PoS(ICHEP 2010)536 http://pos.sissa.it/ [email protected] An overview of models oflittle electroweak symmetry and breaking show isof how presented. avoiding it the is little First manifested hierarchy in we inhiggs SUSY supersymmetric explain at models theories. LEP the is or shown, increasing Then which the ways fall quarticof into self the coupling two MSSM. of classes: the In hiding higgs, the the both second ofare half which strongly reviewed, call interacting for including theories extensions technicolor of and electroweakpaid symmetry monopole breaking to condensation warped models. extra dimensional Particularhiggs theories attention models. and is its cousins (higgsless, little higgs and composite Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

35th International Conference of High EnergyJuly 22-28, - 2010 ICHEP2010, Paris France Csaba Csáki Institute of High Energy Phenomenology Laboratory of Elementary Cornell University Ithaca, NY 14853, USA E-mail: A (Critical) Review of Electroweak Symmetry Breaking PoS(ICHEP 2010)536 (2.1) (1.1) is the λ 1 percent. 10 TeV, thus ∼ where − 5 v λ ∼ hierarchy problem: 2 √ big SUSY = m H π m ˜ t t m m , both of which have to obtain a VEV d , u 2 log H Λ 2 t 2 2 λ 2 π 2 t π g 4 m 16 hierarchy refers to the puzzle of why have we not 2 3 is the top yukawa coupling. In order to push this t ∼ limit) the quartic can be maximized, and in this limit + λ 2 Z 2 H β little m M ∆ = 2 H m 1 TeV, and whatever that new physics is it will make the higgs new physics: ∼ Λ any the one-loop contributions! Here one needs to secretly reintroduce a not-so-small . The most straightforward resolution of this problem would be that the scale of Λ  are the top and stop masses, and soften ˜ t is the scale of new physics. One should emphasize that this sensitivity could just be a H , t m Λ m The standard Higgs mechanism is an eminently successful description of electroweak sym- The little hierarchy problem of the MSSM is mainly due to the fact that the Higgs quartic where above 114 GeV (the bound at LEP2)corrections one have needs to very be large almost one-loop as corrections: largein in as order fact the to the tree-level one term. loop However is introduced quartic). In the MSSMto there yield are fermion and two gauge higgsdirection boson doublets along masses. which the Only two VEVs onebigger are combination than equal of the will other these not (the have receives so a a called quartic). large quartic By tan (the making one VEV much yet seen some indirect hintsbe showing for up the at existence 1 ofof TeV. In any new fact of physics in these most to models new be electroweak particles more precision that like observables are force 5-10 supposed the TeV, leading to scale to a new fine tuning of order of one finds that the lightest mass at one loop is metry breaking. The analysiscoupled higgs of boson, electroweak below about precision 200 data GeV.ementary However, it higgs suggest is would that very remain hard there light. to is understand Examiningis how quadratically quantum a such sensitive corrections an light to one el- weakly finds that the higgs mass A (Critical) Review of Electroweak Symmetry Breaking 1. The SM, big vs. little hierarchy where finite contribution from a new physics couplingthe to presence the of higgs any boson, so divergences. itwhy This does is is not necessarily what imply is usuallynew referred physics to is as actually the low, insensitive to further quantum corrections abovesuperpartners, the or TeV of scale strong (for dynamics). example The via the appearance of Supersymmetric theories are somewhatprecision special, observables since from tree-level in corrections, that which would case imply R-parity 4 protects electroweak self interaction term is relatedsince to it the sets gauge the couplings size by of supersymmetry. the This physical quartic higgs is boson essential mass (like in the SM superpartners of 500 GeVminimal - supersymmetric TeV extension could of still thelittle hierarchy be standard problem, allowed. model somewhat specific (MSSM) to However, is supersymmetry. as nevertheless plagued we by will a show2. below the The little hierarchy in the MSSM PoS(ICHEP 2010)536 d is H f u , re- later (2.2) form u H η SH η m λ 150 GeV ∼ < Z h M m coupling shows , with the η ηη 2 h → h ] (which is referred to as 5 ] is that the Higgs has un- 2 , 1 will preferentially decay either to -term can be replaced by η µ ˜ 2 2 t Λ m is pushed above the GUT scale. the λ S log ˜ 2 t 2 SU(2), and the requisite m 2 π t 4 ] of the ALEPH data showed that this channel λ → , which in turn depends on the embedding of the 3 3 3 η − 2 0 . One can see that one possibly promising way to hide m with the dominant higgs decay 1 = η will increase the quartic, though a bound of u 2 H λ m ]. Introducing the singlet ]. 400 GeV, this can indeed be the dominant decay channel. The actual 7 6 1% tuning of the MSSM. ]. In this case the higgs as well as an additional pseudo-scalar − 4 − 1 . 350 ∼ f . However a recent re-analysis [ τ 4 ] (which was dubbed "the buried higgs") or to charm quarks [ → 4 η in the superpotential. Raising still applies if one requires that a Landau pole for An NMSSM quartic [ 2 The other option of solving the little hierarchy problem of the MSSM is to find a way to Clearly, this little hierarchy problem is related to the size of the Higgs quartic. There are An interesting possibility recently explored by many groups [ • → the higgs is by havingThis it can decay be achieved to both 4SU(3) within light global the symmetry jets NMSSM, [ via and an via intermediate an state extension with of two the pseudo-scalars. MSSM assuming an the "charming higgs"). In both casesobserve the at final the states LHC. are Methods four for non-bsubstructure finding jets, were these which given buried in will higgs [ be like quite scenarios hard using to the methods of jet 2.2 Other SUSY approaches increase the quartic self-coupling of the Higgsto without introducing the additional higgs quadratic bosons. divergences Here I present a list of the options that have been considered recently. conventional decays to a pseudo-scalar decaying to two SM particles.h The most popular possibility for a long while has been the decay the 5 Goldstone bosons from the breaking SU(3) A (Critical) Review of Electroweak Symmetry Breaking loop correction, and that can onlysplitting contributes be to done the by soft increasing breaking the mass top-stop parameter splitting. of the However higgs the boson: same This parameter however gives a direct contribution to the Z-mass and is expected was almost as stronglythis constrained conference as are the summarized SM in Table channels. The LEP constraints as of the time of gluons [ SM fermions into the SU(3)is global a remnant symmetry. of The agauge most full anomalies gauge natural all SU(3) forms vanish. extension (where In of this the the case global electroweak) one are SU(3) can the show that cases the when the extended sulting in the generic 0 up as a derivative couplingsufficiently between small the Goldstones.final If state the depends global on symmetry the breaking further scale decay of the two distinct potential ways tohiggs get eluded around detection this at problem: LEPcontributions either to since the the it quartic quartic. has is Both unconventional call indeed decays, for small, extensions or but of there the the need MSSM. 2.1 to Hiding be the additional Higgs at LEP PoS(ICHEP 2010)536 - is = S i R TC u N L u the VEV h ∼ so ft m -like non-renormalizable 2 ) d is the number of additional H u D N H ( ) GeV ( 86 82 , where 115 113 117 110 115 110 TC 3 ]. An NMSSM-like effective theory can be N 9 Limit D N . The most simple remedy for this is to introduce τ g 3 -parameter is generically not calculable, and thus TeV. This will give the right gauge boson masses, 4 4 4 S 28 ∗ , , . -parameter in generic technicolor theories is usually b c ∼ 0 . S 4 4 ZZ , TC ¯ ∼ τ ∗ → → Λ τ S , ¯ b j j γγ invisible ηη ηη b WW ]. Usually D-terms from additional gauge interactions decouple → → → → → → → h h h h h model indep Decay channel h h 10 ]. In this case the NMSSM Landau-pole is replaced by a weakly coupled 8 . These condensates do give rise to masses for the W and the Z boson, except their The LEP bounds on the mass of the Higgs boson in various decay channels as of July 2010. 3 π f -parameter. SU(2) doublets introduced that participatethe in number the of strong technicolors. technicolor However interactions, the it and is not clear whether orS not some non-QCD-like technicolor theories could produce a small of the field breaking the gauge symmetryraise then the the D-terms higgs may mass not to fully as decouple, high and might as 400 GeV. if the gauge symmetry breaking is completely supersymmetric. However if Electroweak precision corrections. The assumed to be too large.parameter If would a be scaled-up QCD-like of contribution the was reliable order the resulting A "fat higgs" [ Seiberg dual once the interactionject, becomes and strong. the large The quartic higgs the is effect effectively of a theA composite underlying non-renormalizable strong ob- dynamics. quartic superpotential [ obtained without the introduction of a singlet, but from a term in the superpotential. A non-decoupling D-term [ i ∼ It is well-known that an elementary higgs boson may not be necessary for electroweak sym- R • • • • d Table 1: L d metry breaking. Theelectroweak vacuum symmetry just structure as of it does a in QCD: strongly here interacting the quarks gauge form theory vacuum condensates might break the 3. Models of strong dynamics 3.1 Technicolor type theories h contributions are too small by about a factor of 10 a scaled-up QCD called technicolor, with however it faces two difficult problems: A (Critical) Review of Electroweak Symmetry Breaking PoS(ICHEP 2010)536 . L ¯ qq − (3.1) ¯ ("UV qq B relives 2 F 1 R Λ = ¯ ψψ z is small, then the e TeV. Possible ways to get around charges proportional to their 4 Y ) 10 10 However TeV. the same physics will 2 ] where the dimension of the composite < dz > ], and can incorporate the right monopole 11 − 2 14 dx ( 2 5 are technifermions. In order to obtain a sufficiently  ]. In such theories a single extra dimension with the ψ z R 15 implies that if the electric coupling  n = π 2 2 ("IR brane" or "TeV brane"), then all physical quantities will = ds 0 R should not be too large eg F = Λ z ] suggest that it is difficult to sufficiently suppress the FCNC’s without ] for replacing technicolor theories is based on magnetic monopoles. 12 13 are SM fermions and q is necessarily large. Thus if there were magnetically charged chiral fermions g where ¯ ψψ is close to one, thereby acting almost like an elementary higgs from the point of view ¯ qq 2 F 1 ¯ Λ Experiments require that this scale be quite large the hierarchy reemerging. this problem involve walking technicolor, where a large anomalous dimension of ψψ of flavor physics. However recent resultsat on this conference the [ simplest conformal field theories presented Fermion masses. There is a built-in tensionfermion in generic masses. technicolor models The when SM one quark considers masses should be produced by 4-fermi operators of the sort heavy top mass the scale some of the tension, and conformal technicolor [ generically also give rise to flavor changing four SM fermion operators of the form A very popular theme of the past decade has been the study of warped extra dimensions as A recent new idea [ • is assumed. The reason why suchthe theories are mass so scales interesting vary for along electroweak phenomenology thethat is the extra that dimension extra dimension the is same abrane" way finite or as "Planck slice the brane") of metric and the factor. anti-de If Sitter one space, assumes with boundaries at models of electroweak symmetry breaking [ condensates that can act like the ordinarywith higgs ordinary VEV. A GUT-like monopole small modification charge of assignments theconfine can model the also in ordinary ensure analogy electric that photon the and condensatesW that and do magnetic the couplings not only Z. affect This the wayof photon, one condensation, but would which not find could the a be pair-produced theory at withdue the massive LHC. to QED-like The the monopoles main Dirac drawback above quantization of the condition this scale where model the is theory perturbation that is theory always is strongly well interacting, defined.LHC there cross is Thus no sections it regime (or is even hard to to verify that make the any right quantitative condensates predictions3.3 actually for do Warped form). extra dimensions metric The Dirac quantization condition magnetic coupling quantum numbers. This is an anomaly free theory [ 3.2 Monopole condensation (and assuming that the running offreedom) the the U(1) magnetically gauge charged coupling particles would isdynamically necessarily still broken condense driven thus phase by resulting the for in electric the a degreesthat electroweak similar of interactions might potentially as be in in technicolor this models.of phase chiral A is fermions, toy based model which on an however extension also of carry the magnetic SM U(1) with a fourth generation A (Critical) Review of Electroweak Symmetry Breaking PoS(ICHEP 2010)536 will remain, 2 KK m / 2 v π 12 ∼ S 3 TeV. The main observable at > KK m ]. ] localized close to the UV brane, signifying TeV one can naturally recover the exponential 15 18 -paremeter of size ∼ S 6 to incorporate custodial symmetry and thus set the 0 L R / − B . This implies that picking all bare quantities of the order 0 and 1 R U(1) / . In particular, a Higgs field localized on the IR brane will Pl 1 TeV, which still corresponds to a tuning of the percent level. 0 × R R R M > / bare ) ∼ R v π 4 = SU(2) ( bare / v × Λ e f f L ]: based on this such 5D models with a warped space can be interpreted in v ∼ ]. A contribution to the ] (and their lightest KK modes corresponding to the SM gauge fields mostly ∼ R 16 19 h 17 / m ∆ ]. 20 This modified RS model can give a realistic theory of electroweak symmetry breaking, how- The original Randall-Sundrum model was assuming that all the SM fields are localized on the A very nice interpretation of this solution to the hierarchy problem can be obtained in terms of -parameter to zero [ the LHC would be thebrane) lightest is KK-mode most of strongly coupled thethe to gluon, top production the which cross top (since section, quark. however itcollimated due is [ to Thus the peaked the heavy towards LHC mass the the signal IR top would quark be jets a will be resonance strongly in There are two directions forvery resolving large this on little the hierarchy IR problem: branesymmetry one (leading to can to protect let higgsless the the higgs models) higgs from or the VEV one leading be can loop introduce corrections an via additional the global Goldstone theorem. the fact that these are mostlyvia elementary fields. the The fact lightness that of these theand SM fields thus fermions are is can localized then not far explained pick fromof elementary the up and source a composite of large states, electroweak mass andthe symmetry (in top there breaking, quark, is the which only AdS/CFT is a language quite veryorder the heavy, small to so SM mixing). have it additional fermions should The protection be are only againstcan more exception mixtures electroweak be of is precision extended a corrections to composite the SU(2) mode bulk then gauge elementary. group In which will give a lower bound on the KK mass scale of ever it has its ownbrane is little usually hierarchy of problem the order whichwould of be is 10-100 of TeV, left and order the unaddressed: natural size the of cutoff the scale higgs mass at loop the corrections IR flat), while the SM fermions are in the bulk but [ T terms of a strongly interacting technicolor-like theory.ergy The scale fifth of dimension a can 4D be viewed field asand theory, the and dynamical en- the symmetry emergence breaking. of theto Thus IR composites brane all of is fields the corresponding that strong to are confinement dynamics,by and localized the thus strong on can dynamics the be scale), IR naturally whiletheir brane light the natural correspond (the mass field scale mass localized is scale close very for to large. the the is UV set brane are elementary,IR and brane. Thus the solutioncomposites of of the a hierarchy strong problem dynamics.might in While not this this be case is the would possible, ideal beunderstand there setup: that why are all if good there SM fermions reasons would fields and tothe be are gauge think SM no bosons that fermions are large this on composite, the flavor IR then changinginducing brane, corrections it neutral and to is electroweak similarly currents precision very large observables. (FCNC’s) hard contributions However, inducedproblem to in to order the for one to gauge really solve boson the only Lagrangian hierarchy needswarped the extra higgs dimensional to models be hasfields emerged: on are in the the the IR higgs bulk [ brane! is localized Thus on a the more IR realistic brane, version the of gauge the AdS/CFT duality [ A (Critical) Review of Electroweak Symmetry Breaking be rescaled by the warp factor of the Planck scale 1 have a physical value of hierarchy between the weak and the Planck scales [ PoS(ICHEP 2010)536 ]. ∼ 2 h 27 m ∆ . The localized higgs boson ) . The main LHC signal would i R / 0 quartic is allowed, generating all , 075008 (2009). R 2 WWZ 2 g i g log D80 . ∑ 2 0 ∼ f R + ] ("little higgs with T-parity") gets quite / ( λ v / 29 1 , 049 (2010). 2 WWZ . In order to avoid this one needs usually again = g ) 1 1005 2 + W ( 7 γ , 041801 (2005). M O ]. The main drawback of this model are electroweak 95 2 WW ∼ , 068 (2006). hierarchy in g ] is written down. f 23 ) / = 30 v 0608 10 ( O WWWW g ]. In the AdS/CFT language this is simply a calculable dual of technicolor ]. In a 4D theory this would imply a very large gauge boson mass as well, 24 ]. This will ensure that the higgs mass correction is of the form 21 . Thus the theory has a sharp prediction: these KK modes should be all below 1 [ ALEPH Collaboration ], JHEP 26 0 -parameter does turn out to be too large. However one can show that this can be ] of the WW (and WZ) scattering amplitude happens via the exchange of the KK W S and is not set by the cutoff scale but rather by the global symmetry breaking . Thus one would expect ) 22 et al. ) ], while the more sophisticated models [ 2 2 ] by an appropriate adjustment in the fermion wave functions - but again at the price and π 0 π 28 25 γ , 16 16 0 ( ( . 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