A UV description of a Composite Higgs Tony Gherghetta University - PowerPoint PPT Presentation

A UV description of a Composite Higgs Tony Gherghetta University of Minnesota Lattice for Beyond the Standard Model Physics, Argonne National Laboratory, April 22, 2016 [James Barnard, TG, Tirtha Sankar Ray, arXiv:1311.6562] Friday, 22 April 16 1

Higgs discovery - LHC Run1 h | H | 2 + λ h | H | 4 1 Higgs potential: V ( h ) = − µ 2 h H i = p 2( v + h ) v 2 = µ 2 m 2 h = 2 λ h v 2 ' (125 GeV) 2 h ' (246 GeV) 2 λ h µ 2 h ' (89 GeV) 2 λ h ' 0 . 13 Friday, 22 April 16 2

Higgs couplings Looks very much like a SM Higgs boson! Friday, 22 April 16 3

What is the nature of the Higgs boson? Standard Model/ Elementary? BOSON { Supersymmetry HIGGS OR Composite? New strong dynamics How to obtain a mass ~125 GeV much below the Planck scale? Friday, 22 April 16 4

Composite Higgs Higgs as a pseudo Nambu-Goldstone boson [Georgi, Kaplan `84] Global symmetry G spontaneously broken to subgroup H at scale f m ρ ∼ g ρ f Resonance mass: 1 . g ρ . 4 π ρ ( n ) & TeV coset G/H ⊃ h Higgs mass protected by shift symmetry -- like pions in QCD h BUT global symmetry must be explicitly broken to generate V ( h ) 6 = 0 Friday, 22 April 16 5

Global symmetry broken by mixing with elementary sector [Contino, Nomura, Pomarol `03; Agashe, Contino, Pomarol `04] SM matter and strongly-coupled gauge fields Higgs sector Ψ L,R O Ψ + g V A µ J µ L mix = λ L,R ¯ Ψ i , A µ O i h h h h Higgs potential t L,R h ∼ g 2 λ h ∼ g 2 h | H | 2 + λ h | H | 4 µ 2 16 π 2 g 2 ρ f 2 16 π 2 g 2 SM V ( h ) = − µ 2 SM where ρ Tuning: ∆ − 1 ∼ v 2 v 2 = µ 2 ✓ ◆ v h f 2 . 10% EWSB p h H i = 2 λ h ( v = 246 GeV , f & 750 GeV) Friday, 22 April 16 6

= g 2 H T Higgs mass: m 2 h ' N c m 2 π 2 m 2 T t f 2 t L t R T m T = fermion resonances (EM charges 5 / 3 , 2 / 3 , − 1 / 3) m T ∼ m ρ & 2 . 5 TeV ( g T ∼ g ρ & 3) m h & m t But, no need for m T ∼ m ρ [Marzocca, Serone, Shu 2012; Pomarol, Riva 2012] m h ∼ 125 GeV m T < m ρ light fermion resonances! Friday, 22 April 16 7

LHC Limits: The Missing Resonances Problem m T & 940 − 960 GeV Friday, 22 April 16 8

Partial compositeness: L = λ L ψ L O R + λ R ψ R O L Explains the fermion mass hierarchy [Kaplan 91; TG, Pomarol 00] ψ L λ L x ✓ Λ ◆ dim O L,R − 5 2 where m f ∼ λ L λ R v H λ L,R ∼ Λ UV x ψ R λ R Composite (RH) top quark GAUGE COUPLING [Agashe, Contino, Sundrum ’05] UNIFICATION Friday, 22 April 16 9

Features of Composite Higgs models: • Higgs is pseudo Nambu-Goldstone boson at scale f G → H H ⊃ SO (4) ∼ SU (2) L × SU (2) R where • Partially composite top L = λ L t L O R + λ R t R O L ✓ Λ ◆ dim O L,R − 5 2 where dim O L,R ∼ 5 m t ∼ λ L λ R v λ L,R ∼ Λ UV 2 What is the UV description responsible for these features? • AdS/CFT -- D-brane engineering } Involves scalars • Supersymmetric (e.g. Seiberg duality) [Caracciolo, Parolini, Serone 1211.7290] Look for one without elementary scalars... Friday, 22 April 16 10

Candidate: SO(6)/SO(5) model [Gripaios, Riva, Pomarol, Serra `09] [Other possibilities classified by Ferretti, Karateev 1312.5330] SO (6) /SO (5) ∼ SU (4) /Sp (4) = 2 of SU (2) L + 1 singlet } Higgs doublet f Symmetry breaking-pattern SU (4) → Sp (4) What is the dynamics that realizes this? Friday, 22 April 16 11

Introduce new strong gauge group Sp (2 N c ) with 4 Weyl fermion flavors ψ a ( a = 1 , . . . , 4) SU (4) global symmetry Gauge-invariant fermion bilinear: Ω ij ψ a i ψ b j = 6 of SU(4) Sp (2 N c ) is asymptotically free > 0 and confines SU (4) → Sp (4) Under what conditions does this happen? Friday, 22 April 16 12

SU(4) gauged NJL model Can be rewritten as Like “massive Yukawa theory” where “auxiliary scalar field” Friday, 22 April 16 13

One-loop effective potential Λ = UV cutoff scale where Minimum condition unbroken SU (4) m 1 = m 2 = 0 0 < ξ < 1 { Solutions m 1 = m 2 = ¯ m SU (4) → Sp (4) ξ > 1 2 is a critical point ξ = 1 Friday, 22 April 16 14

Treat Λ as a renormalization scale: UV fixed point at ξ = 1 ( Λ → ∞ with ¯ m finite) m = � 4 π 2 ξ Dynamically generated fermion mass N c Λ 2 h ψψ i ¯ Near ξ ≈ 1 µ 0 = reference scale Large anomalous dimension [Miransky, Yamawaki `89; Kondo, Tanabashi, Yamawaki `92] dim ψψ = 3 − γ m = 1 Four-fermion operator has dimension 2 -- model appears to be renormalisable in the UV! Friday, 22 April 16 15

Need to include gauge interaction and solve Schwinger-Dyson equation [Bardeen, Leung, Love `86] [Appelquist, Soldate, Takeuchi, Wijewardhana`88; Kondo, Mino, Yamawaki `89] For Sp(2Nc) gauge group obtain [Barnard, TG, Sankar Ray 1311.6562] large anomalous Large anomalous dimension for dimension and α ⌧ α ∗ ξ ≈ ξ ∗ α γ m ' 2 � 2 α ∗ small anomalous dimension ( γ m ' 1) Friday, 22 April 16 16

Evolution of couplings: (for upper trajectory) [Barnard, TG, Sankar Ray 1311.6562] Spontaneous breaking of global symmetry driven mainly by 4-fermion interaction! Friday, 22 April 16 17

Top partners Introduce a pair of colored vector-like fermions χ , ˜ χ } transform as two-index antisymmetric representation of Sp(2Nc) Gauge-invariant combinations: transform as } top partner candidates Friday, 22 April 16 18

Recall: L = λ L t L O R + λ R t R O L UV description: O L,R ↔ ψχψ (Diquark approximation to baryons [Ball `90]) } = tightly bound by 4-fermion interaction, bound to χ ψψ ( ξ � p α ) by Sp(2Nc) gauge interaction dim O L,R = dim ψχψ ≈ dim ψψ + 3 = 5 α 2 + Marginally irrelevant! 2 2 α ∗ } 3 − γ m Allows for order-one top Yukawa coupling! ξ � p α Top partners are naturally lighter than uncolored partners! Friday, 22 April 16 19

In addition there are scalar bound states: } Coloured bound states cannot get a VEV Coloured scalars must be stabilised by the SU(3) gauge interactions. Require: < d α ∗ α d α 3 α 3 Friday, 22 April 16 20

Conclusion • The Higgs boson could be composite --- Higgs is a pseudo Nambu-Goldstone boson --- Partially composite top sector • SO(6)/SO(5) model has a simple UV description --- Only fermions and gauge bosons, no elementary scalars! --- Large anomalous dimension implies four-fermion interaction is renormalisable • This simple framework can be applied to other coset groups Friday, 22 April 16 21