From Higgsless to Composite Higgs Models

Transcription

1 From Higgsless to Composite Higgs Models E = mc 2 based on works in collaboration with E = hν G. Giudice, A. Pomarol and R. Rattazzi hep-ph/ = JHEP062007)045 R. Contino, M. Moretti, F. Puccinini and R. Rattazzi work in progress R µν 1 2 Rg µν = 16πG T µν Ch!"ophe Grojean CERN-TH & CEA-Saclay-IPhT Christophe.Grojean[at]cern.ch)

2 Main Question for the LHC What is the mechanism of EW symmetry breaking? what we usually mean by that question is really what is canceling these infamous diagrams? d 4 k 1 2π) 4 k 2 m 2 Λ2 d 4 k k 2 2π) 4 k 2 m 2 ) 2 Λ2 supersymmetry, gauge-higgs, Little Higgs But this is assuming that we already know the answer to

3 Main Question for the LHC What is unitarizing the WW scattering amplitudes? W L & Z L part of EWSB sector W scattering is a probe of Higgs sector interactions ɛ l = k M, E M k k ) L L W L & Z L part of EWSB sector we have already discovered A = g 2 E M W ) 2 L L 75% of the Higgs doublet!) WW scattering is a probe of Higgs sector interactions Weakly coupled models Strongly coupled models other ways? TeV QCD prototype: Susy susy partners ~ 100 GeV prototype: Technicolor rho meson ~ 1 TeV

4 Strongly coupled models a technical challenge: how to evade EW precision data The resonance that unitarizes the WW scattering amplitudes TC = +... generates a tree-level effect on the SM gauge bosons self-energy S parameter of order 1. Not seen at LEP a theoretical challenge: need to develop tools to do computation

5 Back to Technicolor from Xdims AdS/CFT correspondence for model-builder G Warped gravity with fermions and gauge field in the bulk and Higgs on the brane A 5 A ɛ H Strongly coupled theory with slowly-running couplings in 4D h h + a pseudo-goldstone of a strong force H H 0 5D 4D KK modes vector resonances mesons in QCD) motion along 5th dim RG flow UV IR UV brane IR brane UV cutoff break. of conformal inv. bulk local sym. global sym. Advantages weakly coupled description calculable models new approach to fermion embedding and flavor problem

6 Higgsless Models

7 Warped Higgsless Model UV brane z = R UV ~ 1/M Pl SU2) L xsu2) R x U1) B-L IR brane z = R IR ~ 1/TeV Csaki, Grojean, Pilo, Terning 03 ds 2 = R z ) 2 ηµνdx µ dx ν dz 2) SU2) L xu1) y A R ± µ =0 g 5B µ g 5 A R 3 µ =0 5g 5 B µ + g 5A R 3 µ )=0 { U1) em U1) B-L xsu2) D A La µ A Ra µ =0 5 A La µ + A Ra µ )=0 Ω= R IR R UV GeV BCs kill all A 5 massless modes: no 4D scalar mode in the spectrum light mode: M 2 W = log suppression KK tower: 1 R 2 IR logr IR/R UV ) M 2 KK = MZ 2 g2 5 +2g g5 2 + g 2 RIR 2 logr IR/R UV ) cst of order unity R 2 IR

8 Unitarization of Elastic) Scattering Amplitude Same KK mode in and out p q q ɛ µ p = M, E p ) M p p θ A = A 4) E M ) 4 + A 2) E M ) n n n n n n n g 2 nnnn g nnk g nnk g nnk g nnk k k g nnk g nnk k n n A 4) = i contact interaction n ) ) g 2 nnnn k A 2) = i n s channel exchange g 2 nnk 4g 2 nnnn 3 k n n t channel exchange n n n u channel exchange ) f abe f cde 3 + 6c θ c 2 θ) + 23 c 2 θ)f ace f bde) g 2 nnk M 2 k M 2 n ) f ace f bde s 2 θ/2 f abe f cde)

9 KK Sum Rules Csaki, Grojean, Murayama, Pilo, Terning 03 A 4) g 2 nnnn k g 2 nnk A 2) 4g 2 nnnn 3 k g 2 nnk M 2 k M 2 n In a KK theory, the effective couplings are given by overlap integrals of the wavefunctions g 2 mnpq = g 2 5D RIR dz R z f mz)f n z)f p z)f q z) g mnp = g 5D RIR dz R z f mz)f n z)f p z) R UV R UV E 4 Sum Rule g 2 nnnn k g 2 nnk = g 2 5D RIR R UV dz R z f 4 nz) g 2 5D RIR R UV dz R z RIR R UV dz f 2 nz)f 2 nz ) k R z f kz)f k z )=0 A 4) =0. R z f kz)f k z )=δz z ) k Completness of KK modes

10 Collider Signatures unitarity restored by vector resonances whose masses and couplings are constrained by the unitarity sum rules Birkedal, Matchev, Perelstein 05 He et al. 07 WZ elastic cross section g WW Z g WWZM 2 Z 3MW M W ΓW WZ) αm 3 W 144s 2 wm 2 W a narrow and light resonance W production discovery LHC 10 events) q Z 0 W ± W Z 0 W ± q q VBF LO) dominates over DY since couplings of q to W are reduced q Number of events at the LHC, 300 fb GeV 10 fb 1 1 TeV 60 fb 1 should be seen within one/two year

11 Composite Higgs Models

12 Minimal Composite Higgs Model UV brane S05)xU1) B-L IR brane ds 2 = Agashe, Contino, Pomarol 04 R z ) 2 ηµνdx µ dx ν dz 2) SU2) L xu1) y SO4)xU1) B-L Ω= R IR R UV GeV z = R UV ~ 1/M Pl z = R IR ~ 1/TeV warped dual to composite Higgs model SO5) h 1 SO4) h 2 h 3 h 4 h 1 h 2 h 3 h 4 0 SO4) Adj 4 A μ A 5 SO5)/SO4) contains a doublet

13 Unitarity with Composite Higgs Technicolor: W L and Z L are part of the strong sector Higgs = composite object part of the strong sector too) its couplings deviate from a point-like scalar Georgi, Kaplan 84 strong = light Higgs partial unitarization heavy rho unitarization halfway between weak and strong unitarizations! susy: no naturalness pb no need for new particles to cancel Λ 2 divergences technicolor: heavier rho smaller oblique corrections; one tunable parameter: v/f. Ŝ UV g2 N 96π 2 v 2 f 2

14 How to obtain a light composite Higgs? g SM Higgs=Pseudo-Goldstone boson of the strong sector SM proto-yukawa gauge g 2 SM/g ρ Strong BSM g ρ global symmetry m Higgs =0 when g SM =0 G / H residual global symmetry m ρ = g ρ f 4πf UV completion 10 TeV usual resonances of the strong sector v f 246 GeV Higgs = light resonance of the strong sector strong sector broadly characterized by 2 parameters m ρ = mass of the resonances g ρ = coupling of the strong sector or decay cst of strong sector f = m ρ g ρ

15 Testing the composite nature of the Higgs? if LHC sees a Higgs and nothing else*: evidence for string landscape??? it will be more important then ever to figure out whether the Higgs is composite! Model-dependent: production of resonances at m Model-independent: study of Higgs properties & W scattering Higgs anomalous coupling strong WW scattering strong HH production gauge bosons self-couplings * a likely possibility that precision data seems to point to, at least in strongly coupled models

16 What distinguishes a composite Higgs? L c H 2f 2 µ H 2) µ H 2 ) U = e 0 i@ H /f H/f 1 A U 0 Giudice, Grojean, Pomarol, Rattazzi 07 c H O1) f 2 tr µ U µ U ) = µ H 2 + f 2 H 2 ) 2 + f 2 H 2 H 2 + f 2 H H 2

17 What distinguishes a composite Higgs? H = L c H 2f 2 µ H 2) µ H 2 ) v+h 2 0 ) L = c H v 2 Giudice, Grojean, Pomarol, Rattazzi 07 f 2 ) c H O1) 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 c H v 2 f 2 ) g 2 E2 M 2 W no exact cancellation of the growing amplitudes unitarization restored by heavy resonances Falkowski, Pokorski, Roberts 07 Strong W scattering below mρ?

18 SILH Effective Lagrangian strongly-interacting light Higgs) Giudice, Grojean, Pomarol, Rattazzi 07 extra Higgs leg: H/f extra derivative: /m ρ Genuine strong operators sensitive to the scale f) c H 2f 2 µ H 2 )) 2 c T 2f 2 H D µ H custodial breaking ) 2 c y y f f 2 H 2 fl Hf R +h.c. c 6 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

19 EWPT constraints ˆT = c T v 2 f 2 c T v 2 f 2 < removed by custodial symmetry Ŝ =c W + c B ) m2 W m 2 ρ m ρ c W + c B ) 1/2 2.5 TeV There are also some 1-loop IR effects Ŝ, ˆT = a log m h + b Ŝ, ˆT = a 1 c H v 2 /f 2 ) log m h + c H v 2 /f 2 log Λ ) + b effective Higgs mass m eff h = m h Λ m h Barbieri, Bellazzini, Rychkov, Varagnolo 07 modified Higgs couplings to matter ) ch v 2 /f 2 >m h LEPII, for m h ~115 GeV: c H v 2 /f 2 < 1/3 1/2 IR effects can be cancelled by heavy fermions model dependent)

20 Flavor Constraints 1+ c ij H 2 ) y ij fli Hf Rj = f 2 mass terms 1+ c ijv 2 2f 2 ) yij v fli f Rj c ijv 2 2f 2 ) yij 2 h f Li f Rj Higgs fermion interactions mass and interaction matrices are not diagonalizable simultaneously if c ij are arbitrary FCNC SILH: c y is flavor universal Minimal flavor violation built in

21 Higgs anomalous couplings L = L SM + m2 H 2v c 6 3c H /2)h 3 + m f v Lagrangian in unitary gauge ffc y + c H /2)h c H m 2 W v hw µ + W µ m 2 ) Z v c H v hz µz µ 2 f h h f f W + W g SM 1 cy + c H /2)v 2 /f 2) g SM 1 ch v 2 /f 2) Γ h f f ) SILH =Γ h f f ) SM [ 1 2cy + c H ) v 2 /f 2] Γh gg) SILH = Γ h gg) SM [ 1 2cy + c H ) v 2 /f 2]

22 Higgs anomalous couplings Γ h f f ) SILH =Γ h f f ) SM [ 1 2cy + c H ) v 2 /f 2] c H v 2 /f 2 =1/4 c y v 2 /f 2 =1/4 Γh gg) SILH = Γ h gg) SM [ 1 2cy + c H ) v 2 /f 2] LHC? ATLAS Ldt = 300 fb 1 Duhrssen 03 LHC can measure c H v 2 f 2,c y v 2 f 2 up to 20-40% composite scale 5-7 TeV) ILC could go to few % ie test composite Higgs up to 4πf 30 TeV)

23 Higgs anomalous couplings for large v/f The SILH Lagrangian is an expansion for small v/f The 5D MCHM gives a completion for large v/f m 2 W = 1 4 g2 f 2 sin 2 v/f g hw W = 1 ξ g SM hw W Fermions embedded in spinorial of SO5) m f = M sin v/f g hff = 1 ξ g SM hff Fermions embedded in 5+10 of SO5) m f = M sin 2v/f g hff = 1 2ξ 1 ξ g SM hff universal shift of the couplings no modifications of BRs BRs now depends on v/f

24 Higgs BRs Fermions embedded in 5+10 of SO5) BRs BRs 1 m H = 120 GeV 1 m H = 180 GeV 0.8 bb WW 0.8 WW bb cc ZZ cc v 2 /f 2 v 2 /f 2 h WW can dominate even for low Higgs mass BRs remain SM like for large value of v/f

25 Strong W scattering Even with a light Higgs, growing amplitudes at least up to ) m ρ A ZLZ 0 L 0 W + L W ) L = A W + L W L Z0 LZL 0 ) = A W ± L W ± L W ± L W ± ) c H s L = f 2 A W ± ZL 0 W ± ZL 0 ) c H t = f 2, A W + L W L W + L W ) c H s + t) L = f 2 A Z 0 LZ 0 L Z 0 LZ 0 L) =0 q q W W σ pp V L V LX) ch = leptonic vector decay channels forward jet-tag, back-to-back lepton, central jet-veto with 300 fb signal-events and 10 background-events Bagger et al 95 Butterworth et al. 02 c H v 2 f 2 ) 2 σ pp V L V LX) H LHC is sensitive to c H v 2 f 2 bigger than 0.5 ~ 0.7

26 Strong Higgs production O4) symmetry between W L, Z L and the physical Higgs strong boson scattering strong Higgs production A Z 0 LZ 0 L hh ) = A W + L W L hh) = c Hs f 2 q W h signal: hh bbbb q W h hh 4W 3 ± 3ν+jets Sum rule with cuts η <δ and s<m 2 ) 2σ δ,m pp hhx) ch = σ δ,m pp W + L W L X) c H tanh 2 δ 2 ) σ δ,m pp Z 0 L ZLX 0 ) c H

27 Strong Higgs production q q W W h h + ν - ν ν + ξ =0 ξ =0.5 ξ =1 σ =0.01 fb σ =0.1 fb σ =0.3 fb Dominant backgrounds t t2w b b4w 3l3ν2b2j t tw 2j b b3w 2j 3l3ν2b2j t tw 1j b b3w 2j 3l3ν2b1j WZ4j 3l1ν4j σ =3.5 fb σ =1.9 fb σ =3.1 fb σ = 40 fb Cuts on M jj > 400 GeV & j max >2 ~ 10 events for signal and ~ 3 events for fb -1 )

28 Gauge boson self-couplings L V = ig cos θ W g Z 1 Z µ W +ν W µν W ν W + µν) ig cos θw κ Z Z µν + sin θ W κ γ A µν ) W + µ W ν g Z 1 TGC are sensitive to the form factor operators = m2 Z m 2 ρ c W κ γ = m2 W m 2 ρ gρ LHC 100fb -1 g Z 1 1% κ γ κ Z ILC ) 2 chw + c HB ) κ Z = g Z 1 tan 2 θ W κ γ not competitive with the measure of S at LEPII sensitive to resonance up to mρ~800 GeV sensitive to resonance up to mρ~8tev T. Abe et al, Snowmass 01

29 Conclusions EW interactions need a UV moderator to unitarize WW scattering amplitude Oblique corrections are a test of new physics WW scattering and Higgs anomalous couplings should be able to tell us if the EWSB sector is strongly or weakly coupled. LHC and ILC are complementary in the exploration of the TeV scale population