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Strong Dynamics and Electroweak Symmetry Breaking

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Strong Dynamics and Electroweak Symmetry Breaking FERMI–PUB–02/045-T BUHEP-01-09 March, 2003 Strong Dynamics and Electroweak Symmetry Breaking Christopher T. Hill1 and Elizabeth H. Simmons2,3 1Fermi National Accelerator Laboratory P.O. Box 500, Batavia, IL, 60510 2 Dept. of Physics, Boston University 590 Commonwealth Avenue, Boston, MA, 02215 3 Radcliffe Institute for Advanced Study and Department of Physics, Harvard University Cambridge, MA, 02138 Abstract arXiv:hep-ph/0203079v3 4 Mar 2003 The breaking of electroweak symmetry, and origin of the associated “weak scale,” vweak = 1/ 2√2GF = 175 GeV, may be due to a new strong interac- tion. Theoretical developmentsq over the past decade have led to viable models and mechanisms that are consistent with current experimental data. Many of these schemes feature a privileged role for the top quark, and third genera- tion, and are natural in the context of theories of extra space dimensions at the weak scale. We review various models and their phenomenological impli- cations which will be subject to definitive tests in future collider runs at the + Tevatron, and the LHC, and future linear e e− colliders, as well as sensitive studies of rare processes. Contents 1 Introduction 4 1.1 LessonsfromQCD ............................... 4 1.2 TheWeakScale................................. 5 1.3 Superconductors, Chiral Symmetries, and Nambu-GoldstoneBosons . 7 1.4 TheStandardModel .............................. 13 1.5 PurposeandSynopsisoftheReview . .. 17 2 Technicolor 19 2.1 DynamicsofTechnicolor . 19 2.1.1 The TC QCDAnalogy ....................... 19 ↔ 2.1.2 Estimating in TC by Rescaling QCD; fπ, FT , vweak ......... 21 2.2 The Minimal TC Model of Susskind and Weinberg . .... 24 2.2.1 Structure ................................ 24 2.2.2 Spectroscopy of the Minimal Model . 25 2.2.3 Non-Resonant Production and Longitudinal Gauge Boson Scattering 31 2.2.4 Techni-Vector Meson Production and Vector Meson Dominance . 33 2.3 Farhi–SusskindModel ............................. 37 2.3.1 Structure ................................ 37 2.3.2 Spectroscopy .............................. 38 2.3.3 Production and Detection at Hadron Colliders . ..... 40 + 2.3.4 Production and Detection at e e− Colliders ............. 49 3 Extended Technicolor 57 3.1 TheGeneralStructureofETC. 57 3.1.1 Master Gauge Group ....................... 58 GET C 3.1.2 LowEnergyRelicInteractions . 59 3.1.3 The α-terms: Techniaxion Masses. 60 3.1.4 The β terms: QuarkandLeptonMasses . 62 3.1.5 The γ terms: Flavor-Changing Neutral Currents . 64 3.2 ObliqueRadiativeCorrections . .... 65 3.3 SomeExplicitETCModels .......................... 69 3.3.1 Techni-GIM ............................... 69 3.3.2 Non-CommutingETCModels . 71 3.3.3 TumblingandTriggering . 73 1 3.3.4 GrandUnification............................ 73 3.4 WalkingTechnicolor .............................. 74 3.4.1 SchematicWalking . .. .. .. 74 3.4.2 Schwinger-Dyson Analysis . 75 3.5 Multi-ScaleandLow-ScaleTC. .. 78 3.6 Direct Experimental Limits and Constraints on TC . ....... 82 3.6.1 Searches for Low-Scale Color-singlet Techni–ρ’s and Techni–ω’s (and associatedTechnipions). 83 0 0 3.6.2 Separate Searches for color-singlet P ,P ′ .............. 87 3.6.3 Separate searches for color-singlet PT± ................. 89 3.6.4 Searches for Low-Scale Color-octet Techni–ρ’s (and associated Lep- toquarkTechnipionss) . 91 3.6.5 Searches for W ′ and Z′ bosons from SU(2) SU(2)......... 96 × 3.7 Supersymmetric and Bosonic Technicolor . ......100 3.7.1 Supersymmetry and Technicolor . 100 3.7.2 Scalars and Technicolor: Bosonic Technicolor . ......101 4 Top Quark Condensation and Topcolor 107 4.1 Top Quark Condensation in NJL Approximation . .107 4.1.1 The Top Yukawa Quasi-Infrared Fixed Point . 107 4.1.2 TheNJLApproximation . .107 4.2 Topcolor.....................................111 4.2.1 GaugingTopCondensation . .111 4.2.2 Gauge Groups and the Tilting Mechanism . 113 4.2.3 Top-pion Masses; Instantons; The b-quark mass . .118 4.2.4 Flavor Physics: Mass Matrices, CKM and CP-violation . ......120 4.3 TopcolorPhenomenology. 123 4.3.1 Top-pions ................................123 4.3.2 Colorons: NewColoredGaugeBosons . 125 4.3.3 New Z′ Bosons .............................129 4.4 TopSeesaw ...................................134 4.4.1 TheMinimalModel. .135 4.4.2 DynamicalIssues . .. .. ..137 4.4.3 Including the b-quark..........................141 4.5 TopSeesawPhenomenology . 143 2 4.5.1 SeesawQuarks .............................143 4.5.2 Flavorons ................................149 4.6 ExtraDimensionsattheTeVScale. 151 4.6.1 Deconstruction .............................152 4.6.2 LittleHiggsTheories . .157 5 Outlook and Conclusions 159 6 Acknowledgements 160 Appendix A: The Standard Model 161 Appendix B: The Nambu-Jona-Lasinio Model 168 Bibliography 172 3 1 Introduction 1.1 Lessons from QCD The early days of accelerator-based particle physics were largely explorations of the strong interaction scale, associated roughly with the proton mass, of order 1 GeV. Key elements were the elaboration of the hadron spectroscopy; the measurements of cross-sections; the elucidation of spontaneously broken chiral symmetry, with the pion as a Nambu- Goldstone phenomenon [1, 2, 3]; the evolution of the flavor symmetry SU(3) and the quark model [4, 5, 6]; the discovery of scaling behavior in electroproduction; [7, 8, 9]; and the observation of quarks and gluons as partons. Eventually, this work culminated in Quantum Chromodynamics (QCD): a description of the strong scale based upon the elegant symmetry principle of local gauge invariance, and the discovery of the Yang-Mills gauge group SU(3) of color [10, 11]. Today we recognize that the strong scale is a well- defined quantity, ΛQCD 100 MeV, the infrared scale at which the perturbatively defined running coupling constant∼ of QCD blows up, and we are beginning to understand how to perform detailed nonperturbative numerical computations of the associated phenomena. There are several lessons in the discovery of QCD which illuminate our present per- spective on nature. First, it took many years to get from the proton, neutron, and pions, originally thought to be elementary systems, to the underlying theory of QCD. From the perspective of a physicist of the 1930’s, knowing only the lowest-lying states, or one of the 1950’s seeing the unfolding of the resonance spectroscopy and new quantum numbers, such as strangeness, it would have seemed astonishing that those disparate elements came from a single underlying Yang-Mills gauge theory [12]. Second, the process of solving the prob- lem of the strong interactions involved a far-ranging circumnavigation of all of the ideas that we use in theoretical physics today. For example, the elaboration of the resonance spectrum and Regge behavior of QCD led to the discovery of string theory1! QCD em- bodies a rich list of phenomena, including confinement, perturbative asymptotic freedom [13, 14], topological fluctuations, and, perhaps most relevant for our present purposes, a BCS-like [15, 16] mechanism leading to chiral symmetry breaking [1, 2, 3]. Finally, the strong interactions are readily visible in nature for what might be termed “contingent” reasons: the nucleon is stable, and atomic nuclei are abundant. If a process like p e+ +γ occured with a large rate, so that protons were short-lived, then the strong interactions→ would be essentially decoupled from low energy physics, for √s < 2mπ. A new strong dynamics, if it exists, presumably does not have an analogous stable sector (else we would have seen it), and this dynamics must be largely decoupled below threshold. QCD provides direct guidance for this review because of the light it may shed on the scale of electroweak symmetry breaking (EWSB). The origin of the scale ΛQCD, and the “hierarchy” between the strong and gravitational scales is, in principle, understood within QCD in a remarkable and compelling way. If a perturbative input for αs is specified at 1Proponents of concepts such as nuclear democracy, duality, and Veneziano models (which contain an underlying string theory spectrum) believed this perspective, at the time, to be fundamental. 4 some high energy scale, e.g., the Planck scale, then the logarithmic renormalization group running of αs naturally produces a strong-interaction scale ΛQCD which lies far below MPlanck. The value of scale ΛQCD does not derive directly from the Planck scale, e.g. through multiplication by some ratio of coupling constants. Rather ΛQCD arises naturally and elegantly from quantum mechanics itself, through dimensional transmutation [17]. Hence, QCD produces the large hierarchy of scales without fine-tuning. The philosophy underlying theories of dynamical EWSB is that the “weak scale” has a similar dynamical and natural origin. 1.2 The Weak Scale We have mentioned two of the fundamental mass scales in nature, the strong-interaction 1 19 scale Λ and the scale of gravity, M = (√G )− 10 GeV. The mass scale, QCD Planck N ≈ which will figure most directly in our discussion, is the scale of weak physics, vweak = 1 ( 2√2GF )− = 175 GeV. The weak scale first entered physics, approximately 70 years ago,q when Enrico Fermi constructed the current-current interaction description of β- decay and introduced the constant, GF , into modern physics [18]. The Standard Model [19, 20, 21] identifies vweak with the vacuum expectation value (VEV) of a fundamental, isodoublet, “Higgs” scalar field. Both the gravitational and weak scales are associated with valid low energy effective theories. In the case of MPlanck we have classical
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