Implications of a 125 GeV Composite Higgs Alex Pomarol, UAB - PowerPoint PPT Presentation

Implications of a 125 GeV Composite Higgs Alex Pomarol, UAB (Barcelona)

A 125 GeV Higgs-like state has been discovered -1 -1 CMS s = 7 TeV, L = 5.1 fb s = 8 TeV, L = 5.3 fb m = 125.5 GeV ATLAS 2011 - 2012 H m = 126.0 GeV H → W,Z H bb ∫ -1 s = 7 TeV: Ldt = 4.7 fb H → τ τ H → γ γ ∫ -1 s = 7 TeV: Ldt = 4.6-4.7 fb (*) → → ν ν H WW l l ∫ -1 s = 7 TeV: Ldt = 4.7 fb H ZZ ∫ → -1 s = 8 TeV: Ldt = 5.8 fb → γ γ H ∫ -1 s = 7 TeV: Ldt = 4.8 fb ∫ -1 s = 8 TeV: Ldt = 5.9 fb H WW → (*) → → H ZZ 4l ∫ -1 s = 7 TeV: Ldt = 4.8 fb ∫ -1 s = 8 TeV: Ldt = 5.8 fb H → τ τ Combined ∫ -1 = 1.4 0.3 µ ± s = 7 TeV: Ldt = 4.6 - 4.8 fb ∫ -1 s = 8 TeV: Ldt = 5.8 - 5.9 fb H bb → -1 0 1 -1 0 1 2 3 Signal strength ( ) µ Best fit / σ σ SM with no significant deviations from a SM Higgs!

Road Map of possible BSM scenarios Unknown Planckian y r o t i r r e t l a r Territory u SM only ) t ? a e n s r n e U v i t l u M ( M P Strong Dynamics territory MSSM PGB Higgs 1979-2012 TeV NMSSM, ... Higgs territory TC Energy S u s y t e r r i t o r y 100 GeV

Purpose of my talk here: How well this recently discovered 125 GeV Higgs fit in Composite Higgs Models ?

Composite PGB Higgs inspired by QCD where one observes that the (pseudo) scalar are the lightest states Spectrum: GeV ρ 100 MeV π Are Pseudo-Goldstone bosons (PGB) Mass protected by the π global QCD symmetry! π → π + α

Can the light Higgs be a kind of a pion from a new strong sector? We’d like the spectrum of the new strong sector to be: TeV ρ h 100 GeV Pseudo-Goldstone bosons (PGB)

Potential from some new strong dynamics at the TeV: H e.g. SO(5) ➝ SO(4) 4 Goldstones ➠ Higgs doublet

Potential from some new strong dynamics at the TeV: H e.g. SO(5) ➝ SO(4) 4 Goldstones ➠ Higgs doublet SM-field couplings to the strong sector H break the global SO(5) SM-loop effects: EWSB minimum

Potential from some new strong dynamics at the TeV: H e.g. SO(5) ➝ SO(4) 4 Goldstones ➠ Higgs doublet two symmetry- SM-loop breaking scales: H effects f ≳ 500 GeV EWSB v ≈ 246 GeV minimum

Higgs Mass contribution from the strong sector h h it’s a Goldstone = 0 SM fields h h h h + V ( h ) = g 2 SM m 2 Difficult to get predictions 16 π 2 h 2 + · · · ρ ➥ due to the intractable strong dynamics !

A possibility to move forward has been to use the... AdS/CFT approach Strongly-coupled Weakly-coupled systems Gravitational systems in the Large N c in higher-dimensions Large λ ≡ g ² N c Very useful to derive properties of composite states from studying weakly-coupled fields in warped extra-dimensional models

Holographic composite PGB Higgs model Agashe,Contino,A.P . hard/soft in a AdS 5 throat wall Mass gap ~ TeV ds 2 = L 2 dx 2 + dz 2 ⇤ ⇥ z 2 Holo. coordinate z ~ 1/E

Holographic composite PGB Higgs model Agashe,Contino,A.P . SO(5) gauge theory hard/soft in a AdS 5 throat wall Mass gap ~ TeV ds 2 = L 2 dx 2 + dz 2 ⇤ ⇥ z 2 Holo. coordinate z ~ 1/E

Holographic composite PGB Higgs model Agashe,Contino,A.P . SO(5) gauge theory hard/soft in a AdS 5 throat wall Mass gap ~ TeV ds 2 = L 2 dx 2 + dz 2 ⇤ ⇥ z 2 Symmetry : SO(4) Breaking of symmetry by boundary conditions Holo. coordinate z ~ 1/E

Massless Spectrum hard/soft h wall Higgs = 5th component of the SO(5)/SO(4) gauge bosons (Gauge-Higgs unification, Hosotani Mechanism,...) ➥ Normalizable modes = Composite

Massless Spectrum A µ hard/soft h wall : SO(4) ~SU(2)xSU(2) Gauge Bosons A µ ➥ Non-normalizable modes = External states = Some of them dynamical (SU(2)) Achieve, as in Randall-Sundrum models, by a brane at z~0

What about fermions? (Main difficulty in composite models)

The fermionic sector: We have to choose the bulk symmetry representation of the fermions and b.c. giving only the 4D massless spectrum of the SM Up-quark sector: s 5 2 / 3 of SO(5) × U(1) X .   � q � � � q � � L ( − +) R (+ − ) ( 2 , 2 ) q , ( 2 , 2 ) q L = R =   q L (++) q R ( −− )   ξ q = ( Ψ q L , Ψ q R ) =   ( 1 , 1 ) q , ( 1 , 1 ) q L ( −− ) R (++) � � ( 2 , 2 ) u L (+ − ) , ( 2 , 2 ) u R ( − +) ξ u = ( Ψ u L , Ψ u R ) = , ( ( 1 , 1 ) u L ( − +) , ( 1 , 1 ) u R (+ − ) IR-bound. mass: × q q R + � L ( 2 , 2 ) u R ( 1 , 1 ) u m u ( 2 , 2 ) � M u ( 1 , 1 ) L + h.c.

Simple geometric approach to fermion masses ψ ( z ) hard/soft wall ψ ( z ) h 3rd family 1st & 2nd family ( Top = Most Composite) (Elementary)

Contino,AP 4D CFT Interpretation SM fermions are linearly coupled to a CFT operator: Ψ L = λ Ψ · O Ψ + L CFT Dim[ O Ψ ] = 3 2 + | M Ψ + 1 2 | 5D mass Irrelevant coupling M Ψ ≥ 1 / 2 → γ λ ≥ 0 | | M Ψ < 1 / 2 → γ λ < 0 Relevant coupling

Contino,DaRold, AP 07 m ρ = 2 . 5 TeV , f = 500 GeV 2.5 1 2/3 2.0 2 1/6 [ TeV ] 2 7/6 1.5 mKK 1.0 0.5 115 125 135 145 155 165 175 185 [ GeV ] mHiggs

Contino,DaRold, AP 07 m ρ = 2 . 5 TeV , f = 500 GeV 2.5 1 2/3 2.0 2 1/6 [ TeV ] 2 7/6 1.5 mKK 1.0 0.5 115 125 135 145 155 165 175 185 [ GeV ] mHiggs For a 125 GeV Higgs, the fermionic resonances of the top are lighter ~ 600 GeV

Why this correlation? m 2 h ∼ N c m Q ⌘ 2 Q ∼ (125 GeV) 2 ⇣ t m 2 f 2 m 2 π 2 700 GeV But why the model can accommodate light resonances? Is it natural?

Why this correlation? m 2 h ∼ N c m Q ⌘ 2 Q ∼ (125 GeV) 2 ⇣ t m 2 f 2 m 2 π 2 700 GeV But why the model can accommodate light resonances? Is it natural? Yes Dim[ O Ψ ] = 3 2 + | M Ψ + 1 AdS/CFT dictionary: 2 | M Ψ = − 1 / 2 Dim[ O Ψ ] = 3 / 2 → 5D mass: free parameter becomes a free field ~ decouple from the CFT ➥ in this limit, new light states

Why this correlation? m 2 h ∼ N c m Q ⌘ 2 Q ∼ (125 GeV) 2 ⇣ t m 2 f 2 m 2 π 2 700 GeV But why the model can accommodate light resonances? Is it natural? Yes The more we localize the top towards the IR boundary , the more composite it is If fully composite, it must come in full reps of SO(5): ➥ there must be extra massless partners

Simpler derivation of the connection: Light Higgs - Light Resonance

Simpler derivation of the connection: Light Higgs - Light Resonance ✒ Deconstruction: Matsedonskyi,Panico,Wulzer; Redi,Tesi 12 ✒ “Weinberg Sum Rules”: Marzocca,Serone,Shu; AP, Riva 12 ➥ As Das,Guralnik,Mathur,Low,Young 67 for the charged pion mass: π 0 ' 3 α m 2 π + � m 2 2 π m 2 ρ log 2 ' (37 MeV) 2 γ Exp. (35 MeV) ² π + π + quite successful!

Higgs potential Gauge contribution (limit g’=0): d 4 p V ( h ) = 9 � (2 π ) 4 log Π W 2 h W W Encode the strong-sector contribution to the gauge propagator in the h-background g 2 + sin 2 h/f Π W ' p 2 [ h J ˆ a J ˆ a i � h J a J a i ] 2 Broken and Conserved current-current correlators of the strong sector

Easy derivation using spurion techniques : L = L strong + L SM + J µ strong W µ promote them to an SO(5) rep: 10=6+4 A µ ∈ The most general SO(5) invariant action as a function of after integrating out the strong sector: A µ L e ff = 1 h + Π 1 ( p ) Σ A µ A ν Σ T i A µ A ν ⇤ + O ( A 3 ) ⇥ Π 0 ( p ) Tr 2 P µ ν parametrizes Σ = Σ 0 e Π /f π , Σ 0 = (0 , 0 , 0 , 0 , 1) the coset SO(5)/SO(4) (equivalent SO(4) vacuums)

L e ff = 1 h + Π 1 ( p ) Σ A µ A ν Σ T i A µ A ν ⇤ + O ( A 3 ) ⇥ Π 0 ( p ) Tr 2 P µ ν A µ = W µ h Σ i = (0 , 0 , 0 , 0 , 1) h Σ i = (0 , 0 , 0 , sin h/f, cos h/f ) 4 sin 2 h Π W = Π 0 + Π 1 Π a = h J a J a i = Π 0 f π a i = Π 0 + 1 h a = h J ˆ Π ˆ a J ˆ 2 Π 1 } Π 0 ' p 2 g 2 g 2 + sin 2 h/f Π W ' p 2 [ h J ˆ a J ˆ a i � h J a J a i ] 2

Higgs Mass from Weinberg Sum Rules Gauge contribution: d 4 p = 1 V ( h ) = 9 � h h 2 + · · · 2 m 2 (2 π ) 4 log Π W 2 h ' 9 g 2 d 4 p Π 1 ( p ) Z ➥ m 2 2 f 2 (2 π ) 4 p 2 F 2 ∞ F 2 ∞ a i � h J a J a i ] = f 2 + 2 p 2 X X � 2 p 2 ρ n a n Π 1 = 2 [ h J ˆ a J ˆ p 2 + m 2 p 2 + m 2 a n ρ n } n n Large N Euclidean momentum } X = n F a n = h 0 | J ˆ a | a n i of SO(4) a n ∈ 4 F ρ n = h 0 | J a | ρ n i ρ n ∈ 6

Higgs Mass from Weinberg Sum Rules Gauge contribution: d 4 p = 1 V ( h ) = 9 � h h 2 + · · · 2 m 2 (2 π ) 4 log Π W 2 h ' 9 g 2 d 4 p Π 1 ( p ) Z ➥ m 2 2 f 2 (2 π ) 4 p 2 F 2 ∞ F 2 ∞ a i � h J a J a i ] = f 2 + 2 p 2 X X � 2 p 2 ρ n a n Π 1 = 2 [ h J ˆ a J ˆ p 2 + m 2 p 2 + m 2 a n ρ n n n Procedure: 1) Demand convergence of the integral: p 2 →∞ p 2 Π 1 ( p ) = 0 , “Weinberg Sum Rules” p 2 →∞ Π 1 ( p ) = 0 , lim lim