PoS(HEP2005)399 http://pos.sissa.it/ eaking cs e Commons Attribution-NonCommercial-ShareAlike Licence. † ∗ riccardo.rattazzi@.ch Speaker. On leave from INFN, Sezione di Pisa, Italy. I review recent theoretical work on electroweak symmetry br ∗ † Copyright owned by the author(s) under the terms of the Creativ c International Europhysics Conference on High Energy Physi July 21st - 27th 2005 Lisboa, Portugal

Riccardo Rattazzi Physics Beyond the CERN, Switzerland E-mail: PoS(HEP2005)399 (2.1) rigin of eletroweak LEP paradox, approximation ’. g to be desired. An appropriate Whatever more electromagnetic hy problem, and paradox. Indeed, lays a remarkable lk I will illustrate mental parameters, e as (or bigger than) cerning for instance when regarded from uccessfully tested at of human endeavour: ill emerge that, while borings’ that came up lk. In the second part I C, and forming what is t, because the hierarchy s, suggested that the SM we must now understand for tuning on models with ches, a radically different involves the use of variants , which is related to the physical mass , barring unwarranted cancellations, it 2 H . m NP . (This way of estimating the size of the Λ 2 NP NP Λ Λ 2 2 t π λ 8 3 2 ∼− 219GeV. On the other hand, the SM suffers from the 2 H < m h δ m .). The leading quantum correction is then expected to come from the top 0 π 2 m − + 2 π , is affected by uncalculable cut-off dependent quantum corrections. m 2 H m 2 agreement with the SM for a relatively light Higgs. More precisely, a global − ) 3 = − 2 h The large set of data collected in electron–positron collision at LEP/SLC disp I have been assigned this broad title but my talk will be mostly concerned with the o There are two different sides from which to regard the legacy of LEP/SL m 10 ( also known as the LEP paradox [1].the From Standard one side Model it is (SM) anthe impressive is triumph per-mille a precision. complete theory Thatare of essential means fundamental in that processes the smallthe s comparison quantum other between corrections side, theory to and this theproblem, experiment. great Born which success inspired However, theoretical becomes speculations ashould for huge the be last conceptual overthrown three right bafflemen decade atwhy. the I will weak discuss scale. the paradoxical Thatwill LEP/SLC attempt legacy did in to not the give happen, first an part overview so on of on my the the ta new phenomenological ideas side, that were andthe stimulated use partly partly of by by extra-dimensions field the and theorypotentially branes) realistic developments on and (con certainly the very theoretical ingenious, side. theseIn attempts fact I still it leave think somethin may it even w because be of fair to the say increasing that senseapproach these of to models the frustration concretely hierarchy with embody problem the theof has standard LEP recently the approa been anthropic advocated. principle That such to as explain the the cosmological puzzling constanthow values or anthropic considerations the of can Higgs apparently explain mass. the funda puzzlinglow In need, energy after the . LEP2, third part of my ta 2. The legacy of LEP/SLC O fundamental theory replaces the SM above some scale also by analogy withcontribution well-known to quantities in low energy physics, such as the Higgs mass is made reasonable by many explict examples that solve the hierarc fit [2] gives with 95% CL the bound is reasonable to expect the Higgsthe mass SM parameter to contribution be computed at with least a of the cut-off same scale siz Physics Beyond the Standard Model 1. Introduction sector and is estimated to be the electroweak scale. I will attemptafter to the give an end overview of of the the theoreticalsubtitle LEP ‘la for era my and talk in could preparation thus to be the ‘Electroweak Symmetry commissioning Breaking of after the LEP/SLC LHC. by : the Lagrangian Higgs mass parameter PoS(HEP2005)399 ible , the (2.3) (2.2) (2.5) (2.4) (2.6) ) 6. The 1 ( = O only if the d ∼ 2 h various mass i m c Riccardo Rattazzi e center of mass al operators, with fects. In this case s and Dark Matter ion is high enough than their center of . Now, the question tric particles identi- n to the Higgs mass ε e same time does not g else at or below the id LEP/SLC not detect roup (RG) logarithms. n this lower bound and √ ere, in addition to elec- 6 TeV we need to tune . m the above we deduce / tation of these results is st dimension, hich case

= ... tly mild problem. But notice ... NP + Λ + ˜ t H I m . Planck τ † M H ..., ln GeV µν ˜ 2 t ) can in general be parametrized by adding + ... B ˜ m 2 t , so that for 2 t NP I [3]: m µν ∼ h λ ) NP Λ 2 W µ 1 m NP Λ 2 ( 3 π c Λ 2 ∼ O 200GeV 3 , + ˜ t ( + + 2 -parity, arguably the leading candidate New Physics m ) 200 GeV. In view of this problem, things would look 2 2 × R e µ µ ∼ µ = 2 2 γ ¯ 600 Z e H − , neglecting the effects of all the others and normalizing ( i m m 1 < O c ∼ − = 6 operators have been studied in ref. [4]. The lower bound  then the bound is relaxed by a factor 1 NP 2 H = ε Λ m 2 NP 1 d 2 Λ = ∼− NP 2 Z grows quadratically with e f f m ε L 600 TeV would not lead to any tension with electroweak precision tests. It is < NP Λ . However the attraction of Supersymmetry largely lies in its giving a very plaus NP and Λ π for each individual operator 4 / 1, ranges between 2 and 10 TeV. Turning several coefficients on at th NP α = Λ | ∼ i i c definitely better if New Physicsc affected low energy quantities only via loop ef If we allow a fine-tuning of order where we have not displayed thethat normally the less natural relevant expectation contributions. isvector Fro to boson have scale the stop, the charginos and everythin to the SM renormalizable Lagrangian thecoefficients whole suppressed tower by of the higher suitable dimensional powers of loc to 1 part in a hundred in order to have is: if the energy range of validityany of the deviation SM from is as the low as SMenergy 500–1000TeV, predictions why of d in these their experiments rich isto set significantly make of lower them data? than sensitive to 1TeV, new Evenmass still virtual though energy. their effects The th associated precis effects to from a new physics much at higher a scale scale constraints on the whole set of Physics Beyond the Standard Model In the absence of tuning, this contribution is compatible with the allowed range of at first reassuring that Supersymmetry with At leading order it is also sufficient to consider only the operators of lowe scenario, precisely enjoys thisfied property, with with the mass scale of supersymme cut-off is rather low picture for physics way above thetroweak weak scale symmetry and breaking up (EWSB), to the alsofit Planck Gauge very scale well. Unification, wh neutrino In masse thisparameter is extrapolation, not however, the eq. (2.1) leadingIn but quantum the the contributio larger Minimal one Supersymmetric associated Standard toparameters Model is renormalization then (MSSM) g roughly the relation between the | on generic lower bound on the neweq. threshold (2.2) is defines a what few is TeV. The known as tensionthat the betwee the LEP paradox. needed This tuning is an apparen qualitatively change the result, unlessthat parameters if are New tuned. Physics The affects interpre electroweak observables at tree level, for w PoS(HEP2005)399 0 = (2.7) 500– i 6 N , due to > ∼ h ˜ t , by adding n for New i m 1 % accuracy simplest sce- H al mass of the h , at the per mille Riccardo Rattazzi i Perhaps not, but 2 sitive contribution lysis shows [5, 6], H ften heard criticism problem is ‘robust’, ort in the context of h st in the MSSM, the can exceed its direct the stop mass by the sion is that in several ture of the soft terms. radiative correction to t of fine tuning can in Physics h weaker and thus giving m l models. These are the h in the MSSM is, strictly his did not happen, and so omaly mediation, the soft to the Z-boson is a factor m h ghly bigger tuning than the 1–5% m h . and a still sizeable stop contribution t mixing. This is because the sizeable h m R / m ˜ t ˜ t – m L ˜ t ln 2 2 t 1 (which always entails some tuning), the mass π λ 2 3 ≫ 4 2 t β m 4 GeV. However, this generically requires . This allows a relaxation of the lower bound on the . + 2 2 Z H 1 m ≤ NH 2 h m tuned somewhat close to H m 4 GeV. This is because the coupling of . to the model, thus upgrading the theory to the so-called NMSSM. In the N there is an additional positive contribution to the right-hand side of eq. (2.7) N smaller than the one in the SM. In some regions of the supersymmetric parameter ) α − While the problem is ‘robust’ within the MSSM, it can be somewhat relaxed just I now want to illustrate the impact of electron–positron data by focusing on the In the end, should we really worry about tuning at the few per cent level? β ( -terms that are needed for that to happen require some tuning too. Another o the impression that thethe need parameter space for region where tuning this happens isestimated corresponds above. relaxed. to This an is even because However one needs as tan a direct ana space this suppression can become significative, making the bound on The second term on thethe right-hand side Higgs corresponds quartic to coupling. the leading It top/stop is then only thanks to this correction that to the Higgs quartic coupling. Physics Beyond the Standard Model The above relation raised great hopesupersymmetry of can new no discoveries longer at be LEP/SLC.situation viewed T as is completely made natural. even worse Inlower by fact, bound the at on indirect, lea the and lightest stronger,lightest Higgs bound Higgs mass. placed has an As on upper is bound, well which know, in in 1-loop the accuracy MSSM reads the rou physic presence of a single superfield experimental (95% CL) lower bound of 114 sin the superpotential trilinear coupling of the second CP-even Higgs rather hard to obtain, thatthe is NMSSM to is say perhaps very desirable. tuned. Some extra model building eff A we should keep in mindPhysics that at once the we LHC are becomeslevel, willing the weaker. to sparticles accept are Notice out some indeed of tuning, reach that, the at already the motivatio 2.1 with LHC. a Technical parenthesis: tuning LEP1 & LEP2 bounds on New Electroweak nario for New Physics in the electroweak sector, the so-called universa 1000 GeV, which when comparedis to needed. eq. Although (2.5) the implies descriptionin that we the a give sense here cancellation is that with somewhat it 1In schematic, does to particular the not 5 things depend are in notto any dramatically the significant right-hand improved way by side on of considering the eq. full the (2.7) struc extra that po arises for large stop mass. A detailedgeneral analysis, be described relaxed in to ref. about [7],attractive 10%. shows scenarios that This for the is supersymmetry amoun encouraging,terms breaking, although have such such my a as impres structure gauge as or to an make the desired electroweak vacuum with to the above simple argument concerns the fact that the bound on speaking, lower than 114 PoS(HEP2005)399 . It (2.8) (2.9) 2 NP Λ / 2 L q , we are left ) Z − ss [9], showing and retain only m Riccardo Rattazzi , cts at around the ssify the vacuum 2 deed have a more o encompasses the q e Taylor expansion and in der term in a given gs and vector fields EM ing the third-family in the 90’s. However, α r custodial symmetry s at LEP2, let me start g. However, since the 2 NP , rinstein and Wise [10], erimental control) only − − + + + + + F Λ tant aspects were always gh vector boson vacuum in full generality, as we / actically’, since the more G 2 ( i to our criterion the quantity µ ′ 3 H h W gg ) µ / 2 B q ) µν ( 2 2 2 B ′ q 33 g ( g 2 a µν Π 2 / so that it can always be safely neglected. µ BB 2 / as a power series in 2 3 W | 1. According to this criterion, and after 2 ) ) ˆ Π T ) ) W H 2 µ H a µν ≪ µ the symmetries they respect or break. We a q µν B + ≪ ( τ W D B ˆ † µ ρ † T 2 NP − Π + ρ + H D ∂ Λ 2 H W 6 effective Lagrangian for the Higgs and gauge is somewhat above the energy of LEP2. It then 2 NP µ | 5 / m W or Λ B ) 2 Z = ) 2 NP = ( = ( = ( = 2 ∼ + M q d Λ q ( ( H − BB B WB O (the two relevant symmetries of the problem). Within any WW + 3 O O L O Π Π ) µ µ )) 3 + 2 ( 0 W W ( − SU + = + Π NP is expected to be − ) )  ) 0 L 0 ) ( 0 ( 0 ) ( ( ′′ BB 0 ′′ 33 33 ( − Π B Π ′ + Π ′ 3 2 W ( 2 W Π M 2 Π 2 M 2 2 W 2 2 ′ 2 g − g M g g ) 0 = = = = ( b ′ 33 S b Adimensional form factors Operators Custodial SU(2) T Y W Π 2 g . This is because, barring accidental cancellations that make the lowest-or The electroweak constraints on universal models were widely discussed 2 pole that are smaller by at least a factor = q 0 reabsorbing the trivial redefinition of the electroweak input parameters follows, however, from our discussiondid not that assume they we are could expandgeneric the in strongly leading the coupled Higgs effects Higgsless field, scenario. and We our stress that parametrization according als fields. They are thus the leading terms in a double expansion in makes sense to expand the vacuum polarizations have also indicated the lowest dimension effective operator involving the Hig associated to each form factor.the As 4 was leading already form pointed out factors long parametrize ago the by G the leading terms. Inpolarizations order to in decide eq. which (2.8) termsand according are under to the leading, electroweak their it group is transformation useful properties to unde cla class anomalously small, the higher-orderZ terms in the same class will give effe Most Technicolor, Little Higgs and Higgslessthat models it practically is belong not to an this obviouslyrealistic cla idle versions exercise of to focus these onfermions, models universality. and almost I associated say always to ‘pr the display largemajority extra value of effects of the involv the observables top quark (andinvolve the Yukawa arguably couplin fermions those of that the are firstgeneral two under relevance. families, better the exp bounds on universal models in in given symmetry class is then natural to retain only the term of lowest order in th as I will now show, and aseither it missed was or recently not discussed emphasized. in ref. Consistentby [9], with some the assuming impor absence that of new the particle scale of new physics where we have indicated respectively with Physics Beyond the Standard Model models where deviations from the SMpolarizations appear, [8] at leading order, only throu with 4 leading form factors U PoS(HEP2005)399 and since Y (2.11) (2.10) (2.12) ot suf- W ls where and tly consistent cenario where Y 6 8 8 at the per-mille It is interesting . . . Riccardo Rattazzi o popular for so 0 0 0 are equivalent to a W ± ± ± 3 . Other low energy ’s of ref.[12] as 3 4 2 W . . . ε n compositeness or as 10 W vide extra independent 0 0 0 − − − nds from the global (ba- and m a consistent analysis of and 6 2 2 Y . . . would indeed be constrained 1% at LEP1) is compensated 0 1 1 Y . Y 3 ughly: the SM can parametrize Y ± ± ± U , 10 0 1 0 ing them one by one or all together, W . . . T θ , (they involve more derivatives). 2 S b 6 — — 6 0 9 0 0 0 . T . . . . tan 0 0 0 1 b Y T 3 , expressed via the − ± ± ± ± and ) Higgs. − ) 7 1 1 0 10 b S . . . . : W W ) − 3 2 5 0 3 0 − current W at LEP2. These mostly constrain . . . | , ˆ ˆ ¯ 1 0 1 T S f W Y 800GeV W 6 b S , f θ 3 ± ± ± + − + b = T 2 — 2 9 0 0 , h . . . 10 → b S 0 0 0 SM SM SM 1 2 3 sin ( ¯ e ε ε ε , − e W = = = m , 1 2 3 Z ε ε ε m | δρ ( plus vertex corrections and plus four-fermion contact interactions. Two ) and with a heavy (m b T , is indeed a known property of technicolor models [11]. The quantities b Type of fit S U 115GeV pole tests correspond to the measurement of just 3 quantities, and are thus n = One-by-one (light Higgs) All together (light Higgs) One-by-one (heavy Higgs) All together (heavy Higgs) h 0 Z pole. Corrections to Global fit (excluding NuTeV) of dominant form factors includ 0 is the relevant set: it is either redundant or insufficient. pole data: Is this the psychological reason why this inconsistent set was s their effect grows faster with energy than that of Z 0 Because of the ‘uncomputability’ of the Higgs potential, the SM, while a perfec Notice that by the equations of motion the operators associated to U , Z 2. Cross-sections and asymmetries in 1. are also small in the simplest technicolor models, but they can be important in mode T , observables, such as atomic parity violationconstraints, and Moeller but scattering, they also pro are weakersically than LEP1/SLC those + provided LEP2) by fitlevel. LEP2. is The shown message The in should bou the then table: benew clear: electroweak all physics. LEP2 4 data quantities are are crucial bounded to perfor 3. `New' ideas on electroweak symmetry breaking theory, does not give a satisfactory explanation of EWSB. Perhaps ro by the higher center of mass energy, which enhances the effect of ficient to constrain the general set! (As is well known, the set Notice that by long?). Fortunately LEP2 datathat the allow somewhat us lower precision to of fully LEP2 (about and 1% strongly versus about constrain 0 the set. Physics Beyond the Standard Model Table 1: with a light (m The negligibility of there is new structure in thein pure gauge Little sector, Higgs as models. in models OnS with the vector other boso hand there exists, as expected, no motivated s given combination of classes of observables are then affected by W PoS(HEP2005)399 , × NP L . It ) 5 (3.1) Λ 2 A ( should ∼ basically H explicitly should be SU interaction H H 2 H . We can try represent the EM ogress neces- H on associated m d that a gauge illustrate some is construction 0 h of fermionic α its benefits, and en at some level rgon) [13]. The Riccardo Rattazzi π aps less popular 2 QCD therefore inherits , mall pion masses. id the appearance s that Λ + lf-coupling. In fact symmetry is surely and imensional Lorentz H s that vergence is replaced π q m ≪ , with respect to m g this is by introducing ns H ne symmetry explicitly. xtra space dimension, in m 2 QCD is mass degenerate with a is in lowest approximation l symmetry group Λ . H H π EM 4 α 2 Strong Λ  ... + . The quark masses 2 j I this is just eq. (2.1), and we are back to the . In order for this to work the Higgs ) ) α µ π i 2 , we generically expect, in analogy with QCD, . In particular it forbids a Higgs mass term, but 4 A ( α 7 ( µ H . Among several others, the top Yukawa interaction i j Strong A µ SU c 2 ∂ Λ Strong under the symmetry, which forbids any m + Λ ∼ Strong c i π Λ → α + . Consider indeed the expression for the mass of a Higgs 4 NP i 2 H Λ c H m  QCD → Λ = H 2 H and m t α forbids a mass term → α within the same Higgs supermultiplet. The Higgs mass µ EM ∂ receives an electromagnetic correction of order H α + . Since in this case = Ψ π 2 can be associated to the vector polarization along the new dimension: µ m A H 2 Strong δ Λ down to the diagonal isospin group t π α 4 R ) The LEP paradox is overcome if we can construct a theory where 2 ∼ ( 2 H be part of a vectorinvariance. multiplet, However, which the at conflict first iswhich glance solved case if conflicts there with exists ordinary (at 4-d least) one e pseudo-Goldstone boson, to all order in the coupling constants is amusing that alsotype. supersymmetry can Finally another, be perhaps viewed simpler, as possibility an is that extra the dimension, Higgs thoug m LEP paradox. Theof Little the Higgs lowest [14] order is contribution precisely to a clever construction to avo (as it does notThen, involve derivatives replacing of the Higgs field) breaks the Goldsto is much smaller than eq. (2.1)by suggests. making The the Little Higgs Higgs aninspiration (LH) approximate idea for Goldstone is that boson to comes (a achieve from th pseudo-Goldstone low in energy ja hadron physics, where the pio and think of an extensionto of some the new SM strong dynamics where at the a Higgs scale is a composite Goldstone bos break chiral symmetry by aIn small particular amount, thus giving rise to the physical but s Goldstone bosons associated to the spontaneous breakdown of the chira protected from ultraviolet corrections. Theextra only symmetries. way we There know are ofthe various achievin most possibilities, widely by explored now one. well known. By Super supersymmetry the Physics Beyond the Standard Model EWSB but cannot explain it.sarily Sticking involves to computational theories control with of the an Higgs elementary mass Higgs parameter. field, That pr mean the Goldstone boson of a spontaneously broken global symmetry. This mean SU also, which is less exciting,this the is standard a Yukawa more interactions general and problem: thein all Higgs order the se symmetries to I give mentioned rise above toalso must avoiding realistic be the brok models. LEP paradox, Breaking is theof the symmetry these main while model challenge preserving building in efforts. model building. I will now 3.1 The Little Higgs model Higgs fermion transforms by a constant shift by supersymmetry the good UV property ofby the a fermion mass: mild the logarithmic quadraticbut one, di interesting, and possibility the is to hierarchysymmetry promote problem the is Higgs solved. to a gauge Another, field. perh We know indee that does not involve at least one derivative PoS(HEP2005)399 is loc (3.3) (3.2) . The H ) reaking 1 ( U pontaneous . gauge group ) × of same spin is extended to 5 ) (product group ( L 3 naturally have a ) Riccardo Rattazzi ( ks the rotational b broken down to a . Only a subgroup SO , mmetry group and . For instance one t weak ) SU ( glo glo = 3 are controlled by the G s mass, these partners ( is to cancel the 1-loop H G f achieving that define (this is in analogy with / glo to H blet f SU H Z glo ,... i j G mmetry is partially restored c , and i transforms as a triplet of some ) 10TeV, the partners then have c 5 Littlest Higgs, have gauge group L ( ∼ χ ) , 5 2 ( SU and neutral f and the weak scale. Normally 2 = ± SO Strong . H singlet; in the right-handed sector, along g 0 and / Λ L W ) glo ) = = 5 Strong 2 i ( G . In order to realize this structure, the field ( 2 Strong c Λ . The field Y ′ Λ R ) SU is strictly bigger than 2 SU T 2 Strong 1 ) ( Λ 8 π glo U α π 4 α G . The triplet structure for third family fermions is a 4 ( × L L 10TeV, which seems to be what we need to avoid the ) ∼ ∼ ) in QCD). For 2 2 ( ∼ 2 H ( π f an up-type m ′ SU L SU T 2 partners as external sources that transform non-trivially under the Gold- Strong a generic coupling constant and I used the qualitative relation = m i Λ α in larger simple group (simple group models). For instance, within π 0 by cancelling the 1-loop quadratic divergent contribution of the 4 , with vanishes. In that situation only the combined effect of at least two weak / L from SM vector bosons. = i 2 ) can destroy the Goldstone nature of the Higgs thus contributing a mass G weak i ′ g j α c . The role of the extra charged T G α , Y = ) b 2 Strong 1 , α t ( Λ and π W i U down to ordinary 4 α = ( α ) × L 3 2 ∼ ( χ ) , there is then a new up-type quark between the strong scale and the Goldstone decay constant with the Higgs doublet belonging to the Goldstone space 2 H 2 . The ordinary Higgs boson arises as a (pseudo)-Goldstone from the s R ( f is gauged: gauge and Yukawa interactions collectively realize the explcit b SU m survives between the fundamental scale b . Therefore as a combination of spontaneous and explicit breaking only a glo glo π δ SU H G loc 4 glo glo G and × G H ∼ ⊂ 1 R ) ) t ⊂ → ⊂ The partners of the SM states that are needed to enforce the LH mechanism The gauge group can either be extended by adding extra group factors The general symmetry structure of LH models involves a global group 2 3 ( ( loc glo loc Strong correction simplest product group models instead, such as the SU the latter class the Simplest Little Higgs model [15] has a weak gauge group models) or by embedding symmetry selection rules. We can thencouplings in principle (thought think of of as a external cleverwhen choice sources) of any such sy single that coupling the Goldstone sy simple model is the so-called Littlest Higgs for which subgroup G where I indicated by breaking of SU distinct couplings G invariance of atomic levels. As in atomic physics, the coefficients stone symmetry, thus breaking it, very much like an external electric field brea H Λ mass of order LEP paradox. By this equation we then expect with feature of the simplest models, event though content of the SM musta be clearly variety extended, of and Little thepartners many Higgs for different models. basically ways each o SM field. One Whenenforce feature computing the corrections of to selection all the rule Higg these models is the presence corresponding SM field. For instance, in all models the left-handed top dou Physics Beyond the Standard Model We can think of these couplings to it. The symmetry is said to be collectively broken, at least a triplet just the electroweak group the relation between strong scale and PoS(HEP2005)399 with (3.5) 2 data 2 π le would irement of 16 1TeV vec- ∼ ∼ , at which the i rmions as well c ferent diagrams mediate mass is Riccardo Rattazzi g f electroweak data der to give rise to ∼ Strong ve operators. Higgs boson, where for a theory of elec- Λ [16] to the most recent the partner loops cancel further, in that logarith- ymmetry breaking. For 10TeV these effects are ∼ 0 (3.4) ll the new effects are faith- e, but the bounds are roughly =  Strong , T Λ m f  T mixing Yukawa, the heavy top partner T λ Λ t m 2 –  T − 2 ln T λ 2 T m + 2 t 2 9 t λ λ 2 . For instance in the top-quark sector the 3 diagrams  3 π sector gives rise to a negative correction 2 H 8 m T 2 − – π t 2 Strong = 8 Λ 2 H 3 m − δ one in the MSSM. [9, 17]. Simple group models are not universal because of the new = ˜ t 2 H – W t , m Y δ . This is because strong coupling would then demand , In product group models, all such effects arise from the mixing between b T , b S Strong ,... Λ H Z 50TeV [4]. Fortunately, fermion compositeness is not a necessary requ , for 4-fermion contact interactions in eq. (2.3). But with this normalization LEP ± > ∼ H W , and the Goldstone decay constant. An experimental validation of this sum ru Strong Strong T Λ Λ m The first class is associated to the yet unknown physics at the cut-off The second class of effects is mainly associated to the intermediate mass Those we just described are undoubtedly attractive qualitative features As already said, from the viewpoint of the low energy effective theory, = NP not in contradiction with thewere data. composite at The situation would however be bad if light fe current–current interactions associated to the extendedthe gauge same structur [17, 18]. From the first analyses of electroweak data in LH models troweak symmetry breaking. In thethat matters. end, In however, the it LH is models the there comparison are with two classes the of contributions to effecti Higgs is composite. Itvector necessarily bosons gives appear rise only to through operators covariant involving derivatives. just the For fully parametrized by heavy and light bosons. These models are therefore universal and a tor bosons, LH models, although Higgs compositenessthe requires SM some Yukawa extra couplings. interactions in o be a spectacular confirmation ofare the analogic LH to mechanism. what The happens in cancellationsmic supersymmetry. among divergences The dif do analogy not goes cancel, indeed instance and in play the a Littlest role Higgs in model triggering the electroweak s mass thus implying a sum rule involving the top Yukawa, the completely analogous to the Λ imply necessary for the LH mechanism to work. a mass in the TeV range. Notice that the presence of these new states with inter Physics Beyond the Standard Model in the figure add up to a quadratic correction the leading quadratic 1-loop correction to PoS(HEP2005)399 ) H 1 W ( m (3.7) (3.6) O 2TeV, . ∼ 1 H correction > α t accessible H are worth the W , that plays the s. However the f m indirectly limits of parameters is Riccardo Rattazzi ings. However I pling π n models without nly with the LHC H 4 ough the discussion for the new vectors, α ound 500GeV. This g to come up with a ly on this mixing. In , ptable to have such a = .6) the bound on H H e odd. This naturally , mmetry, T-parity, with nsion with electroweak α W ts are tamed provided a n with the Higgs quartic H W m α feature of these models is α Strong to 4-fermion contact terms. H W ) roughly as Λ − α α f t follows I will briefly discuss 1 the LH is not less tuned than 1 . as free parameters. Notice that, 0 q Y < ∼ H 2 W 2 W H and m m α 2 b T . = 3 one gets (with 95% CL) . 1 we must tune the Higgs mass to at least and gauge coupling . 0 0 W TeV H 1TeV, instead of > W H < ∼ ∼ m H α 1 0. The direct bound on H 10 α √ g f α = ∼ > b T H T H W W α m α m 0. This would be a great result, if it wasn’t that with T-parity 1 − = 1 are more model-dependent. However, especially thanks to LEP2, : we are back to the LEP paradox! In fact one may even say that 6TeV for q W . gets larger. For Y 1 H NP = 2 W 2 W H Λ b S > m α m and ; in terms of the mass 2 H b W T W = m b S and b S free, and b T , and for a ‘normal’-size coupling 2 T become weaker as m f ∝ In the end, even if these models are somewhat cornered by LEP data, it is o The basic problem involves the mixing between light and heavy vector boson 2 H m We now see the LEP paradox in action. The Higgs mass is dominated by quantum by keeping it is possible to strongly bound the model even by treating by eq. (3.6), it is the intermediate scale there necessarily appear new and potentially disastrous loop corrections This is precisely what T-paritypartner was for asked each to SM avoid! fermion, including Theseway, the new models light loop with ones, effec T-parity is can added probablyit. with be a T-parity is mass made a ar technically smart idea, lesseffort. but fine-tuned it tha is not clear to me if the extra complications it entails this is just that we will directly test them. The top partners are likely to be the lightest and mos the mass of the top partner (via the bound on the LH decay constant δ Physics Beyond the Standard Model and comprehensive ones [17, 18], muchthe work results has been for done. product In group wha the models contribution as to studied in ref.[17]. One robust on the verge of becominglarge strong. coupling While at it low does energy, notweakly it seem coupled may technically UV perhaps unacce completion of make thenot things LH. limited harder The to when product need group tryin for models, slightlyis but extreme somewhat also choices different holds [17, for 18]. simple Notice groupdata, also ones, that, specific alth in models addition can to have the extracoupling. general tuning te [19], I for do instance not inthink associatio know it whether is fair it to is say that fair for to normally weak emphasize gauge these couplings more specific tun role of the new physics scale 5% accuracy. Alternatively, tuning is minimized, if we are willing to accept a cou supersymmetry. cancellation of the leading quadratic correctionfact to LH the models Higgs mass have does beenrespect not constructed to re [20] which involving SM anforbids particles extra the are mixing, discrete implying even, sy while the heavy vector bosons ar the LH provides an explicit incarnation of the LEP paradox itself. By eq. (3 while the contributions to and on PoS(HEP2005)399 ∈ els α T values H admitting of the 5th α . The gauge new ey connect. A t now the new G by some clever extra Riccardo Rattazzi e so-called moose G the limit of vanish- make up the Higgs ctor of a discovery up to weak e in recent years (see t the large . The Goldstone field 1, this linear structure e group factors, while G new , can be extracted from on, implying that all the glo ≫ deconstruction Kaluza–Klein replicas of G H collisions via the flavour G / α N es, warping, deconstruction, qb , which makes the connection becomes an exact Goldstone. , broken down to respectively ) to light particles, thus leading extra i down to just Σ ( G H 5 , associated to the generators extra ), A ∈ W factor of G extra intermediate dots with gauge group new ,... G breaks down to N G α 6 , as well as extra × f A G or , extra α 5 extra G A G weak are thus extracted from the measured rate and G T = play the role of 11 m i glo represents the set of Goldstone bosons associated to Σ is directly produced in G Σ and T T λ , as shown in the figure. In the limit Σ , and the uneaten Goldstones weak G 3TeV, the sum rule eq. (2.1) can likely be tested within 10% accuracy < → are embedded into each distinct H . The parameters W must be associated to non-local, ie. finite, quantum corrections. new contains the SM Higgs doublet. The extra dimensional gauge symmetry then new m ¯ Tb G G 2 H and LH fully manifest. The moose diagram is called a + m × at each boundary. The scalars 5 weak as a subgroup. The link field W A and G ) , are massless at tree level. Very much as for the LH models, one can build mod or Higgs as `holographic' Goldstone boson / new 1 ∼ weak , linked by replicas of ( 5 G G A weak H U extra weak 5TeV and . G extra G ∼ G × 2 and / G ) These models are indeed closely related to a large class of LH. These are th This is also a pretty ‘old’ idea [22, 23] on which, again, progress was mad H 2 < ( ≡ breaks weak extra T i dimension [25]. The Higgsstates mass that is cut-off calculable the quadratic at divergence 1-loop, are as nicely in interpreted any as LH the model, bu SU forbids the presence of local contributions to the mass of such a Higgs bos contributions to the breaking of the global symmetry group models, which can be represented bythe diagrams links where indicate the scalar dots fields indicatesimple gaug with LH quantum moose, numbers depicted under in the two figure gauge (a), dots involves th one extra gauge group fa G where from the reconstructed mass. The remaining parameter [21]. 3.2 G to a suppression in them DY cross section. One can still conclude that, in case doublet. Notice that this construction realizesing collective symmetry gauge breaking: coupling in for any individual dot (either factors the Drell-Yan (DY) production and decay of the heavy vectors. Notice tha between truly approximates a 5-dimensional theory, with gauge group for instance ref. [24]) thanksetc. to the The use basic of remark new is concepts that such when as the bran gauge group Σ that are favoured by low energy data suppress the coupling of states, in view of tuning considerations. Physics Beyond the Standard Model mixing vertex Now, one may imagine repeating this structure by adding compactification, the extra-dimensional polarizations G PoS(HEP2005)399 ). = and y . At KK (3.8) (3.9) is not R ∞ m (3.10) 0. This = → = y Klein reso- Planck N y M al interval k scale is rather Riccardo Rattazzi dimensional force r, unlike on Earth, es a valid descrip- e, and can be used tomic transition by describes the energy L / y al gauge theories have a , some aspects of a more ories can be alternatively localized near characterizes the distance − e L . Indeed, studying the spectrum of R . Moreover, the more weakly coupled N . The length Strong 2 ... . Strong Λ L / Λ + dy 0, and therefore the effective / R . In this sense it can be considered a serious + ∼ = − 2 KK µ e y m . . Its mass, generated at 1 loop, is of the form in KK 2 dx ∼ 2 N Planck t 12 m µ π dy λ / M , the arguably most interesting one [28] was obtained 5 3 5 dx 16 A KK L A / Planck R 0 ∼ y m : Strong R ∼ 2 , relative to the same process taking place at M L y 2 H − Λ / H e R = m 35. In the model of ref. [28] the Higgs is basically the zero construction. The peculiarity of this model is then that the ∼ − ) the larger = to the weak scale, then the exponential explains the Big Hier- 5 e ∼ H N 2 A : L 5 KK ds / (the KK levels are more or less equally spaced by an amount ∼ Strong A R m Λ H Strong , born within [26], but more and more influential in model Λ is combined with a solution of the Big Hierarchy problem. Unlike most LH which sets a minimal length scale 1 H m holography Strong Λ truly has a physical interpretation as the number of weakly coupled Kaluza– beyond which curvature effects are important. The warp factor N y There are KK resonances for each SM particle. is warped and the metric is At the classical level one may think of achieving the continuum limit by sending Among the various realizations of ] • R , 0 along red-shift of any process taking place at If one succeeds in associating model of some components of is conceptually analogous to theatoms relative sitting red-shift at of different light heights emittedin in in the the a RS gravitational field given metric a of theto the curvature explain Earth. of the space-time Howeve Big is large. Hierarchyis problem. The mediated red-shift by Indeed is a in then massless the hug graviton RS localized model near the effective 4- Physics Beyond the Standard Model the SM fields. So we roughly have eq. (3.8) as expected in any archy for a fairly small radius competitor of supersymmetry. As in supersymmetry,constraining: the extrapolation to the Planc the quantum level, however, that doesUV not cut-off make sense, since 5-dimension calculability of tion of physics up to energies of the order of theory, thanks to the embedding in the RS geometry, the model in ref. [28] giv red-shifted. However the lightest Kaluza-Klein states, for all fields, are the deconstructed theory one gets their mass is red-shifted by a factor so that nances below the cut-off viewed as purely 4D theories with a large number of states building and phenomenology (see e.g. ref. [27]): weakly coupled 5D the The simple construction we have justgeneral sketched idea, displays, perhaps roughly the 5D description (the larger within the Randall–Sundrum (RS) model [29]. In the RS model the 5th dimension [ PoS(HEP2005)399 n ional 10, see iggsless outlined < ∼ ning at the tion in 5D, retty strong: N ntly stronger persymmetric does not have ut also by the , may however d so far, is that b S s are concerned: Riccardo Rattazzi tal description of ffortlessly explain r if non–universal proximation works (in the 1-link moose so that the combined Q 5TeV on the mass of s from . ) [32]. The beta function igher order uncalculable 2 1 , which are by all means e SM should not look so extra ( R t > G U is composite. H W R t m is fixed in any given construction to .). These models are very ambitious 2 Q ) vertex [31]. They lead to a bound of ) H 1 ¯ b W ( m U Zb / Z to m ( and its embedding in new 13 G and the right-handed top new × directly to electric charge G H , which would drastically limit the overall calculability ) weak 1 extra ( G G O ∼ N , unlike the other SM states, strongly interacts with the KK modes. R t can be fully kept under control. , and it is not tunable. This makes it harder to pass the electroweak precisio ¯ b 2 is chosen [9], implying unacceptably strong coupling, or the simplicity of the b π N → 16 . The KK states behave like the resonances of a strongly coupled 4-dimens / N Z π 4 N √ 2 g ∼ KK about 4TeV on the massfew of per the cent top level. KK These stronger partners, bounds, thus unlike implying the a more need robust one for fine tu From the 4-dimensional perspective the interpretation is that be a peculiarity of the specificin model, ref. and [31]. some possibilities to overcome them are the lightest vector KK mode,bounds slightly are stronger here than associated for to LH. corrections However significa to the field theory. The quark and lepton masswhile implementing spectrum a can GIM mechanism be to nicely suppress explained FCNC’s [30]. viaThe their right-handed localiza top The electroweak constraints are similar to thethey LH as require far as about oblique 10% correction tuning corresponding to a bound eq. (3.9). By converse this bound impliesg that the coupling among KK modes is p Perturbativity of the three SM gauge couplings up to the Planck scale implies One last item concerns gauge unification, which in some leading, naive, ap 5D models or moose models, can also be used to construct partially calculable H The ideology underlying model building attempts, such as the ones I describe • • • • the measured parameters of theNature. SM must If be that pointing description toward iswithin a not the unique more perverse, fundamen fundamental any description. apparent tuning Thus within we th must look for theories that e very well, and in a novelare way, totally indeed alternative to not what was just thoughtsubtraction so modified of far the by contribution the of the addition Higgs of the contribution of new states, b [32]. So, whileyet the a idea realization of that unificationunification. can by computationally compare subtraction to is the new fully and weakly interesting, coupled it su theories [33]. This corresponds to choosing be of order effect of the two boundaries is to break since, unlike in models with a Higgs field, the ratio composite states just above the weak scale.effects The are problem, very however, is important that unless h effects such as idea must be spoiled by extra complications [34]. Moreover it is not yet clea tests: either small limit, diagram (a), the link field breaks Physics Beyond the Standard Model 4. Anthropic approach to hierarchy problem(s) PoS(HEP2005)399 the , where c ρ 100 f all hierarchy ter refined into le sets an upper as recently also ∼ has a hospitable Riccardo Rattazzi which we so far alue is nailed by osmological con- c r long considered some, perhaps all, nthropic viewpoint ‘accidentally’ ends Λ s the weak scale, are sed on a multiverse rbit around the Sun: ersymmetruc particle environmental origin. ∼ called the Atomic Prin- with a cosmological con- a tremendous multitude of cosm lting scenario, dubbed Split would then be a multiverse Λ m out in the Landscape. That is reasonably smooth, then the cosm Λ GeV) squarks, leptons and one combination , which is otherwise apparently tuned by 120 13 is that it be small enough to allow the formation cosm 14 Λ cosm ). Λ 120 − be of the same order of magnitude as, or not much smaller 10 ∼ cosm 0, Weinberg predicted a likely value Λ -QCD, etc. The anthropic approach to physics, and to the hierar- 4 Planck 6= θ M / below which galaxies can form. Then, when there was still no obser- cosm c Λ Λ cosm Λ . It is quite remarkable that Weinberg’s logic correctly predicts, to within an [36]. In the meanwhile the Type IA Supernovae data [37] had established c c ρ ρ 7 . 0 10 , which is only about 5 times its experimental value. The Atomic Principle was later i is not a fundamental quantity. ≃ ∼ , thus providing a radically different viewpoint on the least understood o H c h Λ cosm cosm cosm of galaxies. physical parameters vary from region to region. Our local universe represents but a small region of a multiverse in which Λ Λ Λ Further to the success of the Structure Principle, the anthropic viewpoint h • is the critical density for the closure of the Universe. The computation was la 1. 2. The only environmental constraint on c been reinforced by advances is stringdifferent theory, indicating vacua, the forming existence what of iswith called each the different Landscape. region (subuniverse) Theand sitting universe the at frustration a different with vacuu standardon the approaches electroweak have hierarchy stimulated problem. theciple, Ref. use according [38] of to introduced the which what a thethe is request Fermi now that scale complex is chemistry (atoms) anbound exists. environmental on Remarkably quantity the whose Atomic v Princip applied to the MSSM [39, 40] underenvironmental the quantities, assumption and that with the the soft terms, additional(LSP), and request a thu that neutralino, the provide lightest the sup DarkSupersymmetry, Matter features of superheavy the (even Universe. up The toof resu 10 Higgs scalars, while the charginos and the neutralinos have a mass which Weinberg then argued that, if the distribution of values of According to the multiverse assumption, the value of some physical quantities, chy problems in particular,assumption: follows a different ideology, which could be ba considered a fundamental propertyOne of standard Nature, example of may an insteadwhile environmental have not quantity is fundamental, a the its purely radius valueatmosphere of is with Earth’s pretty o the constrained by presencepowerless the of by prior liquid the that water. the great Earth majority, Thestant until anthropic Weinberg principle in 1987 was [35] fo applied it to the c presence of a negative pressurestant energy density component, compatible problems. Weinberg’s assumed that (Structure Principle) vational indication that than, the critical value most natural expectation is that order of magnitude, a mysterious quantity like ρ Physics Beyond the Standard Model the value of the weak scale, orders of magnitude ( roughly PoS(HEP2005)399 (4.1) (4.2) (4.3) ntly from ver the set up is iewpoint on the Riccardo Rattazzi rkably, although ymmetry, shown ly have to ask our- en is to ask: Why the data. The data have enough time. In rk in the last year. It so that by the time the al exchange of the heavy is mantained, as in super- distinctive displaced vertex Planck M ≪ . almost coincide? Given the present ) crit Q crit 2 SUSY SUSY ≪ Q m . . The physical value of the Higgs mass is m crit = and SUSY Q ∼ − SUSY Q m ( ˜ 2 t m ≃ 2 H 15 m SUSY starts positive up at the Planck scale and is driven m m 2 H = SUSY ∼ − m m phys phys | | 2 H 2 H by RG contributions, mostly due to the stops, until the running m m crit the Higgs mass is large and negative (cf. eq. (2.5)) , which by direct glance at the figure is equivalent to Q ˜ 2 t m SUSY ≪ m . A generic expectation is ∼ phys Q | Planck 2 H m M − and is associated to a dimensional transmutation, and is expected to differ significa crit SUSY Q m Let us go back to the well known cartoon of EWSB by RG evolution in supers is frozen at the typical scale of sparticle masses negative below some RG scale the superspectrum is split, the successfulsymmetry unification that of is mostly gauge due couplings torather the predictive. contribution In of particular Higgsinos the and gluino .squarks, decays Moreo giving very rise, slowly, via over the a virtu events. significant portion Split of Supersymmetry parameter haswould space, been be to the fair and subject worthwhile of tothe a review remaining this great work, part amount but of of unfortunately my I wo fine-tuning do problem talk not of I the would MSSM instead [6]. like to present a4.1 new, anthropic, Back v to Supersymmetry up close to the weak scale in order to have the right amount of relic LSP. Rema Physics Beyond the Standard Model in the figure. The Higgs mass parameter Now, then approximatively both running is frozen at As we explained already,favour this instead is unfortunately not the situation favoured by An alternative way ofshould phrasing two the totally fine-tuning unrelated problem parameters of like supersymmetry th constraints, if Supersymmetry is discovered atselves this the question. LHC, we Let me will try almost and certain give an answer right now. PoS(HEP2005)399 , n 0 : / has 1 (4.4) (4.6) (4.5) = . The H n i 6 m m 1 but not H . A small . h i∼− ) It certainly crit eld theoretic Q crit t live in region Q , and the other can range up to i ∼ Riccardo Rattazzi / c 01 and 0 SUSY . , grows like ve at LEP but not at m is reasonably flat and SUSY SUSY SUSY 0 replacing the datum m more tuned, there are e Planck scale. Notice ed because throughout to m m m Planck = < ( in region 1 there can exist i 6 crit . M ln en by SUSY e beta function for h varies. Let us also assume 1 H Q m h SUSY 0 than in the region ≪ m 2 2 = 0. 0. t SUSY but not much bigger (For instance π λ i m = = 2 3 ) H 0, we expect i 6 i is environmental. More precisely, let h . H H = h h ∼− 1 n afew ( ) , SUSY × O crit SUSY 2 2 m t of vacua with π Q λ m to have? The problem is phrased in complete ) 2 / 3 SUSY m m ( i 16 c N 0, implying 0, implying ∼− SUSY SUSY = m m < > ( i . Two possibilities for the patch of Universe we live in ˜ 2 t phys m 15, while it helps to explain the little hierarchy problem ln | . m phys phys 2 2 H 2 0 t | | SUSY π λ m 2 H 2 H ∼ 2 m 3 m m 2 is also fixed, as it depends only on ∼ 0 are then close to the boundary of the two regions, where a little π 2 = / crit 2 i 6 t ˜ 2 t phys Q | λ H m 2 H h m will cross zero immediately above the supersymmetric threshold as we is somewhat bigger than 1, say 2 H vacua, as perhaps suggested by string theory, and if n m , in which case , in which case ) leads to a conditional probability giving the average crit crit 30). So it is reasonable for the ratio in eq. (4.6) to be between 0 500 crit Q Q < ∼ 10 Q ( < > n < O fixed everywhere throughout the multiverse, while i c SUSY SUSY SUSY , then m m m Let us assume that the overall SUSY mass scale Now, what does one do with an argument like the above? Can it be falsified? 2. 1. Planck M much smaller, thus providing an argumentthe why supersymmetry LHC. should Of be course elusi there hasthe been Lanscape a it price is to much pay. Supersymmetry more looks likely tun to be in the region with if there are landscapes [6] where in supersymmetry, falls short to explain it completely. Indeed one can imagine fi To be more precise let me assume the number us assume that up at the Planck scale the various soft parameters are giv Physics Beyond the Standard Model the most likely points with run the soft parameters up in energy. Now, although less typical, or even choices of parameters where this does not happen, for instance when th hierarchy is present. prior can. It predicts that dimensionless couplings, but not on analogy with Weinberg’s approach to the cosmological constant, with featureless, and, which is quite likely, not peaked at so that the expectation is that all the other dimensionless gaugethat and under Yukawa couplings these are conditions fixed at th It is pretty clear we do notanyone live to in region ask 1, this and in question fact2, [38, it what is 41]. not is even Now, the sure compatibly if most with likely the value prior we that expect we mus with the that galaxies exist. Then, under the assumption that the distribution of are then given Notice that the loop factor 3 Higgs mass parameter is then obtained through the brief running from PoS(HEP2005)399 sizeable ly not, as, if n is that fine- symmetry, for om R-parity in sts mostly as a mmetric model is done in most e emerged [32]. od Dark Matter tions of Riccardo Rattazzi has finally made plict incarnations amental about the LEP. In particular of finding a theory troweak symmetry red at the LHC, to e holographic Higgs s it fully comparable ario is that in which ersymmetry is in my is scenario (although largely due to the fact the price of some extra n for physics up to the to compare apples and nation of the size of the or a good portion of the t LEP/SLC. In practically s, the new models compare 1TeV. In fact it is fair to say ∼ NP Λ 3TeV. The comparison of these new ∼ NP Λ 17 -parity in Little Higgs models), so perhaps one should T 10TeV, which describes the underlying new (strong) dynamics. 1TeV, at which lay particles that regulate the Higss mass divergence. ∼ ∼ NP Strong Λ Λ The biggest novelty of the last year is however that the anthropic principle In recent years there have been many new proposals of calculable elec becomes negative at some high RG scale, as it would happen in small deforma • • 2 H approaches to SUSY isoranges. a Supersymmetry fair provides exercise. aPlanck weakly scale. But coupled The calculable one extrapolation descriptio should istuning rather be that constraining is careful and needed not thus in accounts theof f MSSM. electroweak If symmetry we breaking set valid ourselvesLittle only the Higgs to less models, slightly ambitious then above goal supersymmetry thepresented would weak in look scale Ref. [42] less as is tuned. anGoldstone illustration The model of 5D [28] that can supersy possibility. be On extrapolated theto up other the to hand MSSM, the th and Planck also scale, very whichreasonably constrained make well [31]! with supersymmetry More as concretely, Dark perhap Matterthat is any concerned. stable But this relic is withcandidate. weak scale In annihilation the cross-section modelsinstance is at T-parity a hand in potentially the LH go or stabilitysupersymmetry. KK of parity On the in the relic the other follows 5D hand,opinion from models, not the a matched precisely neatness discrete by has of any it gauge of the follows unification new fr in models, sup although new intriguingit twists to hav the gauge hierarchy problem. Weinberg’s impressive anthropic expla not worry too much.portion After of all the the parameterthe LHC space, LHC will which will directly is test test, not the in constrained lower many layer even of indirectly structure these up by models, to a mediation. In the end,supersymmetry is is the discovered, it possibility will to verytuning falsify likely in look supersymmetry, this once like scenario we that. discover so it, Istatistics exciting? could think of be vacua the telling Probab and main us the something lesso nature fund of soft terms up at the Planck5. scale. Summary In all the models there exists already some tension with electroweak precision te consequence of the need for states at a relatively low scale Physics Beyond the Standard Model a zero at the weakit scale. would probably Such be valuesquickly hard, of reach given the a the soft conclusion). precision massesm with Another would which situation rule masses that out are would th measu rule out this scen breaking, all trying to accountall for the the examples baffling there are absence two of separate new energy signals scales a that models such as theof Little the Higgs LEP or paradox. the The Holographiccomplications tension Goldstone (large is boson gauge not are couplings dramatic ex yet or and can be relaxed at PoS(HEP2005)399 ri, Roberto come up with start to unravel ic approach has , 359 (2000). Riccardo Rattazzi me that with the troweak symmetry acua. 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