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.