A not so elementary Higgs boson

Transcription

1 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

2 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

3 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

4 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

5 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

6 A not so elementary Higgs boson Corfu Summer Institute Workshop on Fields and Strings Sept o11 Ch!"ophe Grojean CERN-TH & CEA-Saclay/IPhT ( christophe.grojean@cern.ch )

7 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Christophe Grojean A not so elementary Higgs boson 2

8 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Where are these Goldstone s coming from? Christophe Grojean A not so elementary Higgs boson 2

9 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Where are these Goldstone s coming from? Are they fundamental scalar degrees of freedom? require at least one additional degree of freedom (the Higgs boson!) Christophe Grojean A not so elementary Higgs boson 2

10 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Where are these Goldstone s coming from? Are they fundamental scalar degrees of freedom? require at least one additional degree of freedom (the Higgs boson!) Are they composite fields? What are made of then? require new strong interactions that are likely to produce other bound states Christophe Grojean A not so elementary Higgs boson 2

11 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Where are these Goldstone s coming from? Are they fundamental scalar degrees of freedom? require at least one additional degree of freedom (the Higgs boson!) Are they composite fields? What are made of then? require new strong interactions that are likely to produce other bound states Are they components of gauge fields in higher dimensions? require new space dimensions Christophe Grojean A not so elementary Higgs boson 2

12 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Where are these Goldstone s coming from? Are they fundamental scalar degrees of freedom? require at least one additional degree of freedom (the Higgs boson!) Are they composite fields? What are made of then? require new strong interactions that are likely to produce other bound states Are they components of gauge fields in higher dimensions? require new space dimensions At which scale should we expect to see something? Christophe Grojean A not so elementary Higgs boson 2

13 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? Lee, Quigg & Thacker 77 Christophe Grojean A not so elementary Higgs boson 3

14 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? L mass = m 2 W W + µ W µ m2 ZZ µ Z µ = v2 Goldstone of 4 Tr D µ Σ D µ Σ Σ = e iσ a π a /v SU(2) L xsu(2) R /SU(2) V Lee, Quigg & Thacker 77 Christophe Grojean A not so elementary Higgs boson 3

15 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? L mass = m 2 W W + µ W µ m2 ZZ µ Z µ = v2 Goldstone of 4 Tr D µ Σ D µ Σ Σ = e iσ L mass = 1 2 ( µπ a ) 2 1 6v 2 (π a µ π a ) 2 (π a ) 2 ( µ π a ) a π a /v SU(2) L xsu(2) R /SU(2) V π a π b π c π d contact interaction growing with energy A π a π b π c π d = A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bc A(s, t, u) = s v 2 Weinberg s LET Lee, Quigg & Thacker 77 Christophe Grojean A not so elementary Higgs boson 3

16 The UV behavior of the weak Goldstone symmetry breaking: new phase with more degrees of freedom massive W ±, Z: 3 physical polarizations=eaten Goldstone bosons SU(2) LxSU(2) R SU(2) V UV behavior of these Goldstone s? L mass = m 2 W W + µ W µ m2 ZZ µ Z µ = v2 Goldstone of 4 Tr D µ Σ D µ Σ Σ = e iσ L mass = 1 2 ( µπ a ) 2 1 6v 2 (π a µ π a ) 2 (π a ) 2 ( µ π a ) a π a /v SU(2) L xsu(2) R /SU(2) V π a π b π c π d contact interaction growing with energy A π a π b π c π d = A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bc A(s, t, u) = s v 2 Weinberg s LET the behavior of this amplitude is not consistent above 4πv ( 1 3TeV) Lee, Quigg & Thacker 77 Christophe Grojean A not so elementary Higgs boson 3

17 Higgs as a PGB: a natural extension of SM One solution to the hierarchy pb: Higgs transforms non-linearly under some global symmetry Higgs=Pseudo-Goldstone boson (PGB) SM SO(4) SO(3) W ± L & Z L 3 Goldstone s Chacko, Batra 08 Christophe Grojean A not so elementary Higgs boson 4

18 Higgs as a PGB: a natural extension of SM One solution to the hierarchy pb: Higgs transforms non-linearly under some global symmetry Higgs=Pseudo-Goldstone boson (PGB) SM SO(4) SO(3) G H BSM W ± L & Z L W ± L & Z L & h 3 Goldstone s at least a 4 th Goldstone Chacko, Batra 08 Christophe Grojean A not so elementary Higgs boson 4

19 Higgs as a PGB: a natural extension of SM One solution to the hierarchy pb: Higgs transforms non-linearly under some global symmetry Higgs=Pseudo-Goldstone boson (PGB) SM SO(4) SO(3) W ± L & Z L G H W ± L & Z L & h BSM 3 Goldstone s at least a 4 th Goldstone xamples: SO(5)/SO(4): 4 PGBs=W ± L, Z L, h SO(6)/SO(5): 5 PGBs=H, a SU(4)/Sp(4,C): 5 PGBs=H, s SO(6)/SO(4)xSO(2): 8 PGBs=H 1 +H 2 Minimal Composite Higgs Model Agashe, Contino, Pomarol 04 Next MCHM Gripaios, Pomarol, Riva, Serra 09 Chacko, Batra 08 Minimal Composite Two Higgs Doublets Mrazek, Pomarol, Rattazzi, Serra, Wulzer 11 Christophe Grojean A not so elementary Higgs boson 4

20 How to probe % composite nature of % Higgs? I. Anomal$s c$plings Christophe Grojean A not so elementary Higgs boson 5

21 What is the SM Higgs? A single scalar degree of freedom neutral under SU(2) L xsu(2) R /SU(2) L L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 λ ψ L Σψ R 1+c h v W - W - h W + W + a, b and c are arbitrary free couplings A = 1 v 2 s a2 s 2 s m 2 h growth cancelled for a = 1 restoration of perturbative unitarity Cornwall, Levin, Tiktopoulos 73 Contino, Grojean, Moretti, Piccinini, Rattazzi 10 Christophe Grojean A not so elementary Higgs boson 6

22 What is the SM Higgs? A single scalar degree of freedom neutral under SU(2) L xsu(2) R /SU(2) L L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 λ ψ L Σψ R 1+c h v a, b and c are arbitrary free couplings For a=1: perturbative unitarity in elastic channels WW WW For b = a 2 : perturbative unitarity in inelastic channels WW hh Cornwall, Levin, Tiktopoulos 73 Contino, Grojean, Moretti, Piccinini, Rattazzi 10 a b a Christophe Grojean A not so elementary Higgs boson 7

23 What is the SM Higgs? A single scalar degree of freedom neutral under SU(2) L xsu(2) R /SU(2) L L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 λ ψ L Σψ R 1+c h v a, b and c are arbitrary free couplings For a=1: perturbative unitarity in elastic channels WW WW For b = a 2 : perturbative unitarity in inelastic channels WW hh For ac=1: perturbative unitarity in inelastic WW ψ ψ Cornwall, Levin, Tiktopoulos 73 Contino, Grojean, Moretti, Piccinini, Rattazzi 10 a c Christophe Grojean A not so elementary Higgs boson 7

24 What is the SM Higgs? A single scalar degree of freedom neutral under SU(2) L xsu(2) R /SU(2) L L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 λ ψ L Σψ R 1+c h v a, b and c are arbitrary free couplings For a=1: perturbative unitarity in elastic channels WW WW For b = a 2 : perturbative unitarity in inelastic channels WW hh For ac=1: perturbative unitarity in inelastic WW ψ ψ a=1, b=1 & c=1 define the SM Higgs Higgs properties depend on a single unknown parameter (m H ) L EWSB can be rewritten as H = 1 2 e iσa π a /v 0 v + h D µ H D µ H h and π a (ie W L andz L ) combine to form a linear representation of SU(2) L xu(1) Y Christophe Grojean A not so elementary Higgs boson 7

25 What is a composite Higgs? A σ particle that combines with W L and Z L to form a SU(2) doublet that acquires a vev SU(2) L xu(1) Y linearly realized Standard Model a=b=c=1 renormalizable level = uniqueness Christophe Grojean A not so elementary Higgs boson 8

26 What is a composite Higgs? A σ particle that combines with W L and Z L to form a SU(2) doublet that acquires a vev SU(2) L xu(1) Y linearly realized Standard Model a=b=c=1 renormalizable level = uniqueness non-renormalizable level SU(2) L xu(1) Y linearly realized & a, b, c 1 Composite Higgs deviations of Higgs couplings originate from higher dimensional operators µ H 2 2 H 2 ψhψ H 2 B µν B µν H 2 G µν G µν Christophe Grojean A not so elementary Higgs boson 8

27 Anomalous composite-higgs couplings L c H 2f 2 µ H 2 µ H 2 Giudice, Grojean, Pomarol, Rattazzi 07 c H O(1) 0 1+c H v 2 H = v+h 2 L = 1 2 f 2 ( µ h) Modified Higgs propagator ~ Higgs couplings rescaled by 1 v 1+c 2 H f 2 1 c H v 2 2f 2 1 ξ/2 ξ = v 2 /f 2 a = 1-ξ/2 b = 1-2ξ c = 1-ξ/2 Christophe Grojean A not so elementary Higgs boson 9

28 PGB Higgs: Strong EWSB with 2 Scales ξ = v2 f 2 = (weak scale) 2 (strong coupling scale) 2 ξ =0 ξ =1 SM limit all resonances of strong sector, except the Higgs, decouple Technicolor limit Higgs decouple from SM; vector resonances like in TC Composite Higgs vs. SM Higgs b 1 SM a L EWSB = a v2 h + b 14 h2 Tr D µ Σ D µ Σ Composite Higgs universal behavior for large f a=1-v 2 /2f 2 b=1-2v 2 /f 2 1 Christophe Grojean A not so elementary Higgs boson 10

29 PGB Higgs: Strong EWSB with 2 Scales ξ = v2 f 2 = (weak scale) 2 (strong coupling scale) 2 ξ =0 ξ =1 SM limit all resonances of strong sector, except the Higgs, decouple Technicolor limit Higgs decouple from SM; vector resonances like in TC Composite Higgs vs. Dilaton Higgs b 1 Dilaton b=a 2 SM a L EWSB = a v2 h + b 14 h2 Tr D µ Σ D µ Σ Composite Higgs universal behavior for large f a=1-v 2 /2f 2 b=1-2v 2 /f 2 1 Christophe Grojean A not so elementary Higgs boson 11

30 Composite Higgs vs generic anomalous couplings generic anomalous couplings can be quite complicated, e.g. L h Z = m Z h c 1 Z µ Z µ + c 2 m 2 Z µνz µν + c 3 m 2 µνρσz µν Z ρσ...many coefficients, various possible origins Christophe Grojean A not so elementary Higgs boson 12

31 Composite Higgs vs generic anomalous couplings generic anomalous couplings can be quite complicated, e.g. L h Z = m Z h c 1 Z µ Z µ + c 2 m 2 Z µνz µν + c 3 m 2 µνρσz µν Z ρσ...many coefficients, various possible origins if Higgs emerges as a bound state of strongly interacting theory a few coefficients only and related to symmetries of the coset space c H 2f 2 µ H 2 2 H 2 D µ H c T 2f 2 custodial breaking c y y f f 2 H 2 fl Hf R +h.c. c6 λ f 2 H 6 (other resonances etc give subleading contributions) very predictive models: given the coset space, the Higgs couplings depend only on ξ Christophe Grojean A not so elementary Higgs boson 12

32 Effective Lagrangian extra Higgs leg: H/f Giudice, Grojean, Pomarol, Rattazzi 07 extra derivative: /m ρ Genuine strong operators (sensitive to the scale f) c H 2f 2 µ H 2 2 H 2 D µ H c T 2f 2 custodial breaking c y y f f 2 H 2 fl Hf R +h.c. c6 λ f 2 H 6 Form factor operators (sensitive to the scale mρ) ic W 2m 2 ρ H σ i D µ H (D ν W µν ) i ic B 2m 2 ρ H D µ H ( ν B µν ) ic HW m 2 ρ g 2 ρ 16π 2 (Dµ H) σ i (D ν H)W i µν c γ m 2 ρ g 2 ρ 16π 2 g 2 g 2 ρ minimal coupling: h γz H HB µν B µν Goldstone sym. ic HB m 2 ρ c g m 2 ρ g 2 ρ 16π 2 (Dµ H) (D ν H)B µν g 2 ρ 16π 2 y 2 t g 2 ρ loop-suppressed strong dynamics H HG a µνg aµν Christophe Grojean A not so elementary Higgs boson 13

33 Deformation of the SM Higgs: current constraints L EWSB = v2 4 Tr D µ Σ D µ Σ c=a Σ = e iσa π a /v 1+2a hv + bh2 v 2 Goldstone of SU(2) L xsu(2) R /SU(2) V gaugephobic Higgs λ ψ L Σψ R 1+c h v D µ Σ W µ SM a=1, b=1 & c=1 Current EW data constrain only a (and marginally c ) Espinosa, Grojean, Muehlleitner 10 MCHM4 MCHM5 c=(2a 2-1)/a 1-a 2 1-a 2 fermiophobic Higgs SM limits Christophe Grojean A not so elementary Higgs boson 14

34 Deformation of the SM Higgs: LHC constraints EPS EPS LP LP LHC is now a Higgs exploring machine (and it has quickly surpassed Tevatron) Christophe Grojean A not so elementary Higgs boson

35 Deformation of the SM Higgs: LHC constraints EPS EPS LP not so many places where to hide the SM Higgs anymore LP LHC is now a Higgs exploring machine (and it has quickly surpassed Tevatron) Christophe Grojean A not so elementary Higgs boson

36 Deformation of the SM Higgs: LHC constraints the SM exclusion bounds are easily rescaled in the (m H,a) plane Espinosa, Grojean, Muehlleitner 11 c=a MCHM4 MCHM5 c=(2a 2-1)/a 1-a 2 1-a 2 SM limits LHC is now a Higgs exploring machine (and it has quickly surpassed Tevatron) Christophe Grojean A not so elementary Higgs boson

37 Deformation of the SM Higgs: LHC constraints the SM exclusion bounds are easily rescaled in the (m H,a) plane Espinosa, Grojean, Muehlleitner 11 c=a MCHM4 MCHM5 c=(2a 2-1)/a 1-a 2 1-a 2 SM limits Be careful rescaling combination combination of the rescaled channels (can be particularly important far away from SM) effeciency of the cuts may also depends on ξ Christophe Grojean A not so elementary Higgs boson

38 Higgs anomalous LHC L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 + b h 3 3 v λ ψ L Σψ R 1+c h v + c h 2 2 v a = 1 ξ b =1 2ξ b 3 = ξ 1 2ξ 1 ξ c = ξ, c 2 = (ξ, 4ξ) 1 ξ Minimal composite Higgs model (MCHM): SO(5)/SO(4) Γ(h f f) =(2c 1) Γ(h f f) SM Γ(h ZZ)=(2a 1) Γ(h ZZ) SM a=7/8 c=5/8 LHC can probe Δa & Δc up to ~ i.e. 4πf ~ 5 7 TeV compositeness scale of the Higgs (ILC/CLIC could go to few %, ie, test composite Higgs up to 4πf ~ 30/60 TeV) Giudice, Grojean, Pomarol, Rattazzi 07 Christophe Grojean A not so elementary Higgs boson 18

39 How to probe the composite nature of the Higgs? 2. Strong scattering Christophe Grojean A not so elementary Higgs boson 19

40 How to probe the strong dynamics? Look at pair production of strong states strong WW scattering Giudice, Grojean, Pomarol, Rattazzi 07 W W h W = (1 ξ)g 2 E2 W M 2 W A WLW a L b WLW c L d = A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bc large L int needed no exact cancellation of the growing amplitudes not competitive with the measurement of a via anomalous couplings } A = 1 a 2 s v 2 s f 2 Christophe Grojean A not so elementary Higgs boson

41 How to probe the strong dynamics? Look at pair production of strong states strong WW scattering Giudice, Grojean, Pomarol, Rattazzi 07 W W h W = (1 ξ)g 2 E2 W M 2 W A WLW a L b WLW c L d = A(s, t, u)δ ab δ cd + A(t, s, u)δ ac δ bd + A(u, t, s)δ ad δ bc large L int needed no exact cancellation of the growing amplitudes not competitive with the measurement of a via anomalous couplings strong double Higgs production A Z 0 LZ 0 L hh =(W + L W L access to a new interaction, b A = 1 a 2 s v 2 Contino, Grojean, Moretti, Piccinini, Rattazzi 10 hh) = b a 2 s distinction between active (higgs) and passive (dilaton) scalar in EWSB dynamics Christophe Grojean A not so elementary Higgs boson v 2 } s f 2

42 Double Higgs production: b and d 3 couplings L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 V (h) = 1 2 m2 hh 2 + d m 2 h v h 3 + d m 2 h v 2 h SM: a=b=d 3 =d 4 =1 } } A b a 2 4m 2 hh m 2 hh m 2 W v 2 asymptotic behavior sensitive to strong interaction A cst. + 3ad 3 m 2 h m 2 hh 4m 2 h threshold effect anomalous coupling Christophe Grojean A not so elementary Higgs boson 21 v 2

43 Strong Higgs production: (3L+jets) analysis Contino, Grojean, Moretti, Piccinini, Rattazzi 10 strong boson scattering strong Higgs production A Z 0 LZ 0 L hh = A W + L W L hh = c Hs f 2 m h = 180 GeV fermions in spinorial c H =1 W + W - h h W + W - W + l + ν l - ν l + ν jets p T 30 GeV δr jj > 0.7 η j 5 acceptance cuts leptons p T 20 GeV δr lj(ll) > 0.4(0.2) η j 2.4 W - Dominant backgrounds: Wll4j, ttw2j, tt2w(j), 3W4j... forward jet-tag, back-to-back lepton, central jet-veto v/f fb luminisity for 5σ (fb 1 ) good motivation to SLHC Christophe Grojean A not so elementary Higgs boson 22

44 Measuring the non-linearities of the Higgs Contino, Grojean, Pappadopoulo, Rattazzi, Thamm in progress L EWSB = v2 4 Tr D µ Σ D µ Σ hv 1+2a + bh2 v 2 V (h) = 1 2 m2 hh 2 + d m 2 h v h 3 + (S)LHC is barely sensitive to d 3 and b ILC has a sensitivity on d 3 but not on b CLIC can probe both d 3 and b Christophe Grojean A not so elementary Higgs boson 23

45 How to probe the composite nature of the Higgs? 3. Identifying discrete symmetries of strong sector Christophe Grojean A not so elementary Higgs boson 24

46 Geometry of Coset from W + W - 3h Strong EWSB σ 2π 3π 1 8π E 2 f 4 E 2 (4πf) 2 Contino, Grojean, Pappadopoulo, Rattazzi, Thamm in progress E/f g σ 2π 3π 1 8π g 2 g 2 v 2 16π 2 SM Probe of possible discrete symmetries in the strong dynamics invariance under b 3 G H symmetric space a a a π -π a process with an odd # of PGBs requires a coupling breaking the coset structure ie cannot be mediated by strong interactions alone b a A WW 3h 4i s v 3 a(b a 2 ) 3 4 b 3 =0 for symmetric coset Christophe Grojean A not so elementary Higgs boson } + s } mw s 2 mediated by SM gauge interactions (breaking of coset structure)

47 non-symmetric coset W + W - CLIC + - invariant mass distribution for e e Contino, Grojean, Pappadopoulo, Rattazzi, Thamm in progress -> hhh σ 4fb (σ SM 3ab) PRELIMINARY mass a=1, b=b 3 =d =0 3 Entries Mean 1478 RMS E = 3 TeV E = 5 TeV (GeV) σ 34fb (σ SM 22ab) m HHH Christophe Grojean A not so elementary Higgs boson 26

48 How to probe the composite nature of the Higgs? 4. Detecting heavy resonances Christophe Grojean A not so elementary Higgs boson 27

49 A heavy composite W Grojean, Salvioni, Torre 11 Observing a tower of resonances would a direct evidence of the strong interactions However, in the best configuration, LHC will have access to a few ones only How can we tell the difference between a massive gauge field and a resonance from a strong sector? Christophe Grojean A not so elementary Higgs boson 28

50 A heavy composite W Grojean, Salvioni, Torre 11 Observing a tower of resonances would a direct evidence of the strong interactions However, in the best configuration, LHC will have access to a few ones only How can we tell the difference between a massive gauge field elementary spin-1 and a resonance from a strong sector? g=2 Λ >> M/e W Wγ highly suppressed gyromagnetic ratio of any elementary particle of mass M coupled to photon must be g=2 at tree-level to maintain perturbative unitarity up to energy Λ >> M/e Ferrara, Porrati, Telegdi 92 (g 1)B µν Wµ + Wν dimension-4 operator mediating W Wγ after W-W mixing Christophe Grojean A not so elementary Higgs boson 28

51 A heavy composite W Grojean, Salvioni, Torre 11 Observing a tower of resonances would a direct evidence of the strong interactions However, in the best configuration, LHC will have access to a few ones only How can we tell the difference between a massive gauge field elementary spin-1 and a resonance from a strong sector? g=2 Λ >> M/e W Wγ highly suppressed gyromagnetic ratio of any elementary particle of mass M coupled to photon must be g=2 at tree-level to maintain perturbative unitarity up to energy Λ >> M/e Ferrara, Porrati, Telegdi 92 composite spin-1 g 2 & Λ > 5 10 M (g 1)B µν Wµ + Wν W Wγ allowed and potentially large dimension-4 operator mediating W Wγ after W-W mixing Christophe Grojean A not so elementary Higgs boson 28

52 Conclusions EW interactions need Goldstone bosons to provide mass to W, Z EW interactions also need a UV moderator/new physics to unitarize WW scattering amplitude We ll need another Gargamelle experiment to discover the still missing neutral current of the SM: the Higgs weak NC gauge principle Higgs NC? Strong EWSB w/o an elementary Higgs can be very similar to SM it might take some time to decipher the true dynamics of EWSB! Christophe Grojean A not so elementary Higgs boson 29

53 Higgs = emergency tire of the SM Blois 10 Christophe Grojean A not so elementary Higgs boson 30

54 An Emergency Tire Even Beyond the SM Higgs = emergency tire of the SM Blois 10 BSM Higgs [picture courtesy to Andreas Weiler] Christophe Grojean A not so elementary Higgs boson 30