HIGGS COMPOSITENESS: CURRENT STATUS (AND FUTURE STRATEGIES) Roberto Contino Università di Roma La Sapienza & INFN Roma

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1 HIGGS COMPOSITENESS: CURRENT STATUS (AND FUTURE STRATEGIES) Roberto Contino Università di Roma La Sapienza & INFN Roma SUSY ICTP, Trieste 6-31 August, 013

2 Outline Strong vs Weak EWSB Current Status of Higgs Compositeness: 1. Higgs mass. EW Precision Tests 3. Impact of Searches for top partners 4. Impact of data on Higgs couplings

3 Strong vs Weak EWSB

4 In the {SM-H} χ χ χ χ A(W L W L W L W L )=A(χχ χχ) E v g (E) In the {SM-H} + H + h c V A E v (1 c V ) c V m h v s s m h 4

5 χ χ In the {SM-H} A(W L W L W L W L )=A(χχ χχ) E v g (E) χ χ In the {SM-H} + H + h c V A E v (1 c V ) c V m h v s s m h =0 g(e) Elementary Higgs: c V =1 weak m h v 4 E

6 In the {SM-H} χ χ χ χ A(W L W L W L W L )=A(χχ χχ) E v g (E) In the {SM-H} + Hi + h i c Vi A E v 1 i =0 c Vi Elementary Higgses: (more than one) δc Vi O(1) possible sum rule: c Vi =1 i

7 h Composite Higgs: + + ρ c V =1 coupling strength grows with energy and saturates at g 4π E g(λ S )=4π strong scale Λ S Energy cartoon: g g(m ) m W, Z, h 6

8 Analogy with ππ scattering in QCD: h σ Q: why light and narrow? 7

9 Analogy with ππ scattering in QCD: h σ Q: why light and narrow? A: the Higgs is itself a (pseudo) NG boson Georgi & Kaplan, 80 Kaplan, Georgi, Dimopoulos SO(5) SO(4) ex: 4 NGBs transforming as a (,) of SO(4)~SU()LxSU()R Agashe, RC, Pomarol NPB 719 (005) 165 f µ e iπ/f =( π) + (π π) f + π (π π) f

10 Analogy with ππ scattering in QCD: h σ Q: why light and narrow? A: the Higgs is itself a (pseudo) NG boson Georgi & Kaplan, 80 Kaplan, Georgi, Dimopoulos SO(5) SO(4) ex: 4 NGBs transforming as a (,) of SO(4)~SU()LxSU()R Agashe, RC, Pomarol NPB 719 (005) 165 f µ e iπ/f = Dµ H + c H f µ (H H) + c H f 4 (H H) µ (H H) +... Giudice et al. JHEP 0706 (007) 045 8

11 Analogy with ππ scattering in QCD: h σ Q: why light and narrow? A: the Higgs is itself a (pseudo) NG boson Georgi & Kaplan, 80 Kaplan, Georgi, Dimopoulos SO(5) SO(4) ex: 4 NGBs transforming as a (,) of SO(4)~SU()LxSU()R Agashe, RC, Pomarol NPB 719 (005) 165 f µ e iπ/f = Dµ H + c H f µ (H H) + c H f 4 (H H) µ (H H) +... Giudice et al. JHEP 0706 (007) 045 O(v /f v 1. ) shifts in tree-level Higgs couplings. Ex: c V =1 c H +... f 8

12 Analogy with ππ scattering in QCD: h σ Q: why light and narrow? A: the Higgs is itself a (pseudo) NG boson Georgi & Kaplan, 80 Kaplan, Georgi, Dimopoulos ex: SO(5) SO(4) 4 NGBs transforming as a (,) of SO(4)~SU()LxSU()R Agashe, RC, Pomarol NPB 719 (005) 165 f µ e iπ/f = Dµ H + c H f µ (H H) + c H f 4 (H H) µ (H H) +... Giudice et al. JHEP 0706 (007) 045. Scatterings involving the Higgs also grow with energy 9 A(WW hh) s v (c V c V ) c V c V c 3

13 Linear couplings D.B. Kaplan NPB 365 (1991) RS with bulk fermions Hypothesis: each SM fermion couples to a composite fermionic operator with the same SU(3)cxSU()LxU(1)Y quantum numbers L = λ L q L O R + λ R ū R O L + h.c. 10

14 Linear couplings D.B. Kaplan NPB 365 (1991) RS with bulk fermions Hypothesis: each SM fermion couples to a composite fermionic operator with the same SU(3)cxSU()LxU(1)Y quantum numbers L = λ L q L O R + λ R ū R O L + h.c. Quark masses need two such couplings q L q R m q λ L(µ)λ R (µ) g v µ m 10

15 Linear couplings D.B. Kaplan NPB 365 (1991) RS with bulk fermions Hypothesis: each SM fermion couples to a composite fermionic operator with the same SU(3)cxSU()LxU(1)Y quantum numbers L = λ L q L O R + λ R ū R O L + h.c. Quark masses need two such couplings q L q R m q λ L(µ)λ R (µ) g v µ m Similar to linear couplings of elementary gauge fields: L = ga µ J µ 10

16 Linear couplings D.B. Kaplan NPB 365 (1991) RS with bulk fermions Hypothesis: each SM fermion couples to a composite fermionic operator with the same SU(3)cxSU()LxU(1)Y quantum numbers L = λ L q L O R + λ R ū R O L + h.c. Quark masses need two such couplings break explicitly the Goldstone symmetry q L m q λ L(µ)λ R (µ) g v q R µ m Similar to linear couplings of elementary gauge fields: L = ga µ J µ 10

17 Partial compositeness D.B. Kaplan NPB 365 (1991) RS with bulk fermions Fermionic operators can excite composite fermions at low energy: 0 O χ = λ f same as for a conserved current: 0 J µ ρ = r µ f ρ m ρ 11

18 Partial compositeness D.B. Kaplan NPB 365 (1991) RS with bulk fermions Fermionic operators can excite composite fermions at low energy: vector-like composite fermion 0 O χ = λ f same as for a conserved current: 0 J µ ρ = r µ f ρ m ρ 11

19 Partial compositeness D.B. Kaplan NPB 365 (1991) RS with bulk fermions Fermionic operators can excite composite fermions at low energy: vector-like composite fermion 0 O χ = λ f same as for a conserved current: 0 J µ ρ = r µ f ρ m ρ Linear couplings imply mass mixings: L = ψ i ψ+ χ( i m )χ + λf ψu(π)χ + h.c. rotating to mass eigenbasis: ψ χ cos ϕ sin ϕ ψ sin ϕ cos ϕ χ tan ϕ = λ f m ϕ parametrizes the degree of compositeness of the SM fermions SM = cos ϕ ψ +sinϕ χ heavy = sin ϕ ψ + cos ϕ χ 11

20 Higgs mass Can a 15GeV Higgs be composite?

21 Structure of the Higgs Potential V (h) = m4 g N c 8π λ i A i (h/f)+λ 4 i B i (h/f)+... h H H explicit breaking vacuum A i (x),b i (x) SO(4) structures trigonometric functions: sin (x) θ sin 4 (x)... SO(5) SO(4) = S4 vacuum manifold is the 4-sphere 13

22 Structure of the Higgs Potential V (h) = m4 g N c 8π λ i A i (h/f)+λ 4 i B i (h/f)+... h H H explicit breaking of Goldstone symmetry (spurion couplings) explicit breaking vacuum A i (x),b i (x) SO(4) structures trigonometric functions: sin (x) θ sin 4 (x)... SO(5) SO(4) = S4 vacuum manifold is the 4-sphere 13

23 Structure of the Higgs Potential Potential is FINITE - loop integral fully saturated at the compositeness scale V (h) = m4 g N c 8π λ i A i (h/f)+λ 4 i B i (h/f)+... h H H explicit breaking of Goldstone symmetry (spurion couplings) explicit breaking vacuum A i (x),b i (x) SO(4) structures trigonometric functions: sin (x) θ sin 4 (x)... SO(5) SO(4) = S4 vacuum manifold is the 4-sphere 13

24 Structure of the Higgs Potential Potential is FINITE - loop integral fully saturated at the compositeness scale V (h) = m4 g N c 8π λ i A i (h/f)+λ 4 i B i (h/f)+... h H H explicit breaking of Goldstone symmetry (spurion couplings) explicit breaking vacuum A i (x),b i (x) SO(4) structures trigonometric functions: sin (x) θ sin 4 (x)... To get EWSB ( 0<x π ) at least two SO(4) structures are needed plus some tuning SO(5) SO(4) = S4 vacuum manifold is the 4-sphere v FT = O f 13

25 If EWSB is triggered at O(λ ) t L,R V (h) m4 g N c h 8π λ L,R A f m h N c 4π m f λ L,R v 14

26 If EWSB is triggered at O(λ ) t L,R V (h) m4 g N c h 8π λ L,R A f m h N c 4π m f λ L,R v t L t R y t λ Lλ R g assuming λ L λ R m h N c 4π g3 y t v = 330 GeV g 3 3/ 14

27 If EWSB is triggered at O(λ ) t L,R V (h) m4 g N c h 8π λ L,R A f m h N c 4π m f λ L,R v t L t R y t λ Lλ R g assuming λ L λ R m h N c 4π g3 y t v = 330 GeV g 3 3/ Higgs tends to be too heavy (unless g 1 ) 14

28 If EWSB is triggered at O(λ ) t L,R V (h) m4 g N c h 8π λ L,R A f m h N c 4π m f λ L,R v t L t R y t λ Lλ R g assuming λ L λ R m h N c 4π g3 y t v = 330 GeV g 3 3/ Higgs tends to be too heavy (unless g 1 ) see however arxiv: for SUSY completion with extra spurion suppression Talk by A. Parolini 14

29 O(λ ) If EWSB is triggered at + tr fully composite t L V (h) m4 g N c h 8π λ L A f t L t R y t λ L m h N c 4π m f λ L v λ L y t m h N c 4π g y t v = 175 GeV g 3 15

30 O(λ ) If EWSB is triggered at + tr fully composite t L V (h) m4 g N c h 8π λ L A f t L t R y t λ L m h N c 4π m f λ L v λ L y t m h N c 4π g y t v = 175 GeV g 3 mh=15gev implies top partners are naturally - not too strongly coupled, hence - not too heavy Matsedonskyi, Panico, Wulzer JHEP 1301 (013) 164 Redi, Tesi JHEP 110 (01) 166 Marzocca, Serone, Shu JHEP 108 (01) 013 Pomarol, Riva JHEP 108 (01) 135 Panico, Redi, Tesi, Wulzer JHEP 1303 (013) 051 De Simone et al. JHEP 1304 (013)

31 O(λ ) If EWSB is triggered at + tr fully composite t L V (h) m4 g N c h 8π λ L A f t L t R y t λ L m h N c 4π m f λ L v λ L y t m h N c 4π g y t v = 175 GeV g 3 mh=15gev implies top partners are naturally - not too strongly coupled, hence - not too heavy FT v f m h m 4π N c y t = 55 GeV m Matsedonskyi, Panico, Wulzer JHEP 1301 (013) 164 Redi, Tesi JHEP 110 (01) 166 Marzocca, Serone, Shu JHEP 108 (01) 013 Pomarol, Riva JHEP 108 (01) 135 Panico, Redi, Tesi, Wulzer JHEP 1303 (013) 051 De Simone et al. JHEP 1304 (013)

32 If EWSB is triggered at O(λ 4 ) t L,R + t L L V (h) m4 g N c 8π h λ L,R A f + λ L λ R g h B f t R 16

33 If EWSB is triggered at O(λ 4 ) extra tuning required to suppress O(λ ) terms down to O(λ 4 ) t L,R + t L L V (h) m4 g N c 8π h λ L,R A f + λ L λ R g h B f t R 16

34 If EWSB is triggered at O(λ 4 ) extra tuning required to suppress O(λ ) terms down to O(λ 4 ) t L,R + t L L V (h) m4 g N c 8π h λ L,R A f + λ L λ R g h B f t R m h N c m 4π f λ L λ R g v N c 4π g y t v = 175 GeV g 3 16

35 If EWSB is triggered at O(λ 4 ) extra tuning required to suppress O(λ ) terms down to O(λ 4 ) t L,R + t L L V (h) m4 g N c 8π h λ L,R A f + λ L λ R g h B f t R m h N c m 4π f λ L λ R g v N c 4π g y t v = 175 GeV g 3 FT v f λ g 55 GeV y t m g mh automatically lighter but larger tuning to get EWSB Panico, Redi, Tesi, Wulzer JHEP 1303 (013)

36 EW Precision Tests

37 Constraints on c V from EW Precision Tests , 95, 99 CL m h = 16 GeV W, Z h W, Z c V c V =1 Ε c V = Ε 3 fit from: GFitter coll. Eur. Phys. J. C 7 (01) 05 1 = 3 16π α em cos θ W log Λ m Z 3 =+ 1 1π α em 4 sin θ W log Λ m Z 18 Barbieri et al. PRD 76 (007)

38 Constraints on c V from EW Precision Tests , 95, 99 CL m h = 16 GeV W, Z h W, Z c V =1 c V Λ =4πv/ 1 c V Ε M W c V = Ε 3 fit from: GFitter coll. Eur. Phys. J. C 7 (01) 05 Γ Z Pol Pτ A l 1 = 3 16π 3 =+ 1 1π α em cos θ W log Λ m Z α em 4 sin θ W log Λ m Z 0,b A FB c V a Ciuchini, Franco, Silvestrini, Mishima, arxiv: Barbieri et al. PRD 76 (007)

39 Constraints on c V from EW Precision Tests , 95, 99 CL m h = 16 GeV W, Z h W, Z c V =1 c V Λ =4πv/ 1 c V Ε M W c V = Ε 3 fit from: GFitter coll. Eur. Phys. J. C 7 (01) 05 Γ Z Pol Pτ A l 1 = 3 16π 3 =+ 1 1π α em cos θ W log Λ m Z α em 4 sin θ W log Λ m Z 0,b A FB c V a Ciuchini, Franco, Silvestrini, Mishima, arxiv: Barbieri et al. PRD 76 (007) See talk by S. Mishima on Thursday

40 Constraints on c V from EW Precision Tests , 95, 99 CL m h = 16 GeV W, Z h W, Z c V =1 c V Λ =4πv/ 1 c V Ε M W c V = Ε 3 fit from: GFitter coll. Eur. Phys. J. C 7 (01) 05 Γ Z Pol Pτ A l 19 Precision on cv at the level of ~5%! Contribution from resonances REQUIRED to relax the bound 0,b A FB c V a Ciuchini, Franco, Silvestrini, Mishima, arxiv: See talk by S. Mishima on Thursday

41 S parameter Ŝ = ŜIR + ŜUV Ŝ IR v g Λ f 16π log m Z Ŝ UV g v f 1 g 1 Λ + N c N F 16π log m

42 S parameter Ŝ = ŜIR + ŜUV IR contribution from NG bosons Ŝ IR v g Λ f 16π log m Z Ŝ UV g v f 1 g 1 Λ + N c N F 16π log m

43 S parameter Ŝ = ŜIR + ŜUV IR contribution from NG bosons Ŝ IR v g Λ f 16π log m Z Ŝ UV g v f 1 g 1 Λ + N c N F 16π log m +... tree-level (rho) 0

44 S parameter Ŝ = ŜIR + ŜUV IR contribution from NG bosons Ŝ IR v g Λ f 16π log m Z Ŝ UV g v f 1 g 1 Λ + N c N F 16π log m +... tree-level (rho) 1-loop (fermions) 0

45 S parameter Ŝ = ŜIR + ŜUV IR contribution from NG bosons Ŝ IR v g Λ f 16π log m Z Ŝ UV g v f 1 g 1 Λ + N c N F 16π log m +... tree-level (rho) 1-loop (fermions) 1-loop contribution from fermions can be large (!) Golden, Randall, NPB 361 (1991) 3... Barbieri, Isidori, Pappadopulo, JHEP 090 (009) 09 Grojean, Matsedonskyi, Panico, arxiv: Azatov, RC, Di Iura, Galloway, arxiv:

46 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) 1

47 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) 1

48 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) Example: [ Azatov, RC, Di Iura, Galloway, arxiv: ] ψ 5 =(1, 1) + (, ) L = ψ 1 i /D m 1 ψ1 + ψ 4 i / m 4 ψ4 ζ ψ 4 γ µ d µ ψ 1 + h.c. ψ (,) ψ (,) J a µ J âµ + ψ (,) ψ (1,1) 1 ρ LL,RR ρ BB

49 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) Example: [ Azatov, RC, Di Iura, Galloway, arxiv: ] A + i π / π f +... ψ 5 =(1, 1) + (, ) L = ψ 1 i /D m 1 ψ1 + ψ 4 i / m 4 ψ4 ζ ψ 4 γ µ d µ ψ 1 + h.c. ψ (,) ψ (,) J a µ J âµ + ψ (,) ψ (1,1) 1 ρ LL,RR ρ BB

50 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) Example: [ Azatov, RC, Di Iura, Galloway, arxiv: ] A + i π / π f +... µ π f +... ψ 5 =(1, 1) + (, ) L = ψ 1 i /D m 1 ψ1 + ψ 4 i / m 4 ψ4 ζ ψ 4 γ µ d µ ψ 1 + h.c. ψ (,) ψ (,) J a µ J âµ + ψ (,) ψ (1,1) 1 ρ LL,RR ρ BB

51 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) Example: [ Azatov, RC, Di Iura, Galloway, arxiv: ] A + i π / π f +... µ π f +... ψ 5 =(1, 1) + (, ) L = ψ 1 i /D m 1 ψ1 + ψ 4 i / m 4 ψ4 ζ ψ 4 γ µ d µ ψ 1 + h.c. ψ (,) ζ ζ ψ (,) J a µ J âµ + ψ (,) ψ (1,1) 1 ρ LL,RR ρ BB

52 fermion contribution can be negative Best seen using a dispertion relation: Orgogozo and Rychkov, JHEP 1306 (013) 014 Ŝ UV = g ds 4 sin θ s [ρ LL(s)+ρ RR (s) ρ BB (s)] negative contribution from spectral function of broken SO(5)/SO(4) currents i d 4 xe iq (x y) 0 T (J µ (x)j ν (y)) 0 =(q η µν q µ q ν )Π(q ) ρ(s) = 1 π Im(Π(s)) Example: [ Azatov, RC, Di Iura, Galloway, arxiv: ] A + i π / π f +... µ π f +... ψ 5 =(1, 1) + (, ) L = ψ 1 i /D m 1 ψ1 + ψ 4 i / m 4 ψ4 ζ ψ 4 γ µ d µ ψ 1 + h.c. Ŝ UV = 8 3 m W 16π f N cn F 1 ζ Λ log m +finiteterms (,)

53 SO(5)/SO(4) model: ψ 5 =(1, 1) /3 +(, ) / m 3,1 3.4 TeV 5 TeV m 1,3 1.0 N fχ N c 9=9 m 1,1 1.5 m,.0 ψ 10 =(, ) 1/3 +(1, 3) 1/3 +(3, 1) 1/ AA SM 0.5 ζ Ζ1.1 = SM ζ Ζ0 =0 ζ Ζ1 =1 f100 f800 f S from: Azatov, RC, Di Iura, Galloway arxiv:

54 SO(5)/SO(4) model: ψ 5 =(1, 1) /3 +(, ) / m 3,1 3.4 TeV 5 TeV m 1,3 1.0 N fχ N c 9=9 m 1,1 1.5 m,.0 ψ 10 =(, ) 1/3 +(1, 3) 1/3 +(3, 1) 1/ AA SM 0.5 ζ Ζ1.1 = SM ζ Ζ0 =0 ζ Ζ1 =1 f100 f800 f S from: Azatov, RC, Di Iura, Galloway arxiv: Ex: for f = 800 GeV g ρ =3 S ρ 0.13 S ψ 0.8 (1 ζ ) strong sensitivity on ζ tuning ~10% required to go back into the exp. ellipse 3

55 T parameter ˆT = ˆT IR + ˆT UV ˆT IR v f g Λ 16π log m Z ˆT UV v f g Λ 16π log m ρ + N c λ L 16π λ L g

56 T parameter ˆT = ˆT IR + ˆT UV IR contribution from NG bosons ˆT IR v f g Λ 16π log m Z ˆT UV v f g Λ 16π log m ρ + N c λ L 16π λ L g

57 T parameter ˆT = ˆT IR + ˆT UV IR contribution from NG bosons ˆT IR v f g Λ 16π log m Z ˆT UV v f g Λ 16π log m ρ + N c λ L 16π λ L g loop (rho) 4

58 T parameter ˆT = ˆT IR + ˆT UV IR contribution from NG bosons ˆT IR v f g Λ 16π log m Z ˆT UV v f g Λ 16π log m ρ + N c λ L 16π λ L g loop (rho) 1-loop (fermions) 4

59 T parameter ˆT = ˆT IR + ˆT UV IR contribution from NG bosons ˆT IR v f g Λ 16π log m Z ˆT UV v f g Λ 16π log m ρ + N c λ L 16π λ L g loop (rho) 1-loop (fermions) Custodial symmetry implies: 1. No ˆT at tree-level W a y L y L W a. fermion correction is finite and starts at O(λ 4 L) y L y L (only top partners contribute) 4

60 ˆT >0 possible though not fully generic Carena, et al. NPB 759 (006) 0; PRD 76 (007) Barbieri et al. PRD 76 (007) Lodone JHEP 081 (008) 09 Pomarol, Serra, PRD 78 (008) Example: model with + composite ψ 4 =(, ) /3 L = q L idq L + t R idt R + ψ 4 (i m 4 )ψ 4 + iζ ψ i 4γ µ d i µt R + y Lt f q L U(π)t R + y L4 f q L U(π)ψ 4 + h.c. t R Gillioz PRD 80 (009) Grojean, Matsedonskyi, Panico arxiv: ζ Grojean, Matsedonskyi, Panico arxiv: T Ξ 0.1 m 4 1 TeV y L4

61 ˆT >0 possible though not fully generic Carena, et al. NPB 759 (006) 0; PRD 76 (007) Barbieri et al. PRD 76 (007) Lodone JHEP 081 (008) 09 Pomarol, Serra, PRD 78 (008) Example: model with + composite ψ 4 =(, ) /3 L = q L idq L + t R idt R + ψ 4 (i m 4 )ψ 4 + iζ ψ i 4γ µ d i µt R + y Lt f q L U(π)t R + y L4 f q L U(π)ψ 4 + h.c. t R Gillioz PRD 80 (009) Grojean, Matsedonskyi, Panico arxiv: ζ Grojean, Matsedonskyi, Panico arxiv: blue region allowed by EWPT at 68% (95%) 1 T Ξ 0.1 m 4 1 TeV y L4

62 Searches of top partners

63 Typical spectrum of top partners E m λ L v X /3 X 5/3 B T m λ L f T t 7

64 Typical spectrum of top partners E m λ L v X /3 X 5/3 B T m λ L f T Two main production modes: g from: De Simone, Matsedonskyi, Rattazzi, Wulzer JHEP 1304 (013) 004 t 1000 g pair production 100 pp T b + j pp X 5/3 t + j Σ fb 10 q V L q 1 pp T T g EW single production t/ b M GeV

65 Typical spectrum of top partners E m λ L v X /3 X 5/3 B T m λ L f T Two main production modes: g from: De Simone, Matsedonskyi, Rattazzi, Wulzer JHEP 1304 (013) 004 t 1000 g pair production 100 pp T b + j pp X 5/3 t + j Σ fb 10 mainly set by ζ q V L q pp T T 7 g t/ b EW single production M GeV

66 Two-body decay modes: W + /Z,h W /Z,h W + T,X /3, T b/t B X 5/3 t/b t 8

67 Two-body decay modes: W + /Z,h W /Z,h W + T,X /3, T b/t B X 5/3 t/b t ev ev Current experimental status in a nutshell 1. Almost all decays looked for. Analyses optimized on pair production ATLAS Preliminary Status: Lepton-Photon 013 s = 8 TeV, Forbidden -1 L dt = 14.3 fb 95% CL exp. excl. 95% CL obs. excl. Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] Wb+X [ATLAS-CONF ] SU() (T,B) doub. m T SU() singlet = 650 GeV BR(T ht) Forbidden Forbidden m T m T = 450 GeV = 600 GeV BR(T Wb) ATLAS Preliminary Status: Lepton-Photon 013 s = 8 TeV, 95% CL exp. excl. 95% CL obs. excl. 1 BR(tZ) CMS preliminary SU() (T,B) doub. 0-1 L dt = 14.3 fb Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] BR(bW) SU() singlet s = 8 TeV 19.6 fb Wb+X [ATLAS-CONF ] CMS BG CMS BG BR(tH) T Observed T Quark Mass Limit [GeV]

68 Two-body decay modes: W + /Z,h W /Z,h W + T,X /3, T b/t B X 5/3 t/b t ev ev Current experimental status in a nutshell 1. Almost all decays looked for. Analyses optimized on pair production ATLAS Preliminary Status: Lepton-Photon 013 s = 8 TeV, Forbidden -1 L dt = 14.3 fb 95% CL exp. excl. 95% CL obs. excl. Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] Wb+X [ATLAS-CONF ] SU() (T,B) doub. m T SU() singlet = 650 GeV BR(T ht) Forbidden Forbidden m T m T = 450 GeV = 600 GeV BR(T Wb) ATLAS Preliminary Status: Lepton-Photon 013 s = 8 TeV, 95% CL exp. excl. 95% CL obs. excl. Limits in the GeV range 1 BR(tZ) CMS preliminary SU() (T,B) doub. 0-1 L dt = 14.3 fb Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] BR(bW) SU() singlet s = 8 TeV 19.6 fb Wb+X [ATLAS-CONF ] CMS BG CMS BG BR(tH) T Observed T Quark Mass Limit [GeV]

69 Two-body decay modes: W + /Z,h W /Z,h W + T,X /3, T b/t B X 5/3 t/b t ev ev Current experimental status in a nutshell 1. Almost all decays looked for. Analyses optimized on pair production ATLAS Preliminary Status: Lepton-Photon 013 s = 8 TeV, Forbidden -1 L dt = 14.3 fb 95% CL exp. excl. 95% CL obs. excl. Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] Wb+X [ATLAS-CONF ] SU() (T,B) doub. m T SU() singlet = 650 GeV BR(T ht) Forbidden Forbidden m T m T = 450 GeV = 600 GeV BR(T Wb) ATLAS Preliminary See talks by I.Vorobiev and R.Groeber on Friday Status: Lepton-Photon 013 s = 8 TeV, 95% CL exp. excl. 95% CL obs. excl. Limits in the GeV range 1 BR(tZ) CMS preliminary SU() (T,B) doub. 0-1 L dt = 14.3 fb Ht+X [ATLAS-CONF ] Same-Sign [ATLAS-CONF ] Zb/t+X [ATLAS-CONF ] BR(bW) SU() singlet s = 8 TeV 19.6 fb Wb+X [ATLAS-CONF ] CMS BG CMS BG BR(tH) T Observed T Quark Mass Limit [GeV]

70 Once recast on (simplified) theory space exp. bounds already exclude a big portion of the natural region De Simone et al. JHEP 1304 (013) M4 5 ξ = v f =0. 3 Blue region: ζ y L4 =3 (m B m X5/3 ) 1 Green region: y L4 =0.3 (m B m X5/3 ) m X5/3 9

71 Once recast on (simplified) theory space exp. bounds already exclude a big portion of the natural region De Simone et al. JHEP 1304 (013) M4 5 ξ = v f =0. Effect of single production is NOT negligible Stronger sensitivity from optimizing exp. analyses to include single production 3 Blue region: ζ y L4 =3 (m B m X5/3 ) 1 Green region: y L4 =0.3 (m B m X5/3 ) m X5/3 9

72 Once recast on (simplified) theory space exp. bounds already exclude a big portion of the natural region De Simone et al. JHEP 1304 (013) M4 5 ξ = v f =0. Effect of single production is NOT negligible Stronger sensitivity from optimizing exp. analyses to include single production 3 Blue region: ζ y L4 =3 (m B m X5/3 ) 1 Green region: y L4 =0.3 (m B m X5/3 ) m X5/3 limits for ξ =0.1, ζ =1, y L4 =1 Multiplicity of states, connection among masses and inclusion of single production amplify limits on individual particles T B X X T M GeV

73 Once recast on (simplified) theory space exp. bounds already exclude a big portion of the natural region De Simone et al. JHEP 1304 (013) M4 5 ξ = v f =0. Effect of single production is NOT negligible Stronger sensitivity from optimizing exp. analyses to include single production 3 Blue region: ζ y L4 =3 (m B m X5/3 ) 1 Green region: y L4 =0.3 (m B m X5/3 ) m X5/3 limits for ξ =0.1, ζ =1, y L4 =1 Multiplicity of states, connection among masses and inclusion of single production amplify limits on individual particles T B X TeV masses typically excluded LHC has already eaten up a big part of the natural region X 3 T M GeV

74 Higgs couplings

75 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level v c V =1+F f v gg + O f g c ψ =1+F ψ v f, m i m j v λ + O f g

76 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level O(v /f ) from Higgs nlσm v c V =1+F f v gg + O f g c ψ =1+F ψ v f, m i m j v λ + O f g

77 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level O(v /f ) from Higgs nlσm v c V =1+F f v gg + O f g from heavy resonances h h c ψ =1+F ψ v f, m i m j v λ + O f g

78 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level O(v /f ) from Higgs nlσm v c V =1+F f v gg + O f g from heavy resonances h h c ψ =1+F ψ v f, m i m j v λ + O f g ψ L ψ R ψ L ψ R

79 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level O(v /f ) from Higgs nlσm v c V =1+F f v gg + O f g from heavy resonances h h c ψ =1+F ψ v in the simplest models f, m i m j v λ + O f g ψ L ψ R ψ L ψ R

80 LHC data currently set limits on modifications of the Higgs couplings at the 0-30% level O(v /f ) from Higgs nlσm v c V =1+F f v gg + O f g from heavy resonances h h c ψ =1+F ψ v in the simplest models f, m i m j v λ + O f g from wave-function renormalization ψ ψ ψ L ψ R ψ L ψ R

81 ξ v f MCHM4: MCHM5: c V = c ψ = 1 ξ c V = 1 ξ c ψ = 1 ξ 1 ξ Agashe, RC, Pomarol, NPB 719 (005) 165 RC, DaRold, Pomarol, PRD 75 (007) Carena, Ponton, Santiago, Wagner, PRD 76 (007) c ψ.0 CMS Preliminary -1-1 s = 7 TeV, L " 5.1 fb s = 8 TeV, L " 19.6 fb MCHM4! V,! f c ψ 3 1 ATLAS Preliminary -1 s = 7 TeV, Ldt = fb -1 s = 8 TeV, Ldt = fb MCHM4 SM Best fit 68% CL 95% CL MCHM5 0 MCHM ! c V Red points at c V ξ (v/f) =0., 0.5, 0.8 3

82 ξ v c V = c ψ = MCHM4: 1 ξ f MCHM5: c V = 1 ξ c ψ = 1 ξ 1 ξ Agashe, RC, Pomarol, NPB 719 (005) 165 RC, DaRold, Pomarol, PRD 75 (007) Carena, Ponton, Santiago, Wagner, PRD 76 (007) Minimal Composite Higgs MCHM5 c ψ.0 CMS Preliminary -1-1 s = 7 TeV, L " 5.1 fb s = 8 TeV, L " 19.6 fb MCHM4! V,! f MCHM5 Likelihood from arxiv: c ψ 1 0 ATLAS Preliminary ATLAS s = 7 TeV, Ldt Combined = fb -1 s = 8 TeV, Ldt = fb MCHM4 MCHM5 m h 16 GeV CMS -1 SM Best fit 68% CL 95% CL ! c V v f ξ =(v/f) < 0. at 95% m new 1.6 TeV c V g 3 33

83 ξ v c V = c ψ = MCHM4: 1 ξ f MCHM5: c V = 1 ξ c ψ = 1 ξ 1 ξ Agashe, RC, Pomarol, NPB 719 (005) 165 RC, DaRold, Pomarol, PRD 75 (007) Carena, Ponton, Santiago, Wagner, PRD 76 (007) Minimal Composite Higgs MCHM5 c ψ.0 CMS Preliminary -1-1 s = 7 TeV, L " 5.1 fb s = 8 TeV, L " 19.6 fb MCHM4! V,! f MCHM5 Likelihood from arxiv: c ψ 1 0 ATLAS Preliminary ATLAS s = 7 TeV, Ldt Combined = fb -1 s = 8 TeV, Ldt = fb MCHM4 MCHM5 m h 16 GeV CMS -1 SM Best fit 68% CL 95% CL ! c V v f ξ =(v/f) < 0. at 95% m new 1.6 TeV c V g 3 Sensitivity comparable to direct searches

84 Modifications to loop-level couplings ggh, γγh suppressed due to the Goldstone symmetry h γ γ B µνh H Effective operators violate the Higgs shift symmetry: g g h G µνh H H i H i + ζ i 34

85 Modifications to loop-level couplings ggh, γγh suppressed due to the Goldstone symmetry h γ γ B µνh H Effective operators violate the Higgs shift symmetry: g g h G µνh H H i H i + ζ i δγ v =1+O Γ SM f g + O v m λ g long-distance SM loops with modified couplings short-distance loops of top partners 34

86 Large modifications possible in Azatov, RC, Di Iura, Galloway, arxiv: Γ(h Zγ) δγ(zγ) v Γ SM (Zγ) = O f g + O v m Relevant operator is O HW O HB O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)Wµν i h Z γ 1. Invariant under Higgs shift symmetry. Odd under LR exchange 35

87 Large modifications possible in Azatov, RC, Di Iura, Galloway, arxiv: Γ(h Zγ) δγ(zγ) v Γ SM (Zγ) = O f g + O v m Relevant operator is O HW O HB O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)Wµν i h Z γ 1. Invariant under Higgs shift symmetry. Odd under LR exchange Strong dynamics MUST break LR 35

88 Large modifications possible in Azatov, RC, Di Iura, Galloway, arxiv: Γ(h Zγ) δγ(zγ) v Γ SM (Zγ) = O f g + O v m Relevant operator is O HW O HB O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)Wµν i h Z γ 1. Invariant under Higgs shift symmetry. Odd under LR exchange Strong dynamics MUST break LR A(h Zγ) =A SM F (ξ)+δa δa A SM N c N F g v v N c N F m f m m 35

89 Large modifications possible in Azatov, RC, Di Iura, Galloway, arxiv: Γ(h Zγ) δγ(zγ) v Γ SM (Zγ) = O f g + O v m Relevant operator is O HW O HB O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)Wµν i h Z γ 1. Invariant under Higgs shift symmetry. Odd under LR exchange Strong dynamics MUST break LR A(h Zγ) =A SM F (ξ)+δa δa A SM N c N F g v v N c N F m f m m 35 shift of tree-level Higgs couplings from nlσm v 1+O f

90 Large modifications possible in Azatov, RC, Di Iura, Galloway, arxiv: Γ(h Zγ) δγ(zγ) v Γ SM (Zγ) = O f g + O v m Relevant operator is O HW O HB O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)Wµν i h Z γ 1. Invariant under Higgs shift symmetry. Odd under LR exchange Strong dynamics MUST break LR A(h Zγ) =A SM F (ξ)+δa δa A SM N c N F g v v N c N F m f m m 35 shift of tree-level Higgs couplings from nlσm v 1+O f multiplicity of composite states

91 Large modifications possible in Γ(h Zγ) Azatov, RC, Di Iura, Galloway, arxiv: Relevant operator is O HW O HB hzγ SM f 500 GeV 0.1 r.5 f 800 GeV 0.1 r.5 O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)W i µν 0.5 Rescaling treelevel couplings nlσm δg g hvv =v /f v f mm Rescaling from 1. Invariant under Higgs shift symmetry. Odd under LR exchange A(h Zγ) =A SM F (ξ)+δa δa A SM N c N F g v v N c N F m f m m 36 shift of tree-level Higgs couplings from nlσm v 1+O f multiplicity of composite states

92 Large modifications possible in Γ(h Zγ) Azatov, RC, Di Iura, Galloway, arxiv: Relevant operator is O HW O HB hzγ SM f 500 GeV 0.1 r.5 f 800 GeV 0.1 r.5 O HB =(D µ H) (D ν H)B µν O HW =(D µ H) σ i (D ν H)W i µν 0.5 Rescaling treelevel couplings nlσm δg g hvv =v /f v f mm Rescaling from 1. Invariant under Higgs shift symmetry. Odd under LR exchange See talk by A. Azatov on Friday A(h Zγ) =A SM F (ξ)+δa δa A SM N c N F g v v N c N F m f m m 36 shift of tree-level Higgs couplings from nlσm v 1+O f multiplicity of composite states

93 37 Summary: CH vs SUSY

94 Summary: CH vs SUSY Higgs mass term (FT) Finite in CH m H 3λ 8π m Log divergent in SUSY m H u 3y t Λ 4π m t log m t 37

95 Summary: CH vs SUSY Higgs mass term (FT) Finite in CH m H 3λ 8π m Log divergent in SUSY m H u 3y t Λ 4π m t log m t Higgs quartic coupling CH: tends to be too large λ 4 3 8π g3 y t SUSY: tends to be too small λ 4 g + g 4 + 3y4 t m t log 8π m t 37

96 Summary: CH vs SUSY Bounds on top partners from direct searches SUSY: stops 700 GeV CH: heavy tops/bottoms 1 TeV 38

97 Summary: CH vs SUSY Bounds on top partners from direct searches SUSY: stops 700 GeV CH: heavy tops/bottoms 1 TeV Corrections to EW precision observables SUSY: CH: bound on Higgs compositeness / tree-level UV large shifts in Higgs couplings allowed / loop-level UV 38

98 Summary: CH vs SUSY Bounds on top partners from direct searches SUSY: stops 700 GeV CH: heavy tops/bottoms 1 TeV Corrections to EW precision observables SUSY: CH: bound on Higgs compositeness / tree-level UV large shifts in Higgs couplings allowed / loop-level UV Largest effects in Higgs sector expected in: 38 SUSY: CH: coupling to bottom (cb); γγ and gg rates; production of Heavy Higgses tree-level couplings; h Zγ rate; double Higgs production (gg hh)