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The Big Deal with the Little Higgs Edinburgh, 8.12.2005 J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 The Big Deal with the Little Higgs Jürgen Reuter DESY, Hamburg Edinburgh, 08.Dec.2005 I Formal Solution: Introduction of a field which makes Lagrangian gauge-invariant: ⇒ Higgs field I Spontaneous symmetry breaking: Higgs gets a Vacuum Expectation value v ∼ 250 GeV I Data prefers a weakly interacting theory at the TeV scale ⇒ Higgs field corresponds to light Higgs particle (mh < 300 GeV) 2 2 I Fine-tuning/Hierarchy problem: quantum corrections δmh ∝ Λ Λ new physics scale I Solution: Symmetry cancels quantum corrections, broken at lower scale F ∼ 1 TeV J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 The Higgs boson: pros and cons Electroweak interactions mediated by massive gauge bosons: (SU(2) × U(1) gauge theory) Problem: Mass terms for W, Z and fermions not gauge invariant 2 2 I Fine-tuning/Hierarchy problem: quantum corrections δmh ∝ Λ Λ new physics scale I Solution: Symmetry cancels quantum corrections, broken at lower scale F ∼ 1 TeV J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 The Higgs boson: pros and cons Electroweak interactions mediated by massive gauge bosons: (SU(2) × U(1) gauge theory) Problem: Mass terms for W, Z and fermions not gauge invariant I Formal Solution: Introduction of a field which makes Lagrangian gauge-invariant: ⇒ Higgs field I Spontaneous symmetry breaking: Higgs gets a Vacuum Expectation value v ∼ 250 GeV I Data prefers a weakly interacting theory at the TeV scale ⇒ Higgs field corresponds to light Higgs particle (mh < 300 GeV) J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 The Higgs boson: pros and cons Electroweak interactions mediated by massive gauge bosons: (SU(2) × U(1) gauge theory) Problem: Mass terms for W, Z and fermions not gauge invariant I Formal Solution: Introduction of a field which makes Lagrangian gauge-invariant: ⇒ Higgs field I Spontaneous symmetry breaking: Higgs gets a Vacuum Expectation value v ∼ 250 GeV I Data prefers a weakly interacting theory at the TeV scale ⇒ Higgs field corresponds to light Higgs particle (mh < 300 GeV) 2 2 I Fine-tuning/Hierarchy problem: quantum corrections δmh ∝ Λ Λ new physics scale I Solution: Symmetry cancels quantum corrections, broken at lower scale F ∼ 1 TeV Little Higgs: Global Symmetries: =⇒ Quantum corrections of parti- cles of like statistics cancel Why is the Higgs light in Little Higgs models? Nambu-Goldstone Theorem: Spontaneous breaking of a global sym- metry leads to massless (Goldstone) boson(s) in the spectrum Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as Pseudo-Goldstone boson ⇔ spontaneously bro- ken (approximate) global symmetry w/o Fine-Tuning: v ∼ Λ/4π J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Higgs as Pseudo-Goldstone Boson Traditional (SUSY): Spin-Statistics =⇒ Contribu- tions from bosons and fermions cancel Nambu-Goldstone Theorem: Spontaneous breaking of a global sym- metry leads to massless (Goldstone) boson(s) in the spectrum Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as Pseudo-Goldstone boson ⇔ spontaneously bro- ken (approximate) global symmetry w/o Fine-Tuning: v ∼ Λ/4π J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Higgs as Pseudo-Goldstone Boson Traditional (SUSY): Little Higgs: Spin-Statistics =⇒ Contribu- Global Symmetries: =⇒ tions from bosons and fermions Quantum corrections of parti- cancel cles of like statistics cancel Why is the Higgs light in Little Higgs models? Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as Pseudo-Goldstone boson ⇔ spontaneously bro- ken (approximate) global symmetry w/o Fine-Tuning: v ∼ Λ/4π J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Higgs as Pseudo-Goldstone Boson Traditional (SUSY): Little Higgs: Spin-Statistics =⇒ Contribu- Global Symmetries: =⇒ tions from bosons and fermions Quantum corrections of parti- cancel cles of like statistics cancel Why is the Higgs light in Little Higgs models? Nambu-Goldstone Theorem: Spontaneous breaking of a global sym- metry leads to massless (Goldstone) boson(s) in the spectrum J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Higgs as Pseudo-Goldstone Boson Traditional (SUSY): Little Higgs: Spin-Statistics =⇒ Contribu- Global Symmetries: =⇒ tions from bosons and fermions Quantum corrections of parti- cancel cles of like statistics cancel Why is the Higgs light in Little Higgs models? Nambu-Goldstone Theorem: Spontaneous breaking of a global sym- metry leads to massless (Goldstone) boson(s) in the spectrum Old Idea: Georgi/Pais, 1974; Georgi/Dimopoulos/Kaplan, 1984 Light Higgs as Pseudo-Goldstone boson ⇔ spontaneously bro- ken (approximate) global symmetry w/o Fine-Tuning: v ∼ Λ/4π Boson masses radiative (Coleman-Weinberg), but: Higgs protected by symmetries against g g m ∼ 1 2 Λ quadratic corrections @ 1-loop level H 4π 4π O(10 TeV) Λ Scale Λ: global SB, new dynamics O(1 TeV) F Scale F : Pseudo-Goldstone bosons, new vectors/fermions O(250 GeV) v Scale v: Higgs, W/Z, `±, ... J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Collective Symmetry Breaking and 3 Scale-Models New Ingredience: Arkani-Hamed/Cohen/Georgi/. , 2001 Collective Symmetry Breaking: 2 different global symmetries, anyone unbroken ⇒ Higgs exact Goldstone boson O(10 TeV) Λ Scale Λ: global SB, new dynamics O(1 TeV) F Scale F : Pseudo-Goldstone bosons, new vectors/fermions O(250 GeV) v Scale v: Higgs, W/Z, `±, ... J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Collective Symmetry Breaking and 3 Scale-Models New Ingredience: Arkani-Hamed/Cohen/Georgi/. , 2001 Collective Symmetry Breaking: 2 different global symmetries, anyone unbroken ⇒ Higgs exact Goldstone boson Boson masses radiative (Coleman-Weinberg), but: Higgs protected by symmetries against g g m ∼ 1 2 Λ quadratic corrections @ 1-loop level H 4π 4π J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Collective Symmetry Breaking and 3 Scale-Models New Ingredience: Arkani-Hamed/Cohen/Georgi/. , 2001 Collective Symmetry Breaking: 2 different global symmetries, anyone unbroken ⇒ Higgs exact Goldstone boson Boson masses radiative (Coleman-Weinberg), but: Higgs protected by symmetries against g g m ∼ 1 2 Λ quadratic corrections @ 1-loop level H 4π 4π O(10 TeV) Λ Scale Λ: global SB, new dynamics O(1 TeV) F Scale F : Pseudo-Goldstone bosons, new vectors/fermions O(250 GeV) v Scale v: Higgs, W/Z, `±, ... 0 0 0 ± I Extended Gauge Sector: γ , Z , W I Extended fermion sector: new heavy top: T , maybe also U, C, . m Z0 Φ W 0 ± Φ±± Example: Littlest Higgs Φ± T ΦP γ0 U, C Arkani-Hamed/Cohen/ Katz/Nelson, 2002 h η t W ± Z J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Generic properties of Little Higgs Models I Extended scalar (Higgs-) sector Extended global symmetry I Specific functional form of the scalar potential I Extended fermion sector: new heavy top: T , maybe also U, C, . m Z0 Φ W 0 ± Φ±± Example: Littlest Higgs Φ± T ΦP γ0 U, C Arkani-Hamed/Cohen/ Katz/Nelson, 2002 h η t W ± Z J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Generic properties of Little Higgs Models I Extended scalar (Higgs-) sector Extended global symmetry I Specific functional form of the scalar potential 0 0 0 ± I Extended Gauge Sector: γ , Z , W J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Generic properties of Little Higgs Models I Extended scalar (Higgs-) sector Extended global symmetry I Specific functional form of the scalar potential 0 0 0 ± I Extended Gauge Sector: γ , Z , W I Extended fermion sector: new heavy top: T , maybe also U, C, . m Z0 Φ W 0 ± Φ±± Example: Littlest Higgs Φ± T ΦP γ0 U, C Arkani-Hamed/Cohen/ Katz/Nelson, 2002 h η t W ± Z Low-energy effective theory ⇒ integrating out heavy degrees of 2 2 freedom in path integrals, set up Power Counting: v /F Kilian/JR, 2003 I Experimental precision @ level consistent with truncation of 2 2 expansion at order v /F h Little Higgs Effective Field Theory: SM + Dimension 6 Operators 2 Constraints from contact interactions (SLC/LEP): F & c ×(4.5 TeV) ♦ Constraints evaded ⇐⇒ c 1 γ0,Z0,W 0, ± superheavy (O(Λ)) decouple from fermions J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Phenomenology of Little Higgs Models I Constraints from past/present experiments? Questions: I What can future experiments do? I Signatures? Distinction from other models? I Experimental precision @ level consistent with truncation of 2 2 expansion at order v /F h Little Higgs Effective Field Theory: SM + Dimension 6 Operators 2 Constraints from contact interactions (SLC/LEP): F & c ×(4.5 TeV) ♦ Constraints evaded ⇐⇒ c 1 γ0,Z0,W 0, ± superheavy (O(Λ)) decouple from fermions J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Phenomenology of Little Higgs Models I Constraints from past/present experiments? Questions: I What can future experiments do? I Signatures? Distinction from other models? Low-energy effective theory ⇒ integrating out heavy degrees of 2 2 freedom in path integrals, set up Power Counting: v /F Kilian/JR, 2003 J. Reuter The Big Deal with the Little Higgs Edinburgh, 8.12.2005 Phenomenology of Little Higgs Models I Constraints from past/present experiments? Questions: I What can future experiments do? I Signatures? Distinction from other models? Low-energy effective theory ⇒ integrating out heavy degrees of 2 2 freedom in path integrals, set up Power Counting: v /F Kilian/JR, 2003 I Experimental precision @ level consistent with truncation of 2 2 expansion at order v /F h Little Higgs Effective Field Theory: SM + Dimension 6 Operators 2 Constraints from contact interactions (SLC/LEP): F & c ×(4.5 TeV) ♦ Constraints evaded ⇐⇒ c 1 γ0,Z0,W 0, ± superheavy (O(Λ)) decouple from fermions Neutrino masses Kilian/JR, 2003; del Aguila et al., 2004; Han/Logan/Wang, 2005 Lepton-number violating interactions can generate neutrino masses J.
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