PoS(EPS-HEP 2009)008 and ± W http://pos.sissa.it/ ∗ gauge bosons but they also need an ultra-violet (UV) moderator or new physics to unitarize Z [email protected] the the gauge boson scattering amplitudes. In thisat talk, the I will Fermi present scale: various recent several models deformationsHiggs of of models, physics the holographic composite Minimal Higgs Supersymmetric models, Standard 5D Model, Higgsless Little models. Speaker. Electroweak interactions need three Nambu–Goldstone bosons to provide a mass to the ∗ European Physical Society Europhysics Conference onJuly High 16-22, Energy 2009 Physics Krakow, Poland © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Christophe GROJEAN CERN, Physics Department, Theory Unit, Geneva,and Switzerland Institut de Physique Théorique, CEAE-mail: Saclay, France New theories for the Fermi scale PoS(EPS-HEP 2009)008 ], 3 , 2 , 1 [ 1 gauge bosons 0 Z Christophe GROJEAN and . Gauge theory is not ± Y . While this is certainly ) W − 1 ( W U + × W L ) 2 → ( − e SU + e × c ) 3 ( . This picture still leaves us with the question V ) SU 2 2 ( SU / R ) 2 or the left-right asymmetries in the hadronic and leptonic 2 ( − µ SU g parameter is equal to 1, is certainly a welcome feature in this regards. × L ρ ) ? What is the dynamics of this sector? What are its interactions with 2 V ( ) 2 ( SU 3 standard deviations, there a few discrepancies between EW data and the SU ÷ → R ) 2 ( SU × L ) The Higgs mechanism is at best a description, but certainly not an explanation, of electroweak There are of course additional arguments for the existence of new physics beyond theThe SM: fact that a Higgs doublet comes with an extra approximate global symmetry (the so called custodial symmetry), In the broken phase, a (massive) spin one particle describes three different polarizations: two The strong, weak and electromagnetic interactions of elementary particles are described by 2 1 ( symmetry breaking (EWSB) since thereHiggs is potential no at dynamics the that origin.at would the Moreover, explain quantum it the level also instability since jeopardizes(i) of the the our mass the Higgs current term is potential understanding quadratically suffers of divergentbe while from the (ii) driven two the to SM quartic a sources Higgs-self Landau of interactions pole could radiativemass or easily instabilities: to does a not rolling lie vacuum in at“gauge the very hierarchy", large window value “triviality" around of and 130 the “(meta)stability" and Higgs problems. 170 field GeV. if New the physics Higgs is required(i) to at solve these the level ofSM 2 predictions for quantities like which automatically ensures that the only a way to classifyprinciple that particles predicts and particular couplings assign among quantumhas particles. been numbers And well the to structure tested them of at but these LEP, interactions it for is instance also in a the dynamical process the SM particles? The common lore isscalar that field these transforming extra as degrees a of freedom weakthe are doublet. 3 part eaten This of Nambu–Goldstone Higgs a bosons doublet fundamental and corresponds oneHiggs to physical boson. real 4 scalar real While degree scalar this of fields: picture freedom,the is the notorious in very very fact good agreement that withverified its Electroweak experimentally unique (EW) yet data prediction, leaves open namelybosons: the the e.g., possibility condensates existence for of of other techniquarks, the components originssion of of . Higgs some . . the boson, gauge Nambu–Goldstone fields has along an not extra been dimen- 2. The Higgs boson: a simple picture that calls for new physics of the source ofSU the Nambu-Goldstone bosons: What is the sector responsible for the breaking transverse ones plus an extra longitudinaldard Model one (SM), which the decouples longitudinal in degrees the of massless freedom limit. associated In to the the Stan- true at least for the 3-pointgauge functions, structure namely is the actually interactions badly involvingspectrum: violated at at least the the three observed level particles, mass of the the termssince 2-point the for functions, gauge the namely group leptons in is andcalls the chiral the for mass and a gauge also spontaneous bosons acts breaking non-linearly are of on not the the gauge gauge gauge symmetry. invariant fields. This apparent clash correspond presumably to the eatenglobal Nambu–Goldstone chiral bosons symmetry resulting from the breaking of the gauge interactions based on a symmetry group New theories for the Fermi scale 1. The Standard Model and the mass problem PoS(EPS-HEP 2009)008 × , ) 2 2 (3.2) (3.1) (  2

SU 0 d H ×

) 3 − ( 2

0 u SU H

Christophe GROJEAN  2 0 g 8 + 2 g ) + . c . h + 0 d β H 2 0 u 2 H term. This cancelation requires a fine-tuning of ( cos B µ measures the ratio of the two Higgs vacuum ex- -parity that forbids any interactions between SM 3 2 Z R − β m 2

0 = d 2 h H

m ) d 2 H m : the supersymmetric (SUSY) extensions of the SM certainly + 2 | µ | + ( ): 2 i

0 d u v H /

u ] and LEP2 data together with the lack of discovery of a Higgs boson below ) v 5 u h 2 H m + 2 | µ | ]. Unfortunately, this agreement is limited to small and peculiar regions of the (large) 4 gauge couplings; (v) the possibility to identify the lightest supersymmetric particle (LSP) as mass that should then be canceled by a large Moreover, SUSY models seems to be in even better agreement with EW data than the SM Theorists have always been very good at giving names to things they do not understand. And A tout seigneur, tout honneur = ( ) Z 1 V ( parameter space [ 114 GeV or ofdermining any new its states original has motivation. forcedcomes The from supersymmetry most the into lower stringent bound fine-tuning constraint on territory,potential the on is partially Higgs the dictated boson un- by scale mass. gauge of Indeed interactions: at SUSY tree-level, breaking the shape of the Higgs the order of 1% (the amount of fine-tuning depends exponentially on the Higgs mass bound). This itself [ the Dark Matter . . . One-loop radiative corrections can bring the Higgsmass mass is above heavier the than LEP about bound provided 1the that TeV. But a at stop the same time, the stop will also generate a correction to stand out among the models of newdivergences; physics (ii) for at a least dynamical several reasons: EWSBabsence (i) of driven the large radiatively absence oblique of by corrections quadratic thefields due and top to an the Yukawa odd number interactions; of (iii) heavy fields; the (iv) a precise apparent unification of the clearly the EWSB sectorby has collecting been the an attributes inspirational thatburried, source have composite, fat, been of gauge, associated gaugephobic, creativity intermediate, to to leptophilic,portal, the little, them, private, littlest, Higgs slim, lone, as simplest, boson phantom, twin, it over un- the isbeyond . . last the evident . A scope few description of years: of this theserepresentative talk various of constructions and the is I possible certainly structures will governing limit the myself new to physics needed present around a the few Fermi examples scale. 3. that hopefully Supersymmetric are Higgs(es) New theories for the Fermi scale sectors; (ii) the neutrinoa masses new can scale be is generated introduced;matter-antimatter asymmetry; only (iii) (iv) if no the SM new SM particle states does candance; account (v) not are for with provide the added may dark any be to matter dynamics the(vi) (DM) the exception relic to there SM of abun- is generate the or no the Higgs rationale if boson observed problem for itself, remains the no unexplained; SM pattern (viii) particle of the can fermion chargethe drive masses quantization inflation; SM and most gauge mixing likely group requires angles; into an (vii)(ix) a embedding the gravity of bigger is strong symmetry left CP aside. which would unify all the fundamental interactions; and predicts a light CP-evenpectation Higgs values, scalar (tan U PoS(EPS-HEP 2009)008 ]. ], 13 14 (4.1) (3.3) ]. This ]; 9 11 , 10 ]. Christophe GROJEAN 16 oblique parameter. The T ) ) 246 GeV is the SM Higgs 2 4 3 ) = ( ( d v H SO SO u H = ( ]; R soft ]. 8 ) , where 2 Z 15 ( 2 M V λ and it has to be broken anyway. Therefore ) SU EWSB 2 2 + ( × Λ 2 / L ) ) v d ]; SU ], while keeping the EW vacuum (meta)stable [ 2 7 H ( 4 u 12 H , SU ( ] that the most general non-renormalizable interactions 1 11 ⊂ M , λ 11 Y 10 = ) symmetry itself 1 ] or with the addition of extra fields/symmetry/interactions to ( L 6 ) , which is another formulation of the gauge hierarchy problem. U em 2 ) BMSSM ( × 1 W ( L EWSB ) SU U 2 Λ ( SU is expected with a scaling like S is a typical mass scale of the EWSB sector. One way to reduce this contribution is oblique parameter is notoriously more difficult to handle since the only symmetry S EWSB much smaller than Λ v while the LSP can account for DM relic abundance [ more interactions parametrized by higher dimensional terms: the BMSSM [ effective approach offers a model-independent look atthe the lowest SUSY order, it little has hierarchy been problem. shown [ At At the same time, the window for MSSM baryogenesis is extended and more natural [ more scalars: the NMSSM and its friends [ more gauge fields (with new non-decoupled D-terms) [ can be captured by the superpotential: more global symmetry: such that the SUSY Higgses appear as Goldstone bosons [ with no correction to the Kähler potential.ier These Higgs two and interactions a certainly much lighter allow for stop [ an heav- I thank Ben Gripaios for some valuable discussions on this issue. Symmetries of the EWSB sector can help to preserve the tree-level structure of the SM, i.e., In the absence of any direct evidence for SUSY, it is important to keep an eye open on other 2 • • • • to make v.e.v. and a contribution to can help to keepembedding the oblique corrections under control. For instance, it is well-known that the 4. Little Higgs is enough to ensure that the EWSBsituation will of not the generate a contribution tothat the can protect it is the gauge possible alternatives that havea emerged UV in completion the to recentorigin the years, rooted SM not in valid necessarily recent up aiminghas developments to at provided of the a providing string Planck. new laboratory theory to All (branes, address the various AdS/CFT particle models correspondence) physics I which questions [ will now present have an the minimal SUSY model (MSSM): New theories for the Fermi scale “SUSY little problem" hasallowing driven over for the a years heavier ascale Higgs of burst and SUSY of various breaking mediation activity interesting [ in proposals building have concrete emerged, models either with a low PoS(EPS-HEP 2009)008 . ]. ]. H 3 / G 23 21 (4.4) (4.2) (4.3) , Λ ]. 22 19 . In the case H / ] under which, in -channel [ G t 20 Christophe GROJEAN is vanishing. A mass 2 g -parity [ or T 1 H g / -exchange in , switching on some interactions 2 G W Λ . 2 isospin 2 ) ) 2 2 2 ... 2 g L π ) ) ( 2 1 2 5 5 g g ( ( is the coupling of the symmetry breaking 16 ( SU + g ] is precisely to identify the Higgs doublet / SO SU 1 R = , busion, i.e., ) 18 L 2 h 2 ) ) , 1 ( m 5 4 g 5 ( ( Wb 17 appear as Nambu–Godstone bosons associated to + , where SU → ) 0 SO SO H , × H π / ± / L 4 G ⊂ 2 G ) ( π 2 ) ) / L Λ ( 3 4 H 2 ( ( / = 2 π G SU g SO SO Λ 16 L g = 2 h m individually preserves a subset of the global symmetry such that the 2 L is the dynamical scale of the global symmetry breaking or parameter: the embedding H 1 S / G L Λ -parity in SUSY models, the SM particles are even and their partners are odd. Such . R EWSB Λ / v The compatibility of Little Higgs models with experimental data is significantly improved When part of the global symmetry is weakly gauged, the question of alignement of the gauge group with the The idea behind the Little Higgs models [ 3 Each interaction Higgs remains an exact Nambu–Goldstone boson whenever either when the global symmetry involves a custodial symmetry as well as a term for the Higgs boson canonly. be generated At by one-loop, diagrams involving there simultaneouslythe is both cancellation not interactions of such the a SM diagramFermi quadratic that scale: divergences would is gauge be achieved bosons, quadratically by vector-likeSM quarks, divergent. a particles and set Explicitly, by extra of the massive new original scalars, particles globalparticles which around as symmetry. are the dictated These related by new to the particles, the global with symmetries definite of couplings the to theory, SM are perfect goals for the LHC. unbroken global symmetry arises and can give non-trivial constraints on the parameter space of the models [ allows to identify the full Higgsratio doublet as Nambu-Goldstone boson and leads to a naturally small The way to enforce this selection rule is through a “collective breaking" of the global symmetry: There is also interesting physics associatedproduced by to gluon the fusion partner(s) or single-produced of by the top quark which could be pair- that break explicitly the globalGoldstone symmetry bosons will of generate the a order massinteraction of to and the would-be massless Nambu– of the Higgs boson, the topbreak Yukawa interaction explicitly or (part the of) gauge interactionsTherefore, the obtaining themselves global a will Higgs certainly symmetry mass since aroundof 100 they the GeV act would order demand non-linearly of a 1 on strongdynamical TeV, which dynamical the scale scale is Higgs by known at boson to least leadthat one to a order too Higgs of large mass magnitude oblique is requires generated corrections. an at Raising the additional the 2-loop selection strong level rule only to ensure analogy with Little Higgs models would therefore appear in colliders as jets with missing transverse energy [ as a (pseudo) Nambu–GoldstoneBy boson analogy while with keeping QCD somethe sizable where breaking of non-derivative the the interactions. pions chiral symmetry New theories for the Fermi scale Again, enlarging the symmetry ofcontribution the to EWSB the can provide a solution and ensure a naturally small PoS(EPS-HEP 2009)008 ’s ]: W scat- (5.1) (5.4) (5.3) (5.2) 25 . Both 3.1 TeV), . hh scattering WW ≈ 2 s ( ’s as [ v v → π W L ≈ ) number follows WW . v ) W π s L masses, we have  2 ( 2 2 W √ Z v h A 2 Christophe GROJEAN b = 1 defines the SM Higgs + and v h = with . ± a v b 2 / a W bc = π + δ a a 1 σ i ad e  , δ ) ) × = 2 h u
( Σ m 2 Σ s A µ gauge bosons break the gauge symmetry. − 2 s a D + Z ( . The point † . ) and leads to amplitudes that grow with the 2 with 2 and coupled to the longitudinal Σ bd R v a ) µ δ R and 5.1 2
− ) = D ac ( Σ 2 ± 6 b ( δ . ], the non-trivial scattering of the longitudinal µ ) v W ) = SU Tr t D s 24 ( 2 SU † ( 4 × v Σ A L × µ , contribute to this amplitude and the terms growing with ) 1.2 TeV and new strong dynamics will kick in and soften L ) now simply follows for the contact interactions among b + 2 D ) 4 ) + ( Z 2 h cd ( ( δ Tr and SU V scalar exchange ’s, the scalar gives an additional contribution to the 2 SU ab a L 4 v A − δ W ) h = s µ ( under and the gauge boson mass terms correspond to the pions kinetic term ∂ as well as h mass A µ ± L ∂ isospin , to the ) W 1 2 a ) = 2 -model with a breaking scale d L ( linearly σ = W , singlet under c L SU h / W EWSB R ) 1, cancels the leading contact term at high energy. This is not the end of the story yet: L 2 → can be described by the Nambu–Goldstone bosons, or pions, associated to the coset 3, are the usual Pauli matrices): ( , b = L L 2 a Z , W SU , meson of QCD. In any circumstances, by measuring the a 1 L ± × L ρ W = L ( W ) a Defining the breakdown of perturbativity is subject to arbitrary choices: the 1.2 TeV( Supersymmetric models, Little Models and many other models assume that the answer to the The simplest example of new dynamics that can restore perturbative unitarity consists of a 2 generically denotes 4 , A ( a σ W Thanks to this Goldstone boson equivalence [ from requiring that the real partthe of the tree-level partial amplitude waves remains of the biggerassociated iso-amplitudes than to remains a smaller the than non-linear one-loop ½, one while demanding leads that to the more conventional scale, 4 tering amplitude which, for perturbative unitarity should also be maintained in inelastic channels too,the like energy are canceled for the particular choice Via its linear coupling, the linear and quadratic couplings, boson and it can be showndoublet that transforming the scalar resonance and the pions then combine together to form a energy: pressing question of the origin of EWSB is already known: What is unitarizing the single scalar field, New theories for the Fermi scale 5. Strong vs. weak EWSB amplitude? I said earlier that the masses of the ( four pions obtained by expanding the Lagrangian ( In the absence of anyperturbative new unitarity weakly will be coupled lost elementary around degreesthe of UV freedom behavior canceling of this the growth, to amplitude, the for instance viabeen the guaranteed exchange to of find massive new physics boundlongitudinal around states polarizations the at similar Fermi very scale high to energy. ensure the proper decoupling of the ( Actually, in presence of thesedinal masses, the gauge symmetrySU is realized non-linearly: the longitu- PoS(EPS-HEP 2009)008 , 1 2 1. a are = − = 7 2 b a b 2 = is always a = a b are the linear and b Christophe GROJEAN and ) and they satisfy -1 2 a , are seating on an universal 5.3 v 2  : b=2a f ). The particular point 5D ] seats along the curve 5.3 26 ) and therefore the Higgs boson alone composite Higgs: b=4a-3 MCHM dilaton: b=a f ). When the compositeness scale is lowered 6 ) of Ref. [ D 5 that these deviations scale are controlled by the 7 6 a ] states that the only way to fully ensure perturbative unitarity in all has to be resumed and model dependent effects appear. For 28 f SM / v 1 . In the next section, I will discuss in details the collider signatures 5 scattering amplitude. WW ] for a historical perspective, but they have experienced a recent revival ) describes either an elementary Higgs boson or a composite one emerging ] that, under very generic assumptions, in composite Higgs models, 29 1 (I will show in Section 5.3 27 = b 0 = 0 1 a b (Partial) unitarization of scattering amplitudes with a scalar field. A famous theorem due to Cornwall et al. [ Notwithstanding its simplicity, the appeal of the SM Higgs picture comes from its successful Composite Higgs models are examples of models where the breakdown of perturbative unitar- The Lagrangian ( 5 possible elastic and inelastic channelsexplore is here via the the possibility to exchange delay a the Higgs perturbative boson unitarity in breakdown. a spontaneously broken gauge theory. We other examples with delayed perturbative unitarity breakdowntower thanks of to spin a 1 non-trivial dynamics massive particles. ofsee a Both for classes of instance models Ref. where already [ considered in the eighties, and can now be cast in terms of models with warped extra dimensions. 6. Composite Higgs models agreement with EW precision data, provided that the Higgs boson is rather light. To this regards, towards the weak scale, the series in ity is postponed to higher energy Figure 1: quadratic couplings of the scalar to the gauge bosons defined in Eq. ( instance, the minimal composite HiggsIt model was (MCHM shown insmaller Ref. than [ 1. The dilaton couplingstherefore can the also double be dilaton described production by never becomes the Lagrangian strong. ( of these models. The extra dimensional Higgsless models that will be presented in Section ratio of the weak scale over the Higgs compositeness scale, New theories for the Fermi scale as a bound state ofdeviate a from strongly interacting sector. In the latter case, wefails do to expect fully unitarize the the couplings to corresponds to the SM andenergy. Composite neither Higgs the models elastic with a norline rather the large away inelastic compositeness from scale, scattering the amplitudesdominated SM are (this by growing universal a with behavior the single is operator, the as result I of will the show fact in that Section the scattering amplitudes are PoS(EPS-HEP 2009)008 , ; 2 f f π  / . (6.1) 4 2 c . v h ≈ T contains c ρ + H = m R / ˆ T G H f L ¯ f : 6 1, the couplings of H † Christophe GROJEAN → H f ξ 2 y f is the SM Yukawa coupling to y c f y  + scattering amplitudes). Such a 3 ...
). There are two classes of higher , such that the coset f H ) + H † WW H µν B ν ) are expected to be of order one. λ 2 Peskin–Takeuchi parameter, ∂ 6 f ( 6.1 c T  − defines the compositeness scale of the Higgs H 2 f µ  8 , the latter being favored since it is invariant under to a subgroup ←→ D ) H † f , of the heavy resonances and the dynamical scale, 4 µ ( ]) and modern incarnations have been recently inves- ρ H D m  ←→ 30 SO 0 † 2 ρ / g ) H B m , appearing in Eq. ( is the SM Higgs quartic coupling and 5  2 ic ( λ ... 2 T f is parametrically large than T + SO c c i 2 , ρ ) (for maximally strongly coupled sectors, we expect H or m + c µν ) H 2 2 / W 1, the Higgs boson appears essentially as a light elementary particle gives a contribution to the ( ν

G ’s go to zero and unitarity in gauge boson scattering is ensured by the T D L H → c ( SU † W 2 /  ) f H ], and the effective Lagrangian generically takes the form 3 H / ( 31 2 µ µ v ∂ ←→ D i SU = 2 σ H f † ξ c . All the coefficients, 2 , spontaneously broken at a scale H R ,  G L = f g 2 ρ are the SM EW gauge couplings, 0 W m g 2 ic SILH , Some oblique corrections are generated, at tree-level, by theg operators of this effective La- The composite Higgs models offer a nice and continuous interpolation between the SM and At the eve of the LHC operation, I would like to give a description of the physics of such a 6 L + , associated to the coset f the fermion grangian: (i) the operator the custodial symmetry. Attempts toGeorgi construct and composite Kaplan Higgs (see models for in instance 4D Ref. have [ been made by boson: when (and its couplings approach the onessector predicted become by heavier the and SM) heavier while and thethe decouple; other Higgs resonances on of the boson the other to strong hand, the when technicolor type models. The dynamical scale exchange of the heavy resoances. composite Higgs boson rather than presenting the detailsthe of same the way construction of that an we explicit do model.I not In will need rely of on the refinements aninvolves of effective higher QCD Lagrangian dimensional to to describe operators capture the forand the physics a the of relevant unique the low physics. Higgs pions, energy boson This inby degrees the effective two of minimal Lagrangian quantities: freedom case) and (the the the SM typical strong mass sector particles will scale, be broadly parametrized tigated in the framework of 5Dcorrespondence, warped models the where, holographic according composite togauge the Higgs field principles boson along of now the the 5th originates AdS/CFT dimension from with a appropriate boundary component conditions. of a New theories for the Fermi scale being an elementary scalar is nottions. a virtue It but rather thus a tantalizing flawa to especially strongly-interacting when consider sector. facing the radiative In Higgs correc- orderthat boson to a as maintain mass a a gap good composite separates agreement bound theonances with Higgs state that EW resonance emerging will data, from from ultimately the it other is enforce resonances sufficient a of good strong behavior sector (the of res- the a fourth Nambu–Goldstone bosons thatof can such be coset identified are with the Higgs boson. Simple examples here, I will simply assume that dimensional operators: (i) those that arequalitatively genuinely the sensitive physics to of the the new Higgs strongresonances boson only force and and and will will (ii) simply affect those act thatoperators, as are see form sensitive factors. Ref. to [ Simple the rules spectrum control the of size the of these different mass gap can naturally follows fromsymmetry, dynamics if the strongly-interacting sector possesses a global PoS(EPS-HEP 2009)008 ] y = = c 38 and ˆ S , ξ (6.3) (6.2) H c 37 , since their SM hgg ]. Typically, this 32 and ], provide examples Christophe GROJEAN γγ 26 h ), selects the operators , the series has to be re- reports the amount of lu- ) 1 6.1 3 of the Higgs? The contribu- ( 7 , O ) 2 . For the fermions, this universal f ∼ . ) / 2 2 )) 2 f f 2 v f / 2 ) 2 ( 2 2 v ( / / 2 / H v 2 c v H c H + c y − c − ( 9 1 are logarithmically divergent [ − ( 3. ] for a detailed discussion on this subject). 1 T × ( ÷ 34 2 × , ¯ and f ≥ SM hWW gives a correction to the Higgs kinetic term which can be 33 S SM h f g 2 g v H c = / 2 = ) should be viewed as the first terms in an expansion in f parameter is generated by the form factor operators only, ¯ ) does induce some corrections to the Higgs couplings to the SM f S 6.1 ξ hWW ξ h f 6.1 g g shows the modification in the branching ratios for the Higgs decays to 2 . ) is universal for all Higgs couplings and therefore it does not affect the Higgs 5 ( H c ]. SO , and will simply impose a lower bound on the mass of the heavy resonances, 2 ρ 26 m / 2 W m ) 5 TeV. At the loop level, the situation is getting a bit more complicated: as I am going to B . c 2 , and these corrections prevent the nice cancelation occurring in the SM between the Higgs . When departing significantly from the SM limit, 2 2 The effective Lagrangian ( Will the LHC be able to probe these deviations in the couplings The physics of the composite models, as captured by the effective Lagrangian ( The Higgs anomalous couplings affect the decay rates as well as the production cross sections One may worry that because of the modified Yukawa interactions induced by the operator The effective Lagrangian ( + f f 7 ≥ as the most important ones for LHC studies, as opposed to totally model-independent operator analyses [ / / , the mass matrices and the Yukawa interaction matrices are not simultaneously diagonalizable, W ρ y 2 2 c y All the dominant corrections, i.e. thestructure ones of controlled the by SM interactions, the while stronga the operators, different form preserve Lorentz factor the structure. operators Lorentz will also introduce couplings with shift adds up to the modification of the Yukawa interactions: tion of the operator c which often lead to the conclusion that the dominant effects should appear in the vertices is flavor universal (at leastat among the the leading light level fermions) (see however and Refs. no [ Higgs-mediated FCNC is generated of such a resummation, allowingtechnicolor to limit. study Figure the effects of the anomalous Higgs couplings up to the of the Higgs. Therefore, the searchesexclusion for bounds the are Higgs boson modified at asminosity the compared LHC, needed as to for well the discovery as in SM themodels LEP/Tevatron the of case. Ref. most [ Figure promising channels for the minimal composite Higgs contribution occurs only at loop level. c leading to potentially dangerous flavor changing neutral currents (FCNC). Actually, the operator particles. In particular, the operator brought back to its canonical formuniversal at shift the of price the of Higgs a couplings proper by rescaling a of factor the 1 Higgs field inducing an SM particles in therepresentations minimal of composite Higgs model with fermions embedded into fundamental ( m show below, the couplings ofv the Higgs to theand SM the vectors gauge receive boson some contributions correctionsone-loop and of IR contribution the imposes order v New theories for the Fermi scale which would impose a very largemetry compositeness is scale; however, preserved assuming that bycally; the the custodial (ii) sym- strong a sector, contribution to the the coefficient of this operator is vanishing automati- summed. Explicit models, like the ones constructed in 5D warped space [ PoS(EPS-HEP 2009)008 ], 1, and 41 → γ ]. For 1 ξ , τ 40 WW ZZ bb gg γγ , , b 39 0.8 500 GeV [ in many different = h s 0.6 Christophe GROJEAN √ BR 120 GeV (left plot) and ξ × = h h σ 0.4 m for SM fermions embedded into 2 , it is possible to measure Higgs f 1 / 0.2 − 2 v =180 GeV H 500 GeV and an integrated luminosity = m = ξ 0 ], providing a very sensitive probe on the 1 s 0.1 0.01 42 √

0.001

0.0001 Higgs BRs Higgs 0.00001 10 30 TeV. Moreover, a linear collider can test the ex- 1 ∼ ]. f , a peculiarity of a composite Higgs boson is that it fails 25 π 5 0.8 3 TeV [], will improve these sensitivities by a factor 2. =120 GeV = for two benchmark Higgs masses: H 5, the Higgs is fermiophobic, while in the technicolor limit, . s m ) 0 5 √ ( 0.6 = ξ SO ξ scattering amplitudes which have thus a residual growth with energy L that controls the Higgs self interactions, since the triple Higgs coupling 0.4 can reach the percent level [ W 6 L c h W BR bb WW gg ZZ γγ 0.2 × h 7 TeV. σ ]. CLIC running at ÷ Higgs decay branching ratios as a function of 1 44 of order one, this will translate into a sensitivity on the compositeness scale of the Higgs, [ 0.1 0.01

y 1 0.001

c 0.0001 Higgs BRs Higgs − 180 GeV (right plot). For Deviations from the SM predictions of Higgs production and decay rates could be a hint to- Cleaner experimental information can be extracted from ratios between the rates of processes , up to 5 and f = h π H to fully unitarize the and the corresponding interaction becomes strong, eventually violating tree-level unitarity at the wards models with strong dynamics, especiallyHowever, if they no new do light not particles are unambiguouslycharacteristic discovered imply at signals the the of LHC. a existence composite of Higgs a modelIndeed, have as new to already strong be announced found interaction. in in Section the The very most high-energy regime. precisions on with the same Higgs production mechanism,ratios but of different decay decay rates, modes. many In systematicminations measurements uncertainties at of drop the these LHC out. will However, still thenosity be Higgs upgrade, limited coupling like by deter- the statistics, and sLHC. therefore At they a can linear benefit from collider, a like lumi- a ILC operating at fundamental representations of m the Higgs becomes gaugephobic. From Ref. [ branching ratios, but only thethe total decay Higgs width decay and width the atheavy production the Higgs cross bosons, LHC section. well is above The very the measureinterest two difficult of gauge since and boson we it threshold, consider can a the region beHowever, which for Higgs reasonably is a as done not light a of Higgs, only particular LHC pseudo-Goldstone for experimentschannels: boson, rather can production and measure through therefore the gluon, product relatively gauge-boson light. fusion,(virtual) and weak top-strahlung; decay gauge into bosons. At the LHC withc about 300 fb 4 compositeness scale of the Higgs up to 4 of 1 ab can be measured with an accuracy of about 10% for Figure 2: istence of the operator New theories for the Fermi scale production rate times branching ratio in the various channels with 20–40 % precision [ PoS(EPS-HEP 2009)008 ] 0, 35 = (6.4) ]. For SM 26 g . 2 s f ≈ ) s operator prevents ( ]. H A c Christophe GROJEAN 36 in the limit 2 f / with 2 v bc δ ad δ ) u ( A , measuring the amount of compositeness of 2 f + / 2 bd v δ = ac δ 11 ξ , and to all orders in ) 2 t f ( / s A + cd δ ab δ ) s ( A , using the Goldstone equivalence theorem, it is easy to derive the fol- H c ) = d L W c L W → b scattering at high energies. -model is exact. The growth with energy of the amplitudes is strictly valid only up L Luminosity needed for discovery in the most promising channels with the CMS detector [ σ W a L WW W 5, the Higgs boson becomes leptophilic and thus harder to detect. From Ref. [ ( . From the operator 0 A = This result is correct to leading order in the Higgs boson. These contour plots correspond to the minimal composite Higgs models of Ref. [ as a function of the Higgs mass and the parameter, xi Higgs exchange diagrams fromterms accomplishing growing the with exact energy cancellation, instrong present the in amplitudes. the Therefore, SM, although of the the Higgs is light, we obtain when the Figure 3: lowing high-energy limit of the scattering amplitudes for longitudinal gauge bosons New theories for the Fermi scale cutoff scale. Indeed, the extra contribution to the Higgs kinetic term from the PoS(EPS-HEP 2009)008 = h (6.5) m 3000 depends ξ=0 ’s, though ]. ρ ξ=0.5 ξ=1 m W 25 , as estimated 2500 W M 2000 Christophe GROJEAN s [GeV] ]. The rapid falloff of the √ 1500 0). On the left, the inclusive . s 48 2 6= H , f 2 c f TT LL LT 47 1000 / -channels. From Ref. [ → → → = 2 u v LL LL TT LT
. The behaviour above = hh ρ -3/4 < t/s < -1/4 500 ξ - and m t → 6 5 4 3 7 ) are exactly proportional to the scattering − 10 10 10 10 10 L x x x x x

1 1 1 1 1

squared mass) is shown. The right plot presents

6.4

tot tot W gauge bosons. Thus, a generic prediction is σ

) [fb] ) W W W (W

→ in the

+ + + + t-cut + . L W Z Z 4 , W 25. Within the SM, the scattering cross section of the . 12 W 0 A − 3000 ξ=0 = < ξ=0.5
s / t ξ=1 hh ], but the inelastic channel dominate and strong coupling is 2500 < 45 → 75 0 L . of the order of the . Z 0 v 2000 u 0 L − Z partonic cross section as a function of the center of mass energy for ], as illustrated in Fig. and + s [GeV] t A √ 1500 25 0) and for composite Higgs models ( W . Notice that the amplitudes ( f + = π W ξ 4 TT LT LL 1000 → → → → ∼ LL LL TT LT + W + 500 W ]. The most promising channels correspond to purely leptonic decays of the 6 5 7 10 10 10

x x x

46

1 1 1

tot

σ

(W ) [fb] ) W W W →

+ + + + Will the LHC be able to measure the growth of these scattering amplitudes? Contrary to a In composite Higgs models, another direct probe of the strong dynamics at the origin of EWSB luminosity inside the proton and the numerous SM background that can fake the signal certainly , and not the weak scale itself, f Therefore a significant enhancement over the (negligible) SM rate for the production of two Higgs make the measurement harder, but,the as strong scattering a is matter delayed of totransverse higher fact, energies polarizations already due [ to at a the large partonic pollution from level, the the scattering onset of the of amplitudes obtained in a Higgsless SM, the growth being controlled by the strong coupling scale, naive belief, It is anosity notoriously [ difficult measurement which requires some large integrated lumi- is the cross section for theNambu–Goldstone double boson Higgs and production. its Indeed, properties theGoldstones, are Higgs corresponding directly boson related to appears to as the those a longitudinal of pseudo the other exact (eaten) 180 GeV for the SM ( reached at a scale semileptonic decay channels have also been considered recently [ that the strong gaugeamplitudes boson for scattering double Higgs is production accompanied grow with by the strong center-of-mass energy production as of Higgs pairs.The Figure 4: the hard cross section withlongitudinal a polarizations cut is over-dominated by theof one strong of scattering the in transverse composite polarizations. Higgs Therefore models the is onset delayed to energies much higher than New theories for the Fermi scale cross section (with a cut on by NDA. The enhancementCoulomb of terms the for amplitude the exchange for of the the photon transverse and polarization the is due to the structure of the to the maximum energy of our effective theory, namely on the specific model realization.by Kaluza–Klein In modes 5D exchange [ models, the growth of the elastic amplitude is softened W PoS(EPS-HEP 2009)008 : ): − W 6.1 WW (7.2) (7.1) + will be W 1 − . In order for W vanishes via the ) 2 ( Christophe GROJEAN A of integrated luminosity. ... 1 14 TeV with 300 fb ) and allows to test its relation − + = ) 0 s ( 5.3 ] has shown that the best channel √ A 25 + 2 , 2 ⊥  p 8. With an upgrade of the LHC luminosity E . M − 0  2 3 ) = p ~ denotes the momentum along the usual 3 spatial 2 ( 2 3 − f 13 p ~ A 2 / 2 of the Lagrangian ( E + v b 4 =  2 m E M . A Monte-Carlo simulation with simple kinematic cuts con- 2 . The final states are undeniably more complicated than in the  f j ) 4 / 4 ( 2 T v  A E H c ± = l 2 , simply appears as a mass from the 4D point of view. And the mass − ⊥ l − A p , as predicted by the structure of the higher dimension operators ( + 1 l a discovery can be reached with less than 1 ab = → σ b , is the momentum along the extra dimension): ) , along with two forward jets associated with the two primary partons that ra- 2 pair, is expected. An explorative analysis [ is automatically vanishing due to gauge invariance, while T ⊥ f p W j j ) L p 2 4 4 ( ( W / L 2 → A W v ] that the signal significance at the LHC operating at H c 25 hh j j − In conclusion, in the plausible situation that the LHC sees a Higgs boson and no other direct In composite models, when the compositeness scale gets close to the weak scale, the Higgs 1 → = pp exchange of the physicalscattering Higgs amplitudes boson. follows from the Inthis exchange unitarization 5D of to all Higgsless actually the models, happen, KK the the excitations couplings of unitarization and the of the the masses of the KK excitations have to In the SM, for discovery involves 3 leptons in the final states, with both Higgs bosons decaying to to the linear coupling, diated the cludes [ New theories for the Fermi scale bosons at high a limited to about 2.5 standard(sLHC deviations program), for a 5 problem reduces to a problemgenerate of a quantum transverse momentum mechanics for in the a appropriatearises: box: particles. is Nonetheless, it suitable an better boundary immediate to conditions question generateing will a mass transverse for momentum the than gauge to field? introducescattering In by other amplitude hand words, of a how a symmetry is massive unitarity break- Kaluza–Klein restored? (KK)the In gauge fourth full field and generality, would the the have second elastic terms powers that of grow the with energy evidence of new physics, it willand not tell be for immediate sure to if determine itinteracting the is sector. true an In nature elementary that of particle or situation, this a a Higgsbe composite boson physics easily bound case made. state for emerging a from linear a collider strongly together with the sLHC can 7. 5D Higgsless models boson effectively decouples. This Higgslessoffers limit a new is point easily of reached view on inary the 5D mass conditions dimensional problem. (rather setups In than a and sense,relation by the between EWSB a the itself mass Higgs is and achieved vacuum the via momentum bound- expectation ( value). According to the Einstein’s analyses of gauge boson scattering andHiggs come production does with not smaller suffer branching from pollution ratios,that from but the gives at transverse access least modes to and the it the double it quadratic the only coupling process a transverse momentum, dimension and PoS(EPS-HEP 2009)008 ) Y ]. ) ) 1 ( 1 58 ]). Z ( (7.4) (7.3) , M U 60 2 57 g denote the × ( ) L / n ) ( 2 2 W Z ( and their KK M 4 Z paremeter is too and SU , π S X W Christophe GROJEAN below 1 TeV and with ’s and 0 channel and similar sum rules ] and references therein), which W Z ± . 55 ) ]. Furthermore, delocalizing n W ( ± 2 Z 59 ) W and a n M ( ) symmetry that is implemented as . 0 n ( → 0 ) ] around the scale 4 W ± 2 2 WWZ ( ≡ W g 51 2 WWZ ± , T g n SU ∑ W , n 50 ∑ + 3 15 . 1 + 2 Z 2 WWZ ∼ g M 14 R parameter will vanish. However, some doubts about + / S 0 γ is the cubic coupling between two R 2 WWZ π g 6 2 WW 3 ) correspond to the g log WWX 2 = 7.3 g = g dimension. gauge symmetry. The way the proper symmetry breaking is 2 W th L ≡ M ]: − S B ] ] ) 49 [ 1 2 WWWW 54 56 ( g 8 on the IR brane, which, according to the AdS/CFT principles, appears , U 2 WWWW D g 55 ) self-coupling, × 4 2 ( R W gauge coupling). Thus, we can see that for this scale to be substantially ) , by breaking the bulk gauge group down to the SM group can be tuned away by delocalizing the (light) fermions in the bulk [ 2 ) 5 SU ( S . The two sum rules ( , which (i) automatically ensures a mass gap between the 2 channels. ( 9 parameter is protected by the built-in custodial symmetry, the Z to ] SU R T SU WZ 52 ) × 2 L ( ) is the quartic 2 ( SU ? Not exactly since, as the energy grows, more and more inelastic channels open up and 5 × SU L 2 WWWW ) Alternatively, deconstruction versions have been proposed (see for instance Ref. [ In the SM, the physical Higgs boson is instrumental in bringing the theory is good agreement g For a concrete implementation of the Higgsless idea, one can conveniently use a warped ex- Is this KK unitarization a counter example of the theorem by Cornwall et al. mentioned in 2 9 8 ( is the usual g will apply to other Thus, while the large. Nonetheless, as a spontaneous breaking of the effective theory. with EW data. In the 5D Higgslessobservables model are described given above, by the [ first corrections to the EW precision achieved is, see Fig. the radiative stability of this delocalization setup have been raised [ a bulk on the UV brane, thus ensuring thatsymmetry the among additional the gauge KK symmetry states. only The manifestsSU electroweak itself symmetry as breaking a global is then achieved by breaking For a particular profile ofgauge the boson fermion KK excitations wavefunctions, and the the fermions resulting will almost decouple from the KK excitations of the extend the pioneering BESS model [ ( above the usual unitarity violationKK scale resonance to of be the as SM light without as a possible. Higgs, one The needs existence to of have a the first excitations and (ii) is instrumental to enforce a custodial the fermions in the bulk alsothe precludes model a has nice to dynamical be origin supplemented with of an the additional fermion flavor mass structure hierarchy (see and for instance Ref. [ they ultimately saturate the perturbative unitarity bound [ tra dimension [ New theories for the Fermi scale obey the following sum rules significant cubic couplings to the SM gauge bosons is a robust prediction of Higgsless models. Section The effective couplings among the KKand states it are is dictated easy by tobreaking the show that gauge of the structure gauge two of sum invariance, the rulesconditions 5D i.e., at are theory if the automatically end the satisfied, points provided 5D of there the gauge is 5 fields no hard obey Dirichlet or Neumann boundary PoS(EPS-HEP 2009)008 .  2 dz ] studied is the AdS − and some ν R 67 . , 0 dx R µ 66 = dx z ) = 0 =0 µν Ra µ η Christophe GROJEAN Ra µ A  A L 2 5 R =0 ) g 5 z µ g ]. The model considers a 5D + / B − 5 R ∂ 52 La µ La µ A = ( A R ], by allowing a Higgs vacuum 5 L 2 5 g ( g 5 61 via vector boson fusion. The most ds quantum numbers, (ii) some slight ∂ Z Z , W and the ] or by introducing new fermionic states with W 62 15 the absence of proof is not the proof of the absence ) = 0 =0 3 3 R µ R µ A and the IR brane (also called the TeV brane) is located at =0 5 A =0 g R R 5 ± La µ coupling. The large top mass requires both the left-handed and right- +˜ g R µ = A µ of luminosity will be necessary for the discovery of the resonances in the 5 L − z A ∂ B ¯ b 1 µ R ]. L 5 − B 5 g ( ˜ g 64 5 Zb , ∂ ]). Fortunately, Higgsless models are characterized by other distinctive features, ] included also the more model-dependent possibility of Drell–Yan production. At 63 65 68 The symmetry-breaking structure of the warped Higgsless model [ The most distinctive feature of the Higgsless models is, of course, the absence of a physical The SM has emerged as a successful description, at the quantum level, of the interactions The remaining problem with precision EW data is the compatibility of a large top quark mass curvature scale. In conformal coordinates, the AdS metric is given by handed top quarks to havehanded a top profile (and thus which the is left-handed bottom) localizedof are the toward too bottom close the will to IR be the too IR brane. different brane,by from then However, the separating the if down gauge the and the couplings strange physics left- quarks. whichexpectation This generates value problem the may to be extend top avoided slightly quark into mass the [ bulk [ deviations in the universality of thedeviations light in fermion the couplings gauge to boson the self-interactions SMthe compared gauge production with bosons of the and the SM. (iii) lightest References some KK [ excitations of the scalar state in the spectrum. Yet, such as (i) the presence of spin-1 KK resonances with the the LHC, about 10 fb exotic charges [ 700 GeV mass range.for A some precise deviations measurement in of the theCLIC. SM couplings couplings of will these require resonances a or more the precise search machine, such as8. an ILC Conclusion or with the observed gauge theory in a fixed gravitationalPlanck anti-de-Sitter brane) is (AdS) located background. at The UV brane (sometimes called the other models exist ininstance which Ref. the [ Higgs is unobservable at the LHC (for a recent review, see for recent study [ Figure 5: New theories for the Fermi scale PoS(EPS-HEP 2009)008 (2006) 052 (2003) 61 0608 Christophe GROJEAN 565 (2008) 1. (2004) 008 [arXiv:hep-ph/0310137]. 667 (2006) 19 [arXiv:hep-ph/0606105]. 0401 16 757 [Particle Data Group], Phys. Lett. B [LEP Working Group for Higgs boson searches], Phys. Lett. B et al. et al. gauge bosons. But they also need new dynamics to act as a UV moderator and ensure Z [arXiv:hep-ph/0604147]. [arXiv:hep-ex/0306033]. The LHC is prepared to discover the Higgs boson or whatever replaces it. To this end, the Finally, it should not be forgotten that the LHC will be a top and a top-quark machine. And It is pleasure to thank my various collaborators, especially C. Csáki and J. Terning for fruitful and the ± [5] G. F. Giudice and R. Rattazzi,[6] Nucl. Phys. B J. A. Casas, J. R. Espinosa and I. Hidalgo, JHEP [3] A. Hoecker, these conference proceedings, arXiv:0909.0961[4] [hep-ph]. S. Heinemeyer, W. Hollik, D. Stockinger, A. M. Weber and G. Weiglein, JHEP [2] C. Amsler [1] R. Barate collaboration between experimentalists andfor theorists instance, is that more no importantsignature-motivated unexpected than approaches physics ever like is ’unparticles’, to missed ’hidden make becauseaged. valleys’ sure, of or triggers ’quirks’ and should cuts. be encour- In this regards, there are many reasons totriggering believe the that electroweak the symmetry topawaited breaking. quark to can disentangle More be what an may thanHow is important be ever, electroweak agent the symmetry experimental broken? in most data the pressing are dynamics question eagerly faced by particle physicsAcknowledgements today: works on Higgsless projects andthe G. effective Giudice, description A. of Pomarol compositeis and Higgs based R. models. on Rattazzi A two for lot on-going ourwith of projects construction J.R. material with of Espinosa presented R. and during M. Contino, thissupport. Mühlleitner M. talk and Moretti, I these F. also words Piccinini thank areHEPP and the to division R. tell organizers for Rattazzi them inviting of and me all the tothe my EPS-HEPP’09 present ‘MassTeV’ gratitude ERC conference this for advanced review and their grant talk. the 226371. 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