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Little Higgs Models Little Higgs Models Theory & Phenomenology Wolfgang Kilian (Karlsruhe) Karlsruhe January 2003 How to make a light Higgs (without SUSY) Minimal models: The Littlest Higgs and the Minimal Moose Phenomenology Scales and dynamics Electroweak symmetry breaking (beyond the SM): Dynamics responsible for the electroweak scale? & ' ! ( " #%$ )* , . GeV + - – New idea (and very old): geometrical origin = extra dimensions – Old idea: field-theoretical origin = renormalization-group running and field condensation Why would we like dynamical scale generation? – We see it at work (QCD): ¡ £ ¢ ¤ & 5 3 3 ! " " ( #%$ 0 )* , . + - 4 4 GeV / 2 /10 2 © ! ( " ) * , . + - without GUT: 7 6 8 9 : ¥ ¨ ¦ ; The proton mass is natural § ¨ ¨ ¨ ¨ § § § § W. Kilian, Karlsruhe 2003 Technicolor? Dynamical scale generation: Why not simply copy QCD? Susskind/Weinberg (1979) £ ¤¦¥ 3 ¢ New QCD’ (Technicolor), ¡ TeV § § £ ; © © Compositeness (of ¤¦¥ ¤¦§ ) ¨ ¨ ; Resonances in the TeV range This is elegant, but . EW precision data Flavor Physics suggest: ; TeV-scale physics is weakly interacting ; Strongly interacting physics (if any) " is beyond # TeV and/or decoupled 3 " # # ; There is a GeV scalar: The Higgs boson W. Kilian, Karlsruhe 2003 Supersymmetry? Possible solution: Indirect (dynamical) scale generation Supersymmetric Models: Field condensation in new (hidden) sector with SUSY £ ¥ ¨© ¤ ¦§ ¡¢ ¡ ; SUSY breaking ; Scale generation Scalars are present because of SUSY £ Scalar potential by radiative corrections ¡¢ ¡ Top sector triggers EWSB Little Higgs Models: Field condensation in new sector with global symmetry ¥ ¨ © ¤ ¦ § ¡ ; ; spontaneous symmetry breaking Scale generation Scalars are present because of Goldstone theorem Scalar potential by radiative correctons Top sector triggers EWSB W. Kilian, Karlsruhe 2003 Little Higgs Models Higgs = Pseudo-Goldstone boson: Georgi, Pais (1974); Georgi, Dimopoulos, Kaplan (1984); . 3 Problem: Without fine-tuning, ¢ : ; two-scale model (like technicolor) Three-scale models: Arkani-Hamed, Cohen, Georgi (2001); . 3 3 ¢ ¢ and ; little Higgs : : " § § § " Scale : # # # TeV Compositeness, new dynamics " § § § Scale : ¡ TeV Pseudo-Goldstone scalars, extra vector bosons, extra fermions Scale : ¡ # GeV Higgs bosons, known vector bosons and fermions W. Kilian, Karlsruhe 2003 Little Higgs Models How to make a Little Higgs Model: ¢ ¡ ¡ § £ ¤ , Extended gauge theory: ¥¦ ¢ Compare: GMSB-type SUSY,¥ models ¢ ¡ ¨ £ ¤ , Enlarged global symmetry: ¥¦ embedded in Compare: SM custodial symmetry ¢ ¡ ¤ , Extended top sector: New vector-like quark(s) coupled to both and ¥¦ Compare: See-saw topcolor models W. Kilian, Karlsruhe 2003 W Gener Minimal F LHM ; . er Kilian, F mions: our = ic Kar Extended hea v symmetr lsr ersion: Charged uhe vy 2003 v ector y Gaug breaking under bosons e Theor SM 8¡ patter (at ¢ and 8 y: 8 least): ¡ 6 9 n: & SM’, £ ¤ § ¢ 6 ¢ ¢ & 9 8 £ " neutr £ 9 8¡ 9 & ¦ ¢ ¤ , ¢ , 8 al ¥ 8 ¥¦ 6 £ 9 under ¤ ¢ £ 6 and ¢ 9 ¢ 8¡ 8 ¢ " § § ¤ 9 , 8 8 9 ¢ 6 ¤ ¥ ¥¦ £ 9 ¤ £ ¡ 6 £ ¢ ¢ 9 8 " 9 9 £ Little Hig gs Models W Limits: Couplings: Mass V Larger ; . ector Kilian, ¤ £ Both 6 6 6 & £ & & ¢ scale: Kar ! gauge bosons: 6 lsr ¢ 6 6 6 £ & £ £ uhe 8 ¡ and 9 3 2003 symmetr ; ; ; 6 ; £ ¢ are £ £ £ £ ¢ ¢ ¢ comple ; ¦ ¤¦¥ ¤¦¥ ¤¦¥ y: ¡ ¢ , ¥ T ¢ ¢ ¢ Additional 6 eV 6 superhea superhea masses " ¢ £ and x r ange 6 " ¢ § & £ 8 ¢ of vy vy hea 9 6 order doub " £ £ and and vy v let decouple strongly ectors and , ¤ standard ¦ , , ¤¦¥ e coupled .g. from 6 , " ¢ ¥ ¤ £ f er f mion er 6 to " ¢ & mions £ f er couplings mions 6 £ " ¢ ( £ f er Little miophobic Hig ) gs Models W Embed Enlar Switch . Kilian, Requirement: Some Some Some g Kar ed on the lsr global gauge become become Goldstone uhe gauge 2003 couplings symmetr g ¡ light hea roup and ¤ bosons & vy £ (mass ¤ ¨ (mass ¢ & y don't 6 £ £ 6 & £ § of ¤ ¤ 6 on of £ £ ¨ ¤ comm of : 6 in order & ¢ & Symmetr § order a on larger ¨ ¥ ute ¤ are & 3 £ ¨ y 6 global & eaten ¤ is 6 § £ £ reduced : § ¨ ¥ : ¢ symmetr " ¤ ) ¤ ¥ ¢ ; £ ; ) 6 £ £ ; y T on ¨ eV ¢ ¨ 6 , ¥ & & -scale Higgs £ on ¢ , ¤ § £ ¢ § boson scalars Little ¤ £ ¢ candidates Hig gs Models Little Higgs Models Radiatively generated Higgs potential Heavy scalars: ¡ £ Light scalars: (includes Goldstone bosons ¤¦¥ ) 1-loop Coleman-Weinberg potential for and ¡ : determined by symmetry pattern £ £ § § § ¡ ¢ £ ¡ ¡ ¤ ¡¦¥ ¤ ¤ 8 9 8 9 Integrate out the fields: ¢ § § § ¡ ¤ ¡§¥ ¤ 8 9 ¡ ; is massless to one-loop order £ ; Positive mass at two-loop order ¡ ¡ ; Trilinear couplings : production and decay channels for heavy scalars W. Kilian, Karlsruhe 2003 W Y Y Extended Extr ; ; ; ; ¤ . uka uka Kilian, ¢ loop a T T Higgs T w w op’ op op massiv a a Kar mass Y couplings coupling correction mass lsr uka VEV top uhe e w 2003 © singlet a © quark / § ¡ coupling § (model 2 of ¢ hea ¢ § sector: ; f er £ mion(s) vy dependent): ¢ ¢ " negativ & § scalars T ¢ r " with £ & 8 e Higgs £ top ¢ : ¤ " £ suppressed 8 ¡ ¢ quantum 9 9 mass ¤ ¥ ¨ 8 ¢ squared ¢ " £ ¤ & n b ¡ ¢ umbers: y 9¦ £ £ ¡ : £ ¢ £ ¢ ¡ ¢ ¢ Little Hig gs Models Little Higgs Models Summary: LHM particle content Light Higgs doublet(s), possibly extra light scalar multiplets Heavy Higgs multiplets, coupled to Higgs/Goldstone pairs, decoupled from fermions, 3 mixed with light Higgses (mixing angle ) : Heavy vector bosons: ¢ ¢ ¢ ¦ ¦ 3 § £ £ ¤¦¥ ¤¦¥ ¤ coupled to SM fermions, mixed with (mixing angle ) : ¢ Heavy up-type quark(s): Effective theory above : cancellation of quadratic divergences in Higgs self-energy W. Kilian, Karlsruhe 2003 The Littlest Higgs Two classes of LHM have been proposed: Simple group: ¨ ¨ £ ¤ ¤ Extended gauge symmetry & £ embedded in simple group ¤ ¤ & £ ; exotic Higgs representations, ; low-energy effective theory can be the minimal SM £ " ¢ ¡ ¢ ¢ Minimal version: £ embedded in 8 9 8¡ 8 9 8 9 9 Theory space (Moose Models): ¥ ¤ ¤ ¥ Extended gauge symmetry ¤ embedded in semisimple group 9¡ 8 ; many copies of scalar (and vector) multiplets ; low-energy effective theory contains at least two Higgs doublets £ " ¢ ¡ ¢ ¢ Minimal version: £ embedded in 8 9£¢ 9 9 8 8¡ 8 9 W. Kilian, Karlsruhe 2003 W Spectr The . Kilian, Gauge Global " Littlest – – £ # um Kar scalars Comple Comple lsr (e uhe symmetr symmetr xample): Hig ¨ © ¨ 2003 ¦ remain: x x ¤ gs: tr doub iplet y y let breaking Ar breaking (hea kani-Hamed/Cohen/Katz/Nelson (light) vy) 8¡ ¢ ¥§¦ ¨ © ; ; ¢ © 8 ¡ 8 9 9 Higgs § £ © ¤¢¡ ¢ ¤ 8 " boson 8 ¡ 9 ¦ 9 9 £ ¤ § ; ¦ ¡ ¦ ¢ and (2002) with 8 9 ¨ £ £ / © " ¦ ¢ # 2 3 ¤¦¥ 8 " 9 " with £ : Goldstone ; / ¡ The £ 2 ¦ ¢ ¤¦¥ Littlest bosons ¢ ¤ § ¢ Hig gs The Littlest Higgs Heavy vectors Vector bosons with TeV scale masses: ¢ ¢ ¢ § £ significantly lighter than ¤¦¥ , production at LC 800? $ § § ¡£¢ ¡ § ; Resonance in and4 4 4 4 ( Tevatron Run 2) ¤ ¤ ¢ ¢ ¢ ¢ ; ¡ Fermion couplings suppressed if ¥ , enhanced if 6 6 6 6 & £ & £ $ ¢ £ £ ; Hypercharge boson: coupling to suppressed ; Measurements of mass, width and BRs determine scale , quantum numbers and gauge sector parameters ¢ ¢ ¦ ¥ £ and are heavier ; Indirect constraints from contact interactions ; Effect on triple gauge couplings ; GigaZ W. Kilian, Karlsruhe 2003 The Littlest Higgs Heavy scalars Scalars with TeV scale masses, unsuppressed couplings to light Higgs and Goldstones: ¥ ¡ could be the lightest state $ ¢ ¡ ¡ ¡ § ¡ ; Associated production ¥ ¡ ; ; Fermion couplings suppressed decay into ¦ Charged Higgs $ $ ¢ ¢ ¥ ¡ ¡ § £ £ ; Single production in , decay into ¦ ¦ Doubly charged Higgs $ $ $ $ $ $ § ¡ ¡ £ £ ; Single production in , decay into ¥ Heavy Higgs $ ¢ ¥ § ¡ ¡ ; Higgs-strahlung $ ¢ ¥ ¥ ¡ ¡ £ £ ; Decay into and , but not ¥ £ . but they may be too heavy ; indirect constraints from Higgs, and observables W. Kilian, Karlsruhe 2003 The Littlest Higgs Light scalars 3 Higgs boson ¡ mixes with heavy scalar , mixing angle : : ¡ ; Light Higgs mass significantly decreased ; Yukawa couplings slightly decreased ¡ ¡ ¡ ¡ ¤ ¤ ; Anomalous and couplings Precise measurements of all Higgs couplings very important! Heavy quarks ¢ Top quark mixes with heavy fermion ¢ production at LHC? £ ¡ £ Decay into and Linear collider: Precise measurements of quark couplings! W. Kilian, Karlsruhe 2003 The Littlest Higgs Precision observables £ £ ¢ ; Violation of the custodial symmetry contributions to the parameter ¡ 8 : 9 8 9 ¢ extra hypercharge boson § Higgs triplet extended top quark sector " © # # ¡ [ ¢ GeV] ¢ Light hypercharge boson § Limits from Drell-Yan processes / contact terms at Tevatron, LEP2 ¢ Extra £ £ ¤ Contributions to ¤ couplings and W. Kilian, Karlsruhe 2003 The Littlest Higgs Present limits: Csaki/Hubisz/Kribs/Meade/Terning (2002) ( § ( ¢ ¡ # ¡ ¡ GeV and ¡ TeV Caveat: Top sector neglected Hewett/Petriello/Rizzo (2002) " § © # ¡ ¡ ¡ ¡ TeV and § TeV Caveat: Scalar sector neglected ; Need to take into account all contributions (cancellations!) ; Favored: Models with ¢ – Different hypercharge embedding: § heavier ¢ ¢ ¢ £ ¤ – Custodial symmetry: £ ? 8 9 8 9¤£ 8 9 – Fermiophobic vector bosons Han/Logan/McElrath/Wang (2003) W. Kilian, Karlsruhe 2003 W The . Kilian, T Hea Light Gauge with Global ; " Minimal op singlet, real Kar Hea vy sector f lsr our scalars: tr uhe scalars: vy symmetr symmetr iplets independent 8¡ Moose " v 2003 : ¢ ectors doub ¢ V 8 , ector-lik ¡ 8 ¡ 9 9 Higgs £ real y y let, £ Model: breaking: £ breaking: ¢ " singlets ¦ ¢ e 8 tr ¢ scalar doub 8 ¤¦¥ hea iplet ¡ 9 9 ¥ £ ¢ 9 ¤ vy § Ar ¢ lets § ¢ m 8 kani-Hamed/Cohen/Katz/Nelson/Gregoire/W f and " er ultiplets
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