1. 1 Way Beyond the SM G.F. Giudice IoP meeting on the Physics of the ILC Oxford, 23 May 2007 Original work with C. Grojean, A. Pomarol, R. Rattazzi

2. 2 Supersymmetry is still the most “credible” theory BSM gauge-coupling unification EW breaking triggered by dynamics dark-matter candidate pass EW tests But, increasing difficulty with direct limits  % tuning Reason to look “way beyond”

3. 3 Extra dimensions have brought new theoretical tools Exciting new phenomena: graviton emission, transplanckian scattering, black-hole production They require the largest possible energy: is LHC enough? Nevertheless, ILC can give complementary information, especially for indirect signals Some of the most interesting twists of extra dimension are related to EW breaking Weiglein et al., 2004

4. 4 AdS/CFT correspondence relates 5-d gravity with negative cosmological constant to strongly-coupled 4-d conformal field theory Warped gravity with SM fermions and gauge bosons in bulk and Higgs on brane Technicolor-like theory with slowly-running couplings in 4 dim TeV branePlanck brane 5 th dim  IR  UV RG flow 5-D gravity 4-D gauge theory Motion in 5 th dim RG flow UV brane Planck cutoff IR brane breaking of conformal inv. Bulk local symmetries global symmetries Technicolor strikes back?

5. 5 DUALITY: familiar conceptual distinction between force and spatial dimension becomes blurry Is it a particle or is it a wave?

6. 6

7. 7 TC Technicolor-like theories in new disguise Old problems The presence of a light Higgs helps Light Higgs screens IR contributions to S and T (f pseudo-Goldstone decay constant) Can be tuned small for strong dynamics 4  f at few TeV

8. 8 New constructions with light Higgs & strong dynamics Higgs as pseudogoldstone boson Gauge, Yukawa and self-interaction are non-derivative couplings  Violate global symmetry and introduce quadratic divergences Top sector ● ● ➤ ➤ No fine-tuning Strong dynamics at a low scale, in conflict with LEP data

9. 9 “Collective breaking”: many (approximate) global symmetries preserve massless Goldstone boson ℒ1ℒ1 ℒ2ℒ2 H ℒ1ℒ1 ℒ2ℒ2 LITTLE HIGGS: delays strong dynamics by cancelling one-loop effects only New states at TeV reduce UV sensitivity of m H

10. 10 HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD A M = (A ,A 5 ), A 5  A 5 + ∂ 5  forbids m 2 A 5 2 gaugeHiggs Higgs/gauge unification as graviton/photon unification in KK Correct Higgs quantum numbers by projecting out unwanted states with orbifold The difficulty is to generate Yukawa and quartic couplings without reintroducing quadratic divergences

11. 11 Same thing? (duality) Relation between models of strong dynamics and extra dimensions Common low-energy theory of Higgs interactions (particularly useful for linear collider, as S,T useful parametrization of new physics at LEP) Higgs is the 4 th Goldstone Light Higgs pseudoGoldstone of a strong force Belong to higher-dim gauge multiplet

12. 12 Structure of the theory m  mass of resonances g   coupling of resonances Communicate via gauge (g a ) and (proto)-Yukawa ( i ) quarks, leptons & gauge bosons strong sector Strong sector characterized by In the limit I, g a =0, strong sector contains Higgs as Goldstone bosons Ex. H = SU(3)/SU(2)  U(1) or H = SO(5)/SO(4)  -model with f = m  / g   Take I, g a << g   < 4 

13. 13 g a, i break global symmetry  Higgs mass New theory addresses hierarchy problem  reduced sensitivity of m H to short distances (below m  -1 ) Ex.: Georgi-Kaplan: g  =4 , f = v, no separation of scales Holographic Higgs: g  = g KK, m  = m KK Little Higgs: g , m  couplings and masses of new t’, W’, Z’

14. 14 Production of resonances at m  allows to test models at the LHC Study of Higgs properties allows a model independent test of the nature of the EW breaking sector Is the Higgs fundamental? SM (with m H < 180 GeV) supersymmetry composite? Holographic Higgs Gauge-Higgs unification Little Higgs ILC can give a fundamental contribution to answer this question

15. 15 Construct the Lagrangian of the effective theory below m  From the kinetic term, we obtain the definition of f = m  / g   Each extra H insertion gives operators suppressed by 1 / f Each extra derivative “ “ 1 / m  f: symmetry-breaking scale m  : new-physics mass threshold Operators that violate Goldstone symmetry are suppressed by corresponding (weak) coupling

16. 16 Operators testing the strong self coupling of the Higgs (determined by the structure of the  model) and y f are SM couplings; c i model-dependent coefficients Form factors sensitive to the scale m  Loop-suppressed strong dynamics

17. 17 All Higgs couplings rescaled by Modified Higgs couplings to matter Effects in Higgs production and decay

18. 18 Dührssen 2003 SLHC Report 2002

19. 19 LHC can measure c H v 2 /f 2 and c y v 2 /f 2 up to 20-40% SLHC can improve it to about 10% A sizeable deviation from SM in the absence of new light states would be indirect evidence for the composite nature of the Higgs ILC can test v 2 /f 2 up to the % level ECFA/DESY LC Report 2001 ILC can explore the Higgs compositeness scale 4  f up to 30 TeV !!

20. 20 Effective-theory approach is half-way between model- dependent and operator analyses Dominant effects come from strong self-Higgs interactions characterized by From operator analyses, Higgs processes loop- suppressed in SM are often considered most important for searches However, operators h  and h  gg are suppressed 1/(16  2 m  2 ) Since h is charge and color neutral, gauging SU(3) c  U(1) Q does not break the generator under which h shifts (Covariant derivative acting on h does not contain  or g) Not the case for h  Z (loop, but not 1/g    suppressed)

21. 21 Higgs decay rates

22. 22 Genuine signal of Higgs compositeness at high energies In spite of light Higgs, longitudinal gauge-boson scattering amplitude violate unitarity at high energies h WLWL WLWL WLWL WLWL Modified coupling LHC with 200 fb -1 sensitive up to c H   0.3

23. 23 Higgs is viewed as pseudoGoldstone boson: its properties are related to those of the exact (eaten) Goldstones: O(4) symmetry Can bbbb at high invariant mass be separated from background? h  WW  leptons is more promising Sum rule (with cuts  and s<M 2 )  Strong gauge-boson scattering  strong Higgs production

24. 24 In many realizations, the top quark belongs to the strongly-coupled sector At leading order in 1/f 2 Modified top-quark couplings to h and Z At ILC g htt up to 5% with  s=800 GeV and L=1000 fb -1 From g Ztt,  c R ~ 0.04 with  s=500 GeV and L=300 fb -1 (no accuracy at LHC) FCNC effects

25. 25 CONCLUSIONS Several new classes of theories with light Higgs and strong interactions Experimental question: is Higgs fundamental or composite? Model-independent approach to characterize its phenomenological consequences Modifications of Higgs production and decay rates, strong WW scattering, strong Higgs production ILC can help significantly in settling the issue