The Higgs as a composite pseudo-goldstone boson. Roberto Contino - CERN

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1 The Higgs as a composite pseudo-goldstone boson Roberto Contino - CERN

2 Part I: The need for an EWSB sector and how this could be strongly interacting

3 The physics discovered so far: L = L 0 + L mass L 0 = Ψi DΨ 1 4 (F a µν) 2 L mass = M 2 W W + µ W µ + M 2 Z 2 Z µz µ + Ψ L MΨ R v 2 4 Tr [ (D µ Σ) (D µ Σ) ] Σ = exp (iσ a χ a /v) D µ Σ = µ Σ ig 2 σ a 2 W a µ Σ + ig 1 Σ σ 3 2 B µ

4 W L W L A = 1 (s + t) v2 W L W L 1 new scalar: the Higgs h ( Σ = 1 + h ) e (iσa χ a /v) v an infinite tower of (massive) vectors n ρ n

5 If we do not introduce any longitudinal d.o.f. for W and Z The pions are eaten and the EWS is broken SU(2) L U(1) Y QCD _ _ U(1) Q unbroken: massless photon SU(2)L SU(2)R U(1)B π SU(2)V U(1)B ππ scattering unitarized by ρ s Problems: 1) fπ = 93 MeV M W = g f π /2 =30 MeV! 2) we actually do observe the pions!

6 Idea: what if there is a techni-qcd? Technicolor [Weinberg, Susskind] F π >> f π 1) W long, Z long mostly from πtc : M W g F π /2 =80 GeV 2) still a physical pion in the spectrum, mostly π SU(2)L U(1)Y QCD _ _ _ _ techni-qcd SU(2)L SU(2)R π SU(2)V f π = 93 MeV SU(2)L SU(2)R πtc SU(2)V F π = 246 GeV

7 Why not technicolor? 1 Large corrections to the oblique parameters: Peskin-Takeuchi S parameter L = S 32π W 3 µνb µν W 3 ρ B S 16π ( v m ρ ) 2 N π 0 J µ ρ = ɛ r µ f ρ m ρ m ρ 4π N F π S 99% CL

8 2 Flavor problem (large FCNC) Need to connect QCD with TC in order to generate the quarks masses SU(2)L U(1)Y QCD _ _ _ _ techni-qcd π Extended Technicolor πtc f π = 93 MeV F π = 246 GeV

9 SU(N ET C ) SU(N c ) SU(N T C ) q χ ET C L = 1 Λ 2 ET C ( qq)( χχ) q χ BUT also: L = 1 Λ 2 ET C ( qq)( qq) m q Λ T C ( ΛT C Λ ET C ) 2 Λ T C v Λ ET C cannot be too large ex: Λ ET C 10 TeV to reproduce m s = 150 MeV

10 Better if TC dynamics is not that of QCD (walking TC): suppose the theory flows to an IR fixed point below Λ ET C L = λ ( qq)o(x) O(x) = χχ [O] = d = 3 + γ m q Λ T C ( ΛT C Λ ET C ) d 1 No suppression if we could reach d=1

11 Folk theorem: smallest dimension is d=2 m q Λ T C ( ΛT C Λ ET C ) suppression still too strong: Λ ET C 400 TeV m s = 150 MeV to reproduce UV stability argument: [O 2 (x)] = 2[O(x)] at weak coupling or Unitarity bound d = 1 2 d large N weak coupling viable region at small N Conformal TC [Luty, Okui JHEP 0609:070, 2006]

12 A possible solution to the Flavor problem: Linear couplings: L = λ L q L O R + λ R ū R O L + h.c. [D. B. Kaplan NPB 365 (1991) 259] m q Λ T C ( ΛT C Λ ) γl +γ R γ L,R = [O L,R] 5/2 Unitarity: [O] 3/2 [O] 3/2 γ 1 at large N or weak coupling:

13 q L m q λ L (µ)λ R (µ) q R N 16π 2 m ρ µ d dµ λ = γλ + c N 16π 2 λ For γ > 0 m q N ( 4π v mρ ) γl +γ R Λ very large: Λ FCNC small large hierarchies in the Yukawas naturally γ < 0 For flow to a new fixed point (c>0): λ = γ c 4π N m q v 4π N γl γ R large top mass naturally

14 Sort of GIM mechanism for 4-fermion operators q i q k 1 m 2 ρ yi y j y k y l q j q l small for the 1st and 2nd generations potential interesting signals for the 3rd

15 A possible solution to the EWPT problem: suppose the strong dynamics has also a light scalar bound state playing the role of the Higgs the composite Higgs partially unitarize h the WW scattering until a scale Λ = Λ ξ g hw W = g SM hw W (1 + O(ξ))... until the vector resonances take on n ρ n

16 vector resonances can be heavier: smaller corrections to EWPO the Higgs is composite: Planck/TeV Hierarchy solved

17 Composite Higgs models [Georgi & Kaplan, `80s] Aµ (G SM ) BSM _ _ ψ Requirements: H G G 1) GSM G 2) H is a doublet of SU(2)L Example: SO(5) SO(4) ~ SU(2)L SU(2)R gives 4 real Goldstones: one SU(2)L doublet H

18 1-loop potential for the pseudo-goldstone Higgs only loops with virtual elementary fields generate a potential H t L H Higgs couplings switch off at large momenta finiteness Form Factors t R periodic function (H G/G ) V (h) 3 y2 t 16π 2 m2 ρ f 2 ζ(h/f) λ π 2 y2 t g 2 ρ

19 ξ = ( v f ) 2 new parameter compared to TC (fixed by the dynamics) H H m ρ 4πf N W 3 ρ B S 16π ( v m ρ ) 2 ξ N π ξ 0 [ f ] decoupling limit: All ρ s become heavy and one re-obtains the SM

20 Constraint on the strong sector from the LEP precision tests : Custodial Symmetry ρ = m 2 W m 2 Z cos2 θ W ρ (ρ 1) = 4 v 2 [Π 11(0) Π 33 (0)] The bound from LEP ρ strongly constrains tree-level corrections If the residual symmetry after EWSB is just U(1) Q there will be tree-level corrections from the strong sector to ρ J 1 µj 1 ν J 3 µj 3 ν W 1,3 µ W 1,3 ν J 1,3 µ J 1,3 ν A larger preserved custodial symmetry SU(2) C under which transforms like a triplet can protect ρ J i µ [Sikivie et al. NPB 173 (1980) 189] SU(2) L SU(2) R SU(2) C J 1 µj 1 ν = J 3 µj 3 ν

21 Field theories with a curved fifth dimension give an explicit realization of 4D composite Higgs models Resonances of the strong sector Kaluza-Klein excitations

Example of strong dynamics: a Randall-Sundrum setup UV brane graviton & light fermions AdS5 Higgs IR brane warp factor Scales depend on the position:

22 Example of strong dynamics: a Randall-Sundrum setup UV brane graviton & light fermions AdS5 Higgs IR brane warp factor Scales depend on the position: translation in y 4D rescaling Solution to the Hierarchy Problem geography of wave functions in the bulk k M Pl k e 2kπR TeV ds 2 = e 2ky dx µ dx ν η µν dy 2 0 y πr

23 The holographic description { SM fields live here UV brane Bulk IR brane Higgs profile UV brane Bulk + IR brane Elementary sector { ψ Aµ _ _ H G G Composite sector

24 Hint: z 1 q a brane-to-brane propagator between two sources on the UV boundary probes only up to distances z 1/q, where q is the 4D exchanged momentum: G(q, L 0, z) e qz for qz 1 z = k 1 e yk z = L 0 UV brane q IR brane z = L 1 the Higgs structure along the extra dimension appears like a form factor for an observer on the UV brane

Advantages of the 5D theories : The 5D field theory is weakly coupled (the strong dynamics is solved in 5D) Model Building is simple (especially in the fermionic sector) Feature

25 Advantages of the 5D theories : The 5D field theory is weakly coupled (the strong dynamics is solved in 5D) Model Building is simple (especially in the fermionic sector) Feature of the 5D theories : In the 4D description of the 5D models the SM fields are linearly coupled to the strong sector: W a µ, B µ Ψ _ _ strong sector G G H L int = A µ J µ + ΨO + h.c.

26 Part II: Implications for the LHC 1. How to tell whether the Higgs is composite 2. Direct production of new states

27 An effective Lagrangian for the Strongly Interacting Light Higgs built along the rules of the chiral expansion: Giudice, Grojean, Pomarol, Rattazzi JHEP 0706:045 (2007) 1. each extra Goldstone leg is weighted by a factor 1/f 2. each derivative is weighted by a factor 1/m ρ 3. higher dimensional operators that violate the symmetry of the σ-model must be suppressed by g SM

28 at the level of dimension-6 operators: strong constraint from LEP ρ = c T ξ L SILH = c H 2f 2 µ ( H H ) µ ( H H ) + c T 2f 2 ( c 6λ f 2 ( H H ) ic W g 2m 2 ρ ( cy y f f 2 H ) ( D µ H H ) D µ H ) H H f L Hf R + h.c. ( H σ i ) D µ H (D ν W µν ) i + ic Bg 2m 2 ρ ( H ) D µ H ( ν B µν ) probe strong coupling 1-loop suppressed more than 1-loop suppressed + ic HW g m 2 ρ + c γg 2 m 2 ρ g 2 ρ 16π 2 (Dµ H) σ i (D ν H)W i µν + ic HBg m 2 ρ g 2 ρ 16π 2 g 2 g 2 ρ H HB µν B µν + c gg 2 S m 2 ρ g 2 ρ 16π 2 y 2 t g 2 ρ g 2 ρ 16π 2 (Dµ H) (D ν H)B µν H HG a µνg aµν form factors

29 dominant effect: shift in the Higgs couplings subdominant role in scattering amplitudes one combination constrained by LEP: Ŝ = (c W + c B ) m2 W m 2 ρ L SILH = c H 2f 2 µ ( H H ) µ ( H H ) + c T 2f 2 ( c 6λ f 2 ( H H ) ic W g 2m 2 ρ ( cy y f f 2 H ) ( D µ H H ) D µ H ) H H f L Hf R + h.c. ( H σ i ) D µ H (D ν W µν ) i + ic Bg 2m 2 ρ ( H ) D µ H ( ν B µν ) + ic HW g m 2 ρ g 2 ρ 16π 2 (Dµ H) σ i (D ν H)W i µν + ic HBg m 2 ρ g 2 ρ 16π 2 (Dµ H) (D ν H)B µν + c γg 2 m 2 ρ g 2 ρ 16π 2 g 2 g 2 ρ H HB µν B µν + c gg 2 S m 2 ρ g 2 ρ 16π 2 y 2 t g 2 ρ H HG a µνg aµν directly affect Higgs gluon production and Higgs decay to photons (subdominant compared to c H )

30 shifts in the Higgs couplings: Γ ( h f f ) SILH = Γ ( h f f ) SM [1 ξ (2c y + c H )] Γ ( h W + W ) ( = Γ h W + W ( ) ) [ )] 1 ξ (c SILH H g2 SM gρ 2 ĉ W Γ (h ZZ) SILH = Γ ( h ZZ ( )) [ )] 1 ξ (c H g2 SM gρ 2 ĉ Z Γ (h gg) SILH = Γ (h gg) SM [1 ξ Re Γ (h γγ) SILH = Γ (h γγ) SM 1 ξ Re ( )] 2c y + c H + 4y2 t c g gρi 2 g 2c y + c H 1 + J γ /I γ + c H g2 g 2 ρ ĉ W 1 + I γ /J γ + 4g 2 g 2 ρ c γ I γ + J γ Γ (h γz) SILH = Γ (h γz) SM 1 ξ Re 2c y + c H 1 + J Z /I Z + c H g2 g 2 ρ ĉ W 1 + I Z /J Z + 4c γz I Z + J Z [ ( gρ ) [ 2 ( ĉ W = c W + chw, ĉ Z = ĉ W + tan 2 gρ ) ] 2 θ W c B + chb, c γz = c HB c HW 4π 4π 4 sin 2θ W ]

31 prediction of the SO(5)/SO(4) model [ ] for c y /c H = 1 c H ξ = 0.25 [ Giudice et al. JHEP 0706:045, 2007 ] LHC sensitive up to c H ξ = ATLAS L = 300 fb 1 [ Duhrssen ATL-PHYS ]

32 prediction of the SO(5)/SO(4) model [ ] for c y /c H = 1 c H ξ = 0.25 [ Giudice et al. JHEP 0706:045, 2007 ] LHC sensitive up to c H ξ = ATLAS L = 300 fb 1 [ Duhrssen ATL-PHYS ]

33 as stressed in: Barbieri et al. PRD 76 (2007) the shifts in the Higgs couplings induce an IR correction to the precision parameters ɛ 1,3 = a 1,3 log ( M 2 Z µ 2 ) ɛ 1,3 a 1,3 (1 c H ξ) log ( m 2 h µ 2 ) a 1,3 (c H ξ) log ( m 2 ρ µ 2 ) + finite terms a 1 = π a 3 = 1 12π α(m Z ) cos 2 θ W α(m Z ) 4 sin 2 θ W ɛ 2,b = ɛ SM 2,b ( ) m 2 ɛ 1 =a 1 (c H ξ) log h m 2 ρ ( ) m 2 ɛ 3 =a 3 (c H ξ) log h m 2 ρ Ε UV c H ξ = 0.25 from fermions? m ρ = 3.3 TeV Ε 3

34 WW scattering The Higgs compositeness implies a partial unitarization of the WW scattering: W L W L + + h W L W L A ( W + L W L W + L W L ) = g 2 2 4M 2 W [ s s2 (1 c H ξ) s m 2 h ] + t t2 (1 c H ξ) t m 2 h Unitarity is lost at a scale: Λ = Λ 0 / c H ξ Λ 0 = 1.2 TeV Full unitarity is recovered thanks to the exchange of the heavy vectorial resonances n ρ n

At large invariant (WW) masses one case thus rescale: σ(pp V L V LX) ch ξ (c H ξ) 2 σ(pp V L V LX) no Higgs L = 200 fb 1 c H ξ = 0.5 0.7 with the LHC should be sensitive up to [ Giudice et al.

35 At large invariant (WW) masses one case thus rescale: σ(pp V L V LX) ch ξ (c H ξ) 2 σ(pp V L V LX) no Higgs L = 200 fb 1 c H ξ = with the LHC should be sensitive up to [ Giudice et al. JHEP 0706:045, 2007 ] Strong vector boson scattering is accompanied by strong Higgs production: A (Z L Z L hh) = A ( W + L W L hh) = s v 2 (c Hξ) WORK IN PROGRESS with C. Grojean, M. Moretti, F. Piccinini, R. Rattazzi

36 Part II: Implications for the LHC 1. How to tell whether the Higgs is composite 2. Direct production of new states

37 The Top Partners A light Higgs requires: New vector-like quarks with M 500 GeV in multiplets of SU(2) L SU(2) R U(1) X t R t R T T H H H H T T t L t L

38 Two simple SU(2) L SU(2) R U(1) X assignments: [ Y = T 3R + X ] Model A (2, 1) 1/6 = ( T B) (1, 2) 1/6 = ( ) T B [ X = (B L)/2 ] electric charge +5/3 Model B (2, 2) 2/3 = [ X = 2(B L) ] Q = Q = ) T 2/3 ( T B) ( T5/3 (1, 1) 2/3 = T

39 largest coupling of the heavy fermions to the Higgs degrees of freedom (W L, Z L, h) and to the SM third quark generation couplings to well defined SM quark chiralities [Yukawa couplings ] Z L /h W + L T t L T bl Z L /h W + L T t R T b R suppressed FCNC : absent for a 4th generation!

40 Z L /h W + L t R T 2/3 T 2/3 b R W L Z L /h suppressed B t R B b R W + L T 5/3 t R Single production and decays proceed via these couplings Pair production proceeds via the usual QCD coupling

41 Single vs Pair production: q q W + L g λ T T 5/3 t 10 4 LHC 14 TeV For example, for λ T = 3 : Γ(M = 500 GeV) = 31 GeV 10 3 Γ(M = 1 TeV) = 82 GeV!""[fb] 10 2 _ pp! T 5/3 t j X λ T = 4, 3, pp! T 5/3 T _ 5/3 X M T5/3 [GeV]

42 Example: look for B B and T 5/3 T5/3 in same-sign dilepton final states [ R.C., G.Servant arxiv: ] l + ν q q l + ν l + ν B W + W t b T 5/3 W + W + t b B W t W + b T 5/3 W t W b q q l + ν q q q q For the T 5/3 case one can reconstruct the resonant (tw ) invariant mass

43 # of events/(20 GeV) M = 500 GeV L = 10 fb -1 T 5/3 + B + bck B + bck background with b-tagging: T 5/3 + B + bck M tw [GeV] Discovery Potential L disc M = 500 GeV T 5/3 + B 56 pb 1 B only 147 pb 1 M = 1 TeV T 5/3 + B B only 15 fb 1 48 fb 1 less than 100 pb 1

44 Conclusions Composite Higgs Models interpolate between the two paradigms for EWSB: Technicolor and a fundamental scalar condensate Inspiring connection to extra-dimensional theories Two crucial differences compared to old-fashioned TC: new parameter ξ = (v/f) 2 to suppress the corrections to the EW precision observables new, successful realization of Flavor

45 Conclusions prediction: well defined pattern of new signals at the LHC: couplings to leptons and light quarks suppressed tops and bottoms play a special role: final states populated by tops and bottons different from SUSY: no missing energy

46 Backup slides

47 ex: A minimal 5D model [ R.C., DaRold, Pomarol PRD 75 (2007) ] SU(2) L U(1) Y SO(5) U(1) X O(4) U(1) X O(4) = SO(4) P LR SU(2) L SU(2) R P LR Y = T 3R + X Aâ5(+, +) Alg{SO(5)/SO(4)} Aâ5(x, y) = hâ(x)ζ(y) ζ(y) = e ky 2 e 2πkR 1 a 4 of SO(4) IR localized up quark sector (5D multiples): ξ q = [ ] q (2, 2)q L = L ( +) q L (++) (1, 1) q R (++) ξ u = [ (2, 2) u L (+ ) (1, 1) u R (+ ) ]

Teoria e fenomenologia dei modelli di Higgs composto. Roberto Contino - CERN

Teoria e fenomenologia dei modelli di Higgs composto Roberto Contino - CERN Part I: Quick review of the Composite Higgs Composite Higgs models [Georgi & Kaplan, `80s] EWSB sector H G G _ _ Aµ (G SM ) ψ