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

Transcription

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

2 Part I: Quick review of the Composite Higgs

3 Composite Higgs models [Georgi & Kaplan, `80s] EWSB sector H G G _ _ Aµ (G SM ) ψ Requirements: 1) GSM G SM (elementary) sector 2) H is a doublet of SU(2) L EWSB sector characterized by: m ρ g SM g ρ 4π ( derived scale: f = m ρ /g ρ ) Example: SO(5) SO(4) ~ SU(2)L SU(2)R gives 4 real Goldstones: one SU(2)L doublet H

4 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

5 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

6 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

7 Equivalence with 5D warped field theories: { 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

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

9 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

10 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

11 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 )

12 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 ]

13 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 ]

14 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 ]

15 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 0.01 a 1 = π α(m Z ) cos 2 θ W a 3 = 1 12π α(m Z ) 4 sin 2 θ W ( ) 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

16 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

17 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

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

19 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

20 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

21 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!

22 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

23 Production of the heavy tops ( T, T, T 2/3 ) has been studied in the literature: Single production via bw fusion best channel: T W + b l + νb LHC reach with L = 300 fb 1 : M = 2 (2.5) TeV for λ T = 1 (2) see: Azuelos et al. Eur.Phys.J. C39S2 (2005) 13 [hep-ph/ ] Pair production best channels: T T W + b W b W + b h t W + b Z t final states with 1 charged lepton L disc = 2.1(90) fb 1 for M T = 0.5(1) TeV see: J.A. Aguilar-Saavedra PoS TOP2006:003,2006 [hep-ph/ ] and refs. therein

24 Pair production of the heavy bottom ( B) has also been investigated recently: Skiba and Tucker-Smith PRD 75 (2007) C. Dennis et al. hep-ph/ g B t W Spectacular Final State g B W + t channels investigated: l ± + jets+ E T and l + l + jets+ E T Challenge: t t + jets huge background hard cuts on M eff needed additional strategy proposed by Skiba and Tucker-Smith : look for highly boosted tops and Ws and cut on single jet invariant mass works only for heavy masses M B 1 TeV results depend on the jet energy algorithm used

25 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 t t + jets is not a background anymore [except for charge mis-id] For the T 5/3 case one can reconstruct the resonant (tw ) invariant mass

26 Cuts: jets : p T (1st) 100 GeV p T (2nd) 80 GeV n jet 5, η j 5 leptons : p T (1st) 50 GeV p T (2nd) 25 GeV η l 2.4, R lj 0.4 E T 20 GeV 60 M = 500 GeV L = 10 fb M = 500 GeV L = 10 fb -1 T 5/3 + B + bck # of events/(50 GeV) T 5/3 + B + bck B + bck background # of events/(25 GeV) B + bck background with b-tagging: T + B + bck 5/3 B + bck Total invariant mass [GeV] M inv (hardest 5 jets) [GeV] Discovery Potential: L disc M = 500 GeV T 5/3 + B 56 pb 1 B only 147 pb 1 less than 100 pb 1

27 # of events/(20 GeV) M = 500 GeV L = 10 fb -1 T + B + bck 5/3 B + bck background with b-tagging: T + B + bck 5/ M tw [GeV]

28 Backup slides

29 Signal and Background Simulation Signal and SM background have been simulated using: MadGraph/MadEvent [MatrixElement] + Pythia [Showering - no hadronization or und.event] Quark/Jet matching a la MLM Jets reconstructed with a cone algorithm (GetJet) with R = 0.4, E min T = 30 GeV Jet energy and momentum smeared by 100%/ E to simulate the detector resolution σ [fb] σ BR(l ± l ± ) [fb] T 5/3 T 5/3 /BB + jets (M = 500 GeV) T 5/3 T 5/3 /BB + jets (M = 1 TeV) SM bckg [ m h = 180 GeV] ttw + W + jets ( t th + jets) ttw ± + jets W + W W ± + jets ( hw ± + jets) W ± W ± + jets

30 other backgrounds: Events where one lepton comes from a b-decay these leptons are soft: completely removed by our cut p T (l) 25 GeV t t + jets events where the charge of one lepton is mis-identified ɛ mis charge mis-id probability strongly depends on the lepton s and p T η for t t + jets the hardest lepton has p T (l) 100 GeV ɛ mis 10 4 seems possible t t + jets negligible W l + l + jets events where one lepton is lost technically difficult to simulate with all the needed jets we estimate it to be 30% of the sum of the included backgrounds

31 # jets - with two different cone sizes !R=0.4 E T min = 30 GeV signal! M = 0.5 TeV signal! M = 1 TeV background !R=0.7 E T min = 30 GeV signal! M = 0.5 TeV signal! M = 1 TeV background Number of jets Number of jets

32 jet invariant mass with two different cone sizes 0.10 min!r=0.4 E T = 30 GeV 0.10!R=0.4 E T min = 30 GeV entries/(5 GeV) signal! M = 0.5 TeV signal! M = 1 TeV background entries/(5 GeV) signal! M = 0.5 TeV signal! M = 1 TeV background invariant mass of the hardest jet [GeV] invariant mass of the second hardest jet [GeV] 0.10 min!r=0.7 E T = 30 GeV 0.10!R=0.7 E T min = 30 GeV entries/(5 GeV) signal! M = 0.5 TeV signal! M = 1 TeV background entries/(5 GeV) signal! M = 0.5 TeV signal! M = 1 TeV background invariant mass of the hardest jet [GeV] invariant mass of the second hardest jet [GeV]

33 Strategy and main cuts For R = 0.4 only the M=1 TeV signal has one double jet from boosted W s We demand at least 5 hard jets ( p T 30 GeV) : l ± l ± + n jets + E T (n 5) Reference luminosities: 10 fb 1 for M = 500 GeV 100 fb 1 for M = 1 TeV Main Cuts: jets : p T (1st) 100 GeV p T (2nd) 80 GeV n jet 5, η j 5 leptons : p T (1st) 50 GeV p T (2nd) 25 GeV η l 2.4, R lj 0.4 E T 20 GeV signal signal (M = 500 GeV) (M = 1 TeV) t tw t tw W W W W W ± W ± Efficiencies (ɛ main ) σ [fb] BR ɛ main

34 Mass Reconstruction M=500 GeV l + ν l + ν 1. Reconstruct 2 W s M(jj) m W 20 GeV T 5/3 W + W + t b R jj (1st pair) 1.5 p T (1st pair) 100 GeV R jj (2nd pair) 2.0 T 5/3 W t W b p T (2nd pair) 30 GeV 2. Reconstruct 1 top (t=wj) q q q q M(W j) m t 25 GeV signal (M = 500 GeV) t tw t tw W W W W W W ɛ 2W ɛ top