M. Serone, The Composite Higgs Paradigm
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M. Serone, The Composite Higgs Paradigm

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Balkan Workshop BW2013

Balkan Workshop BW2013
Beyond the Standard Models
25 – 29 April, 2013, Vrnjačka Banja, Serbia

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M. Serone, The Composite Higgs Paradigm M. Serone, The Composite Higgs Paradigm Presentation Transcript

  • The Composite Higgs ParadigmMarco Serone, SISSA, Trieste1Vrnjacka Banja, April 25-28 2013Based mostly on 1205.0770, with D. Marzocca and J. Shu(and 1211.7290, with F. Caracciolo and A. Parolini)Saturday, April 27, 2013
  • PlanIntroduction on Composite Higgs ModelsGeneralized Weinberg Sum Rules and Higgs MassConclusions2A Possible Issue for Partial CompositenessSaturday, April 27, 2013
  • But is this the SM Higgs or not ?Naturalness disfavour a SM Higgs, but a non-SM Higgs shouldcome together with new physics particles, yet to be seenBroadly speaking, there are two ways to gofor naturally motivated new physics:3Strongly coupled (technicolor, little Higgs, composite Higgs)Weakly coupled (Supersymmetry)The Higgs, the missing piece of the StandardModel (SM), is finally a realityFor decades theorists have been thinking to extensionsof the SM, motivated mostly by the so calledhierarchy or naturalness problemGF ￿ GNWhy ?Saturday, April 27, 2013
  • Technicolor, already in trouble for tensions with LEPelectroweak bounds, is essentially ruled out by a 125 GeVHiggs (techni-dilaton too heavy)Little Higgs are also Composite Higgs Models (CHM)4Little Higgs: thanks to an ingenious symmetry breaking mechanism,the Higgs mass is radiatively generated, while the quartic is notComposite Higgs: the entire Higgs potential is radiatively generatedIn principle little-Higgs models are better, because allowfor a natural separation of scales between the HiggsVEV and the Higgs compositeness scaleIn practice they are not, because the above ingenious mechanismbecomes very cumbersome when fermions are includedSaturday, April 27, 2013
  • Fundamental difference between Technicolor and CHM:• Technicolor: the EW group is broken by the strongly coupledsector (techni-quark condensates), no Higgs at all is necessary• Composite Higgs: the EW group is unbroken by the stronglycoupled sector, but a Higgs-like particle appears in thespectrum and breaks the EW group via its VEV, as in the SM5Saturday, April 27, 2013
  • A composite Higgs coming from some strongly coupled theory cansolve the hierarchy problem. At some scale the Higgs compositenessappears and the quadratic divergence is naturally cut-off6The Higgs field might or might not be a pseudo Nambu-Goldstoneboson (pNGb) of a spontaneously broken global symmetry.Models where the Higgs is a pNGB are the most promisingThe spontaneously broken global symmetry has also to be explicitly broken(by SM gauge and Yukawa couplings), otherwise the Higgs remains masslessWhole Higgs potential is radiatively generatedThe symmetry breaking pattern is closely related to the QCD caseThe SU(2)L × SU(2)R global symmetry is replaced byGf ⊃ SU(2)L × U(1)YThe SM gauge group arises as a weak gauging of GfThe SM gauge fields are the analogue of the photon.The Higgs field is the analogue of the pionsSaturday, April 27, 2013
  • 7Not only relatively weakly coupled description of CHM, Higgspotential fully calculable, but the key points of how to go inmodel building have been established in higher dimensionsImportant difference: fermion fields must now be added (no QCD analogue)Implementations in concrete models hard (calculability, flavour problems)Recent breakthrough: the composite Higgs paradigm isholographically related to theories in extra dimensions!Extra-dimensional models have allowed a tremendous progressThe Higgs becomes the fifth component of a gauge field, leading toGauge-Higgs-Unification (GHU) models also known asHolographic Composite Higgs modelsConnection particularly clear in Randall-Sundrum warped modelsthanks to the celebrated AdS/CFT dualitySaturday, April 27, 2013
  • UV Brane IR BraneElementary fieldsComposite fieldsRed-shift effect/dimensional transmutation8BulkSaturday, April 27, 2013
  • Dual 4D interpretation:Flavour hierarchies nicely explained by large RG effects (geography inextra dimensions)partial compositenessOld idea, revived and finally realized within 5D modelsStandard Model fields get a mass by mixing with composite fermionsThe more they mix the heavier they arem ∝ ￿L￿RvHLight generations are automatically screened by new physics effects9Natural mechanism to suppress dangerous FCNCSaturday, April 27, 2013
  • Main lesson learned from extra dimensions reinterpreted in 4DLtot = Lel + Lcomp + LmixElementary sector: SM particles but Higgs (and possibly top quark)Composite sector: unspecified strongly coupled theory withunbroken global symmetry G ⊃ GSMMixing sector: mass mixing between SM fermion and gaugefields and spin 1 or 1/2 bound states of the composite sector10Independently of the nature of composite sector, the pNGB Higgs dynamicscan be parametrized by using the Callan-Coleman-Wess-Zumino (CCWZ)constructionSaturday, April 27, 2013
  • 11Contrary to what happens in 5D models, the Higgspotential is generally incalculable in 4D modelsOne can impose a collective symmetry breaking mechanism onmoose-type models, deconstructed versions of 5D models orimpose generalized Weinberg sum rulesThe composite sector might be intrinsically strongly coupled, with no smallexpansion parameter (e.g. some CFT), or admit some weakly coupleddescription in terms of free fields (e.g. mesons in large N)We assume the second case, where simple parametrizations are possibleSaturday, April 27, 2013
  • Weinberg sum rules￿V aµ (q)V bν (−q)￿ ≡ PtµνδabΠV V (q2)￿Aaµ(q)Abν(−q)￿ ≡ PtµνδabΠAA(q2)In QCD, for SU(2)V × SU(2)A → SU(2)VΠLR = ΠV V − ΠAA is such thatlimp2E →∞ΠLR(−p2E) = 0limp2E →∞p2EΠLR(−p2E) = 0First sum rule (I)Second sum rule (II)(I) consequence of symmetry restoration(II) assumes UV asymptotically free theory12Saturday, April 27, 2013
  • 13Good theoretical prediction of pion mass differenceΠV V (p2E) = p2E￿nf2ρnp2E + m2ρnΠAA(p2E) = f2π + p2E￿nf2anp2E + m2anAt leading order in 1/NcIf one assumes that only first vector and axial resonance contribute to theform factors and impose rules I and II, the pion potential becomes calculableSU(2)L × SU(2)R is explicitly broken by electromagnetic interactionsmass splittings among charged and neutral pions expectedm2π± − m2π0 ￿3αem4πm2ρm2am2a − m2ρlog￿m2am2ρ￿Saturday, April 27, 2013
  • 14Higgs MassBasic question: what is its expected mass in CHM ?Saturday, April 27, 2013
  • 14Higgs MassBasic question: what is its expected mass in CHM ?mH ∼g4πΛ genericallySaturday, April 27, 2013
  • 14Higgs MassBasic question: what is its expected mass in CHM ?mH ∼g4πΛmH ∼g4πmρgenericallyQCD analogue with Weinberg sum rulesonly mass scale in the composite sectormρ = gρf > fSaturday, April 27, 2013
  • 14Higgs MassBasic question: what is its expected mass in CHM ?mH ∼g4πΛmH ∼g4πmρgenericallyQCD analogue with Weinberg sum rulesmH ∼ ? with partial compositeness additional statesand scales complicate the analysisonly mass scale in the composite sectormρ = gρf > fSaturday, April 27, 2013
  • 15Let first consider the top quark.mt ∼￿2Mfvf∼ v ￿2∼ Mf fThe top mixing largest explicit symmetry breaking termsHiggs PotentialCalculable Higgs potential is a crucial portal for new physics.The top must be semi-compositeThe Higgs mass is related to new resonances massesV (h) = Vg(h) + Vf (h)Vg(h) = −γgs2h + βgs4h Vf (h) = −γf s2h + βf s4hsh ≡ sinhf￿ 1Saturday, April 27, 2013
  • s2h = ξ =γ2βNon-trivial minimum atm2h =8βf2ξ (1 − ξ) .16β ￿ βf ∝￿4Nc16π2m2H ∼￿4Nc2π2f2ξ ￿Nc2π2m2t M2f f2v2f2v2f2mH ￿￿Nc2π2mtMffDirect relation between Higgs and resonance masses anda light Higgs implies light fermion resonancesWe can relax the second sum rule. In this way EWSB nolonger calculable, but Higgs mass still predictedSaturday, April 27, 2013
  • Collider Signatures17The deviations to SM couplings might betoo small to be detected at the LHCOn the other hand, the light sub-TeV fermion resonances, necessary toexplain a 125 GeV Higgs, seem a generic and clear prediction for CHMLHC already puts significant constraints on the parameter space of CHM,particularly when the lightest fermion resonance has Q=5/3Roughly one hasm5/3 ￿ 600m2/3 ￿ 400 GeVGeVSaturday, April 27, 2013
  • Partial Compositeness for Light FermionsPartial compositeness for light flavours is a nice and efficientmechanism to suppress dangerous FCNCIt requires one exotic fermion excitation for each SM fermionMany flavours. One should worry about possible Landau polesMinimal case (bottom-up): Gf = SO(5)Composite fermions in the fundamental of SO(5)In total we haveNf = (1 + 5) × 6 = 36active flavours above the fermion mass scale fIn this case α3 blows up at the scale ΛLP ∼ 300ΛΛ = 4πf is cut-off of the effective field theory18Saturday, April 27, 2013
  • 19In vector-like gauge theories with fermion constituentsfermion bound states are typically baryon-likeBut baryons are not light !Anyhow, where do these fermions come from ?Saturday, April 27, 2013
  • 19In vector-like gauge theories with fermion constituentsfermion bound states are typically baryon-likeBut baryons are not light !One possibility is to assume they are meson-like, made by 1 fermion and 1 scalarScalar is unnatural Assume composite sector is supersymmetricIn this case, UV completions of CHM have recently been constructedMost features of bottom-up models derived but the Landau problem remainsAnyhow, where do these fermions come from ?Saturday, April 27, 2013
  • 19In vector-like gauge theories with fermion constituentsfermion bound states are typically baryon-likeBut baryons are not light !One possibility is to assume they are meson-like, made by 1 fermion and 1 scalarScalar is unnatural Assume composite sector is supersymmetricIn this case, UV completions of CHM have recently been constructedMost features of bottom-up models derived but the Landau problem remainsSM gauge couplings develop unacceptably low Landau polesif one assumes partial compositeness for all SM fermionsAnyhow, where do these fermions come from ?Saturday, April 27, 2013
  • ConclusionsGenerically a 125 GeV Composite Higgs seems to imply thepresence of light, sub TeV, colored fermion resonances20It is important that experimentalists start to performdedicated analysis of direct searches for top partnersIn particular, understanding the UV origin of partialcompositeness for all SM fields is an important open problemThe Composite pNGB Higgs with Partial Compositeness seems apromising natural extension of the SM, alternative to SUSYFinding UV completions of such models is possible but non-trivialSaturday, April 27, 2013