New models of New models of EWSBEWSBP. Ko (KIAS)P. Ko (KIAS)

The 8The 8thth ACFA workshop ACFA workshopEXCO, Daegu, KoreaEXCO, Daegu, Korea(July 11-14, 2005)(July 11-14, 2005)

Plan of the TalkPlan of the Talk

Why EWSB ?Why EWSB ? Symmetries and Symmetry Breaking Symmetries and Symmetry Breaking Old models for EWSBOld models for EWSB New models for EWSBNew models for EWSB OutlookOutlook

Why EWSB ?Why EWSB ? Origin of masses of EW gauge bosons (W,Origin of masses of EW gauge bosons (W,

Z), chiral fermions, their mixings, and CP viZ), chiral fermions, their mixings, and CP violation within the SMolation within the SM

Higgs sector has not been tested yet, unlikHiggs sector has not been tested yet, unlike the gauge sectorse the gauge sectors

LHC : a machine for studying EWSB sector LHC : a machine for studying EWSB sector of the SM or its various extensionsof the SM or its various extensions

ILC : precision tests of EWSB sectorILC : precision tests of EWSB sector

Old models for EWSBOld models for EWSB(Before Mid 1990’s)(Before Mid 1990’s)

Standard model HiggsStandard model Higgs Technicolor Technicolor Top condensateTop condensate Many others Many others

New models (After Mid New models (After Mid 90’s)90’s)

Extra dimensional originExtra dimensional origin - - EWSB by boundary conditionsEWSB by boundary conditions - - Higgsless EWSBHiggsless EWSB - - Dynamical EWSB due to KK gluonsDynamical EWSB due to KK gluons - - Cocktail SolutionCocktail Solution ???? -- Warped spacetime (RS-I) Warped spacetime (RS-I) - Gauge-Higgs Unification, ……. - Gauge-Higgs Unification, ……. Little Higgs (Little Higgs (Talk by Jeonghyeon SongTalk by Jeonghyeon Song)) Fat Higgs, String motivated,…..Fat Higgs, String motivated,…..

SYMMETRIES SYMMETRIES AND AND

SYMMETRY BREAKINGSYMMETRY BREAKING

Symmetries of the NatureSymmetries of the NatureExactExact BrokenBroken

InternalInternalGlobalGlobal

Baryon NumberBaryon NumberLepton NumberLepton Number

Isospin, Isospin, Flavor SU(3), etc.Flavor SU(3), etc.

InternalInternalLocalLocal

U(1)emU(1)emSU(3)cSU(3)c

SU(2)SU(2)LL x U(1) x U(1)YY

SU(5), SO(10),... (?)SU(5), SO(10),... (?)SpacetimeSpacetimeGlobalGlobal

Translation : P Translation : P Rotation : JRotation : JBoost : KBoost : K

SUSY (?)SUSY (?)

SpacetimeSpacetimeLocalLocal

General Rel.General Rel. SUGRA (?)SUGRA (?)

Symmetry BreakingSymmetry Breaking Explicit SB : global symmetry Explicit SB : global symmetry - isospin, flavor SU(3), etc.- isospin, flavor SU(3), etc.

Spontaneous Breaking of global symmetry Spontaneous Breaking of global symmetry massless Nambu-Goldstone bosonmassless Nambu-Goldstone boson - chiral symmetry in QCD : massless pion- chiral symmetry in QCD : massless pion - translational symmetry in lattice : acoustic phono- translational symmetry in lattice : acoustic phono

nn - rotational symmetry in ferromagnet : magnon - rotational symmetry in ferromagnet : magnon

Symmetry Breaking Symmetry Breaking (Cont’d)(Cont’d)

Spontaneous Breaking of local sym. Spontaneous Breaking of local sym. H Higgs mechanism :iggs mechanism :

massless NG boson eaten by massless gamassless NG boson eaten by massless gauge boson uge boson massive gauge bosons massive gauge bosons

- U(1)- U(1)emem symmetry in BCS SC symmetry in BCS SC

- - ρρ-a-a11 mass difference in chiral models with S mass difference in chiral models with SU(2)U(2)LL x SU(2) x SU(2)RR chiral symmetry chiral symmetry

- Weinberg model for lepton - Weinberg model for lepton SU(2)SU(2)LL x U(1) x U(1)YY Massive M Massive MWW, M, MZZ … …

Symmetry Breaking Symmetry Breaking (Cont’d)(Cont’d)

Anomalous breaking of global symAnomalous breaking of global sym- - ππoo γγγγ - Chiral U(1)- Chiral U(1)A A and and ηη’ mass (m’ mass (mηη’’ >> m >> mππ ) ) Anomalous breaking of local symAnomalous breaking of local sym- Inconsistent, if present- Inconsistent, if present- Anomaly cancellation in chiral gauge theorie- Anomaly cancellation in chiral gauge theorie

s (s ( Important constraint on model buildin Important constraint on model buildings)gs)

- SM : OK- SM : OK

History on Symmetry History on Symmetry BreakingBreaking

Explicit Symmetry Breaking (Isospin) (HeiseExplicit Symmetry Breaking (Isospin) (Heisenberg; ~1930)nberg; ~1930)

BCS superconductivity (1957)BCS superconductivity (1957) Nambu-Jona-Lasinio model (1961)Nambu-Jona-Lasinio model (1961) Goldstone Theorem (1961, 1962)Goldstone Theorem (1961, 1962) Higgs-Kibble mechanism (1964)Higgs-Kibble mechanism (1964) Weinberg Model of Leptons (1967)Weinberg Model of Leptons (1967)( U( UAA(1) problem, Chiral Lagrangian (1) problem, Chiral Lagrangian

(CA and PCAC), many other examples )(CA and PCAC), many other examples )

BEFORE MID 1990’sBEFORE MID 1990’s

SM Higgs SM Higgs Single Higgs Doublet Single Higgs Doublet ΦΦ(x) (x) V(V(ΦΦ) = ) = λλ ( | ( |ΦΦ||22 – v – v 22 ) ) 22

Mexican Hat PotentialMexican Hat Potential

Linear Sigma model of Gell-Mann-LevyLinear Sigma model of Gell-Mann-Levy MMHH

22 ~ ~ λλ v v 22 and M and MWW22 ~ (g v ) ~ (g v )22

Essential Ingredient : 3 NG bosons, i.e., soEssential Ingredient : 3 NG bosons, i.e., some underlying theory that breaks global SUme underlying theory that breaks global SU(2)(2)LL x SU(2) x SU(2)RR SU(2) SU(2)VV

SM HiggsSM Higgs One unknown parameter : One unknown parameter : λλ Determines MDetermines MH H and Hand H33 , H , H44 couplings couplings One unknown parameter : One unknown parameter : λλ ( or M ( or MHH ) ) Can be measured at ILC Can be measured at ILC SM Higgs picture is not a new one:SM Higgs picture is not a new one:

“ “Old wine in a new bottle.”Old wine in a new bottle.” Severe fine tuning problem Severe fine tuning problem δδMMHH

22 ~ ~ ΛΛ22 at one loop level at one loop level ΛΛ : new physics scale : new physics scale ~ M~ MPlPl , M , MGUTGUT, or M, or MTeV TeV ….….

Extensions with more Higgs Extensions with more Higgs Extend with more Higgs multiplets Extend with more Higgs multiplets SM Singlet or Doublet Higgs : SM Singlet or Doublet Higgs : OK with EW precision measurements at treOK with EW precision measurements at tre

e level (T or e level (T or ΔρΔρ parameter) parameter) Two Higgs Doublet model (including MSSM Two Higgs Doublet model (including MSSM

case) : still consistent with EWcase) : still consistent with EW precision testprecision test Spontaneous EWSB due to two VEV’s of neSpontaneous EWSB due to two VEV’s of ne

utral Higgs doublets (~SM Higgs)utral Higgs doublets (~SM Higgs)

Fine Tuning Problem for Fine Tuning Problem for MMHH

One loop correction to MOne loop correction to MH H

δδMMHH22 ~ ~ ΛΛ22

ΛΛ : new physics scale : new physics scale ~ M~ MPlPl , M , MGUTGUT, or M, or MTeV TeV ….…. EW Precision Test : MEW Precision Test : MHH < ~200 GeV < ~200 GeV Has to fine tune quadratic divergence order Has to fine tune quadratic divergence order

by order in perturbation theory to get Mby order in perturbation theory to get MHH ~ ~ EW scale EW scale

Naturalness Problem Naturalness Problem

Solving Fine Tuning Solving Fine Tuning ProblemProblem

Dimensional Transmutation (e.g. QCD) Dimensional Transmutation (e.g. QCD) MMprotonproton ~ M ~ MPlPl exp(– 8 exp(– 8 ππ22 / g / gss

22 b ) << M b ) << MPlPl

without any severe fine tuningwithout any severe fine tuning Technicolor, Composite Higgs,…Technicolor, Composite Higgs,… SUSY : quantum corrections under control, buSUSY : quantum corrections under control, bu

t has the t has the μμ-problem (tree level)-problem (tree level) Warped spacetime AdSWarped spacetime AdS55 (RS-I) (RS-I) Little Higgs (Talk by J. Song),Little Higgs (Talk by J. Song), Other ideas (conformal sym, .…)Other ideas (conformal sym, .…)

TechnicolorTechnicolor(Susskind, Weinberg, Fahri, …)(Susskind, Weinberg, Fahri, …)

Analogy to QCD with chiral symmetry breakAnalogy to QCD with chiral symmetry breaking : SU(2)ing : SU(2)LL x SU(2) x SU(2)RR SU(2) SU(2)VV

New confining strong interaction (TechnicoNew confining strong interaction (Technicolor) acting on New Fermions lor) acting on New Fermions

(Techniquarks and Technileptons)(Techniquarks and Technileptons) 3 N.G. Bosons (~ 3 N.G. Bosons (~ ππ’s)’s)

Technicolor (Cont’d)Technicolor (Cont’d) When gauged, these techni pions are eaten by gaWhen gauged, these techni pions are eaten by ga

uge bosons (Higgs mechanism)uge bosons (Higgs mechanism) Difficult to construct realistic modelsDifficult to construct realistic models- Strongly interacting theory : perturbative method d- Strongly interacting theory : perturbative method d

oes not workoes not work- Especially for the fermion masses (Extended, Wal- Especially for the fermion masses (Extended, Wal

king,….) without FCNC problem king,….) without FCNC problem EW precision test : strong constraintEW precision test : strong constraint Naïve versions are excluded by EW precision testNaïve versions are excluded by EW precision test

s (Peskin, Takeuchi)s (Peskin, Takeuchi)

Technicolor (Cont’d)Technicolor (Cont’d) Predictions : many TC resonance around weak scPredictions : many TC resonance around weak sc

ale – TeV ale – TeV Collider Signals Collider Signals

Techni rho productionTechni rho production

Composite Higgs Composite Higgs (Mid 80’s by Georgi and Kaplan)(Mid 80’s by Georgi and Kaplan)

Higgs ~ Goldstone boson of some Higgs ~ Goldstone boson of some spontaneously broken global symmetry spontaneously broken global symmetry Again analogy to low energy QCDAgain analogy to low energy QCD Higgs is composite Higgs is composite No hierarchy proble No hierarchy proble

m m Again, difficult to construct realistic model Again, difficult to construct realistic model

(especially fermion mass problem)(especially fermion mass problem) Reincarnation in form of Little Higgs Reincarnation in form of Little Higgs

Bardeen-Hill-Lindner ModelBardeen-Hill-Lindner Model

Top quark is very heavy Top quark is very heavy can be sensitive can be sensitive to the EWSB mechanismto the EWSB mechanism

Assume Nambu-Jona-Lasinio (NJL) type attAssume Nambu-Jona-Lasinio (NJL) type attractive 4-fermion interaction, which make tractive 4-fermion interaction, which make ttbar condenses and breaks chiral symmetrtbar condenses and breaks chiral symmetry of SMy of SM

(cf. Similar to qqbar condensates break chir(cf. Similar to qqbar condensates break chiral symmetry of QCD) al symmetry of QCD)

Higgs ~ t tbar bound stateHiggs ~ t tbar bound state

BHL Model (Cont’d)BHL Model (Cont’d)

Predictions of BHL modelPredictions of BHL model3 generation case3 generation case

4 generation case4 generation case

BHL model (Cont’d)BHL model (Cont’d) Two Main Problems Two Main Problems * Too heavy m* Too heavy mtt (> 200 GeV) (> 200 GeV)

Can be solved if there is a fundamental Higgs iCan be solved if there is a fundamental Higgs in addition to DynEWSBn addition to DynEWSB

Partially composite Higgs (Talk by D.Jung) Partially composite Higgs (Talk by D.Jung) * NJL interactions : ad hoc in BHL model* NJL interactions : ad hoc in BHL model Can be generic in extra dimension scenarios (DCan be generic in extra dimension scenarios (D

obrescu et al ; Yamawaki et al , for flat extra dim obrescu et al ; Yamawaki et al , for flat extra dim case ; Rius and Sanz for RS scenario ; Realistic case ; Rius and Sanz for RS scenario ; Realistic model building in progress)model building in progress)

BHL model (Cont’d)BHL model (Cont’d) Some extensions Some extensions - Two Higgs Doublet Model (Luty)- Two Higgs Doublet Model (Luty)- SUSY Version (Carena et al.) : can accomm- SUSY Version (Carena et al.) : can accomm

odate realistic top massodate realistic top mass- BHL + One Fundamental Higgs - BHL + One Fundamental Higgs (( Talk by D. JungTalk by D. Jung))Cf) For Other Dyn EWSB models, see Cf) For Other Dyn EWSB models, see Phys. RPhys. R

ep. by C.Hill and E.Simmons.ep. by C.Hill and E.Simmons.

AFTER MID 1990’sAFTER MID 1990’s

Barbieri-Hall-Nomura modelBarbieri-Hall-Nomura model 5 d N=1 SUSY with S5 d N=1 SUSY with S11

/Z/Z22 x Z x Z22 orbifold orbifold More symmetry (N=2 More symmetry (N=2

SUSY in 4d)SUSY in 4d) More constraintsMore constraints Calculability of Higgs Calculability of Higgs

massmass Radiative EWSBRadiative EWSB Many new statesMany new states

Spectrum in BHN modelSpectrum in BHN model

BHN model (Cont’d)BHN model (Cont’d) Including various uncertainties,Including various uncertainties, 1/R = (352 +- 20) GeV 1/R = (352 +- 20) GeV MMHH = (127 +- 8 +- 2 ) GeV = (127 +- 8 +- 2 ) GeV Low Energy EFT : Low Energy EFT : One Higgs Doublet + 2 superpartners for One Higgs Doublet + 2 superpartners for each SM particleseach SM particles (Very different from MSSM)(Very different from MSSM) LSP and NLSP : stops with ~(197 +- 20) GeVLSP and NLSP : stops with ~(197 +- 20) GeV Charginos and Neutralinos : heavier Charginos and Neutralinos : heavier (1/R = 352 GeV, 364 GeV, 370 GeV)(1/R = 352 GeV, 364 GeV, 370 GeV)

BHN model (Cont’d)BHN model (Cont’d) Exotic hadrons with stops are collider signExotic hadrons with stops are collider sign

atures of this modelatures of this model Similar to GMSB with stop NLSP Similar to GMSB with stop NLSP Current bound from Tevatron > 150 GeVCurrent bound from Tevatron > 150 GeV Many works in similar approachesMany works in similar approaches (BHN ; Arkani-Hamed et al. ; Nilles et al.; (BHN ; Arkani-Hamed et al. ; Nilles et al.;

Dobado et al ; Quiros et al, Many others …Dobado et al ; Quiros et al, Many others ……) …)

Higgsless EWSB in Extra dimHiggsless EWSB in Extra dim(EWSB by boundary conditions)(EWSB by boundary conditions)

Folklore : Tree level unitarity in WL WL elastic sFolklore : Tree level unitarity in WL WL elastic scattering is achieved by Higgs boson : B.W.Lee, cattering is achieved by Higgs boson : B.W.Lee, C. Quigg, H.B.Thacker (1977) C. Quigg, H.B.Thacker (1977)

Gauge boson scatteringGauge boson scattering

Sum RulesSum Rules

Higgless EWSB (cont’d)Higgless EWSB (cont’d)

So, the folklore is evaded, if there are infinSo, the folklore is evaded, if there are infinitely many KK modes and the sum rules aritely many KK modes and the sum rules are satisfied (Csaki, Gorjean, Murayama, Pilo e satisfied (Csaki, Gorjean, Murayama, Pilo and Terning (2003))and Terning (2003))

Tree level unitarity violation is delayed Tree level unitarity violation is delayed Realistic Model Building by Caski et al.Realistic Model Building by Caski et al. W,Z : the 1W,Z : the 1stst KK modes of the gauge fields KK modes of the gauge fields

in the bulk, and the 0in the bulk, and the 0thth KK modes are proje KK modes are projected out by suitable BC’scted out by suitable BC’s

Higgless EWSB (cont’d)Higgless EWSB (cont’d)

Detailed model buildings in flat and warped Detailed model buildings in flat and warped extra dimensions availableextra dimensions available

EW precision tests stringent EW precision tests stringent - Too large S parameter : can be made small - Too large S parameter : can be made small

by modifying the light fermion structureby modifying the light fermion structure- Large shift in Zbbar coupling with heavy top - Large shift in Zbbar coupling with heavy top

mass : need to be resolvedmass : need to be resolved

Higgsless EWSB (cont’d)Higgsless EWSB (cont’d)

Birkedal, Matchev, Perelstein, PRL (2005)Birkedal, Matchev, Perelstein, PRL (2005)

Dynamical EWSB in Extra Dynamical EWSB in Extra DimDim

NJL model assumes ad hoc 4-fermion interactioNJL model assumes ad hoc 4-fermion interactions for triggering EWSBns for triggering EWSB

Natural if gauge fields live in the bulk Natural if gauge fields live in the bulk due to KK gluon exchange (Dobrescu ; Cheng, Ddue to KK gluon exchange (Dobrescu ; Cheng, D

obrescu, Hill ; Yamawaki et al. )obrescu, Hill ; Yamawaki et al. ) BHL picture can work without introducing new inBHL picture can work without introducing new in

teractions beyond the SM gauge interaction, if tteractions beyond the SM gauge interaction, if there are extra dimensional space with bulk gauhere are extra dimensional space with bulk gauge fields and the 3ge fields and the 3rdrd generation fermion in the b generation fermion in the bulkulk

Dyn. EWSB in Extra Dim (Cont’d)Dyn. EWSB in Extra Dim (Cont’d)

““c” sums all the contributions from KK gluoc” sums all the contributions from KK gluons, thus depends on the number of extra dns, thus depends on the number of extra dim, and compactification radii.im, and compactification radii.

Dyn. EWSB in Extra Dim (cont’d)Dyn. EWSB in Extra Dim (cont’d)

Yamawaki et alYamawaki et al. considered more careful a. considered more careful analysis within flat extra dim.nalysis within flat extra dim.

Rius and SanzRius and Sanz considered the same proble considered the same problem within RS-1 with gauge fields and tR in tm within RS-1 with gauge fields and tR in the bulk, and other fields on the TeV brane. he bulk, and other fields on the TeV brane.

More realistic model building possible ?More realistic model building possible ?

Cocktail Solutions ?Cocktail Solutions ? W/Z mass may be from W/Z mass may be from - fundamental Higgs VEV- fundamental Higgs VEV - nontrivial BC - nontrivial BC - dynamical EWSB- dynamical EWSB * All of them are generic within extra * All of them are generic within extra

dimension scenariosdimension scenarios (Similar to SUSY : SUGRA + GMSB + …)(Similar to SUSY : SUGRA + GMSB + …) Difficult to distinguish from the Difficult to distinguish from the

dominance of a single source of EWSBdominance of a single source of EWSB

New (Non SUSY) Physics New (Non SUSY) Physics SearchSearch

Well motivated New Physics Scenarios Well motivated New Physics Scenarios other than SUSY ?other than SUSY ? Guidelines ( Prejudice ? )Guidelines ( Prejudice ? ) - Solve - Solve Hierarchy ProblemHierarchy Problem ( Longtime Holy G( Longtime Holy G

rail rail Ignored in split SUSY) Ignored in split SUSY) - Gauge Coupling Unification- Gauge Coupling Unification - Dark Matter Candidate (Neutralino, Gravitin- Dark Matter Candidate (Neutralino, Gravitin

o, Axion, Axino, etc. )o, Axion, Axino, etc. )

Scores of some modelsScores of some modelsSMSM SUSYSUSY RS-IRS-I

Quad Div.Quad Div. ProblemProblem Yes(SUSY)Yes(SUSY) Yes (warp Yes (warp factor)factor)

MMw w << M<< MPlPl ProblemProblem Mu probleMu problemm

Yes (warp Yes (warp factor)factor)

G.C.U.G.C.U. NoNo YesYes YesYesCold Cold DMDM

No (axion ?)No (axion ?) Neutralino,gNeutralino,gravitino, axiravitino, axion ?on ?

Yes , if Yes , if grand grand unifiedunified

G.C.U. without SUSY in RS-I (AgashG.C.U. without SUSY in RS-I (Agashe, Delgado and Sundrum)e, Delgado and Sundrum)

RS - I modelRS - I model Therefore I’d like to consider the RS – I sceTherefore I’d like to consider the RS – I sce

nario more seriously, since it has similar mnario more seriously, since it has similar merits and less (?) drawbacks compared witerits and less (?) drawbacks compared with MSSMh MSSM

Put gauge fields in the bulk Put gauge fields in the bulk G.C.U. G.C.U. Put fermions in the bulk Put fermions in the bulk G.C.U. G.C.U. Put Higgs on the TeV branePut Higgs on the TeV brane Extend the gauge group including SU(2)Extend the gauge group including SU(2)RR

T parameter protectedT parameter protected

RS-I model (cont’d)RS-I model (cont’d) Kaluza Klein Graviton (with a few TeV masKaluza Klein Graviton (with a few TeV mas

s) production at LHC and ILCs) production at LHC and ILC (Hewett and Rizzo, …) (Hewett and Rizzo, …) DY DileptonDY Dilepton Higgs – Radion Mixing Higgs – Radion Mixing Higgs pair production Higgs pair production ggKKKK (~ a few TeV) production (~ a few TeV) production (work in progress)(work in progress) LZP : RHN with fractional baryon number (ALZP : RHN with fractional baryon number (A

gashe and Servant) gashe and Servant) Collider signature ? Collider signature ?

Dilepton signals in RS scenario Dilepton signals in RS scenario (Matthews, Ravindran, Sridhar)(Matthews, Ravindran, Sridhar)

Dilepton signal (cont’d)Dilepton signal (cont’d)

OutlooksOutlooks Many interesting ideas proposed so far durMany interesting ideas proposed so far dur

ing the last few decades, but no experimening the last few decades, but no experimental tests available yet, and not so compellital tests available yet, and not so compelling modelsng models

Generation of fermion masses without FCNGeneration of fermion masses without FCNC is not so easy, like SUSY modelsC is not so easy, like SUSY models

Could be due to our limited imaginationCould be due to our limited imagination Nature could be smart enough to show the Nature could be smart enough to show the

way of mass generation and EWSB in a coway of mass generation and EWSB in a completely unexpected way mpletely unexpected way

Outlooks (Cont’d)Outlooks (Cont’d) LHC/ILC will be necessity to test these LHC/ILC will be necessity to test these

fascinating ideas, and deeper fascinating ideas, and deeper understanding of the origin of EWSB, understanding of the origin of EWSB, namely masses, mixings and CPVnamely masses, mixings and CPV

New physics may be around the New physics may be around the corner, but could be in a surprising corner, but could be in a surprising disguise disguise

Let us hope to find something new and Let us hope to find something new and exciting at LHC and ILCexciting at LHC and ILC