tuning ( M ψ � 1 TeV )
Introduction The top sector and the “ top partners ” control the generation of the Higgs potential and the stability of the Higgs mass top ∼ − y 2 h h h h 8 π 2 M 2 top δm 2 � + NP ψ � TeV 1 − loop ∼ h � top ➢ Light top partners are required to minimize the fine-tuning ( M ψ � 1 TeV ) Natural Composite Higgs : Natural SUSY : ⇔ light top partners light stops
Introduction: Main phenomenological features Several features can be used to probe the composite Higgs scenario at hadron colliders ❖ Modifications of the Higgs couplings • induced by the non-linear Goldstone structure ❖ Fermionic resonances (in particular top partners) ❖ Vector resonances
How to describe a composite Higgs: The EFT approach General parametrizations can be obtained using an effective field theory approach [G. P., Wulzer; Matsedonskyi, G. P., Wulzer] Basic assumptions: ➢ Goldstone structure giving rise to the Higgs doublet ➢ calculability of the main observables (eg. Higgs potential, EW parameters) This minimal set of assumptions ensures that the effective theory describes a generic composite Higgs scenario
How to describe a composite Higgs: The EFT approach Main advantages of the effective theory approach: ◮ simplicity ◮ model independence (useful to derive robust predictions) ◮ important tool for collider phenomenology (only relevant resonances are included, easy to implement in an event generator)
Applications of the EFT formalism • Higgs couplings
The Higgs sector To generate the Higgs we assume that the composite dynamics has a spontaneously broken global invariance composite sector Minimal models are based on the symmetry breaking pattern SO (5) → SO (4) h ∈ SO (5) /SO (4) SO (5) → SO (4) ◮ The Higgs is described by a non-linear σ -model � L = f 2 � i h i T i � ∂ µ U t 5 i ∂ µ U i 5 U = exp 2 i • one free parameter: f ≡ Goldstone decay constant
The Higgs sector To generate the Higgs we assume that the composite dynamics has a spontaneously broken global invariance elementary composite sector Minimal models are based on the sector symmetry breaking pattern SO (5) → SO (4) W µ , B µ h ∈ SO (5) /SO (4) SO (5) → SO (4) ◮ The Higgs is described by a non-linear σ -model � L = f 2 � i h i T i � ∂ µ U t 5 i ∂ µ U i 5 U = exp 2 i • one free parameter: f ≡ Goldstone decay constant ◮ SM gauge fields coupled by gauging SU (2) L × U (1) Y ⊂ SO (5) ∂ µ U � D µ U = ∂ µ U − i g A µ U
The SM fermions Following the Partial Compositeness assumption the SM fermions are linearly coupled to the composite dynamics elementary composite sector sector λ L SO (5) → SO (4) q L L ⊃ λ L q L O L + λ R t R O R +h . c . t R h ∈ SO (5) /SO (4) λ R The Yukawa couplings are fixed by the representation of the composite operators • eg. in the MCHM 5 set-up O L,R ∈ 5 of SO(5) � 2 h � L U ) 5 ( U t t 5 L Yuk = c t λ L λ R ( q 5 R ) 5 c t λ L λ R sin t L t R ➠ f
Higgs couplings The effective formalism allows the direct extraction of the modifications of the Higgs couplings � � � � 1 + 2 k V h 1 + k F h µ W − µ � L = m 2 W W + + h.c. − m ψ ψψ v v ψ
Higgs couplings The effective formalism allows the direct extraction of the modifications of the Higgs couplings � � � � 1 + 2 k V h 1 + k F h µ W − µ � L = m 2 W W + + h.c. − m ψ ψψ v v ψ ξ ≡ v 2 /f 2 ❖ The size of the corrections controlled by • The couplings to the gauge fields only depend on the Goldstone structure κ V = √ 1 − ξ MCHM 4 , MCHM 5 • The couplings to the fermions have more model dependence k F = √ 1 − ξ MCHM 4 k F = 1 − 2 ξ MCHM 5 √ 1 − ξ
Higgs couplings Measuring κ V gives a model-independent bound on ξ [Panico, Wulzer 1506.01961] 1.8 LHC ( 7 TeV + 8 TeV ) 1.6 ATLAS ◆ Standard Model ★ Best fit 1.4 68 % CL 95 % CL 1.2 ★ ★ k F 0.1 1.0 ◆ 0.2 0.3 ★ ★ 0.4 0.8 0.5 MCHM 4 CMS 0.6 MCHM 5 0.4 0.7 0.8 0.9 1.0 1.1 1.2 1.3 k V ➢ Current bound driven by ATLAS [ATLAS Collab. 1509.00672] ξ < 0 . 1 ( ξ < 0 . 17 exp.) MCHM 5 @ 95% C.L. ξ < 0 . 12 ( ξ < 0 . 23 exp.) MCHM 4 • Note: much stronger than expected due to shift in central value ( κ V ≃ 1 . 08) ➢ Next runs not expected to improve significantly the bound (unless the central value will still be shifted)
Applications of the EFT formalism • Top partners
Top partners and Naturalness elementary composite sector sector Main breaking of the Goldstone SO (5) → SO (4) symmetry from the mixing of the top q L , t R h ∈ SO (5) /SO (4) λ t to the composite sector Due to the mixing the SM fields are an admixture of elementary states and composite partners | SM n � = cos ϕ n | elem n � + sin ϕ n | comp n � The top partners control the Higgs dynamics ➢ generate the dominant contribution to the Higgs potential ➢ stabilize the Higgs mass and the EW scale
Top partners and Naturalness The general form of the Higgs potential is V [ h ] = − αf 2 sin 2 ( h/f ) + βf 2 sin 4 ( h/f ) Conditions from the Higgs mass and f α = α needed ≃ m 2 β = β needed = α needed h ≫ α needed 4 2 ξ Largest cancellation in α ➠ estimate of the tuning � � 2 ∆ ∼ α expected M ψ ∼ λ 2 t α needed 450 GeV
Top partners at the LHC The effective field theory approach is useful to parametrize the phenomenology of top partners [De Simone, Matsedonskyi, Rattazzi, Wulzer; Matsedonskyi, G. P., Wulzer] The spectrum and the couplings of the resonances are fixed by the Goldstone symmetry ❖ A typical example: � T X 5 / 3 � � � � ψ 4 = ( 2 , 2 ) SO(4) = ψ 1 = ( 1 , 1 ) SO(4) = T B X 2 / 3 • The partners fill complete SO(4) multiplets B ∆ m 2 ∼ y 2 v 2 T • New colored fermions strongly ∆ m 2 ∼ y 2 L 4 f 2 coupled to the top X 2 / 3 ∆ m 2 ∼ y 2 R 4 v 2 X 5 / 3 • Exotic resonances ( X 5 / 3 ) give distinctive signals
Top partners at the LHC: Current bounds Current exclusions are mainly based on pair production [CMS-B2G-12-012, ATLAS Coll. 1505.04306] ◮ model-independent bound M ψ � 800 GeV Including single production can improve the bounds [Matsedonskyi, G. P., Wulzer in preparation] 2.0 1.2 5 � 5 singlet 10 5 � 5 4 � plet Ξ � 0.1 Ξ � 0.1 1.0 1.5 s � 8 TeV s � 8 TeV 5 � � 20 fb � 1 5 0.8 � � 20 fb � 1 y L4 y R1 10 1.0 0.6 20 ∆ V tb � 0.05 10 50 ∆ V tb � 0.1 20 0.4 100 0.5 50 200 100 0.2 800 900 750 850 950 600 800 1000 1200 1400 m X 5 � 3 � GeV � m T � � GeV � regions with minimal tuning ∆ ∼ 1 /ξ ∼ 10 are still allowed
Top partners at the LHC: High-luminosity LHC Top partners up to M ψ ≃ 3 TeV testable at the high-luminosity LHC [Matsedonskyi, G. P., Wulzer in preparation] 2.0 2.5 5 � 5 singlet 5 � 5 4 � plet Ξ � 0.1 100 Ξ � 0.1 2.0 1.5 s � 13 TeV 50 s � 13 TeV � � 20, 100 fb � 1 20 � � 100, 300, 3000 fb � 1 10 20 1.5 y L4 y R1 50 1.0 200 100 1.0 200 500 1000 ∆ V tb � 0.05 � � m � 0.3 0.5 � � m � 0.5 0.5 ∆ V tb � 0.1 500 1000 2000 3000 1000 2000 3000 1500 2500 3500 1500 2500 m X 5 � 3 � GeV � m T � GeV � � ➢ completely probing parameter space with ∆ � 50
Top partners at the LHC: Minimal models In a large class of minimal models (eg. MCHM 4 , 5 , 10 ) the mass of the lightest top partner is connected to the compositeness scale [Matsedonskyi, G. P., Wulzer; Marzocca, Serone, Shu; Pomarol, Riva] √ � 2 � 500 GeV m H 3 M ψ m top � ➠ ξ � π f M ψ ➢ convert constraints on top partners into bounds on ξ
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