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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

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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”

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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

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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?

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

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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

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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

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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

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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

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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

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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

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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’

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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

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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

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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

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

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18 Dührssen 2003 SLHC Report 2002

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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 !!

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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)

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21 Higgs decay rates

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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

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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

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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

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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

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