Beyond the Standard Model Markus Luty UC Davis
Big Picture Three major paradigms for particle physics beyond the standard model • Supersymmetry “Logos” From the Greek: reason, word • Strong dynamics, extra dimensions “Stratus” From the Latin: a cover or spread; low-lying clouds “Chaos” • Multiverse From the Greek: formlessness, confusion
Outline “It is better to uncover a little, than to cover a lot.” V. Weisskopf 1. Motivation for new physics at the TeV scale 2. Strong Higgs sector 3. Composite Higgs/Little Higgs 4. Extra dimensions 5. Multiverse
Motivation
Effective Field Theory An old idea: approximate theory using only degrees of freedom that can be excited at low energy E.g. QED valid for E ≪ m µ Standard model breaks down at high energies ⇒ must be effective theory • Gravity: M Planck ∼ 10 19 GeV • Higgs self-interactions Also lots of concrete motivation for physics beyond standard model (Hambye, Riesselmann 1997) Neutrinos, dark matter, baryogenesis, strong CP problem, gauge coupling unification, origin of flavor,...
Effective Standard Model What effective theory describes our present understanding of strong/electroweak physics? Not the standard model! We haven’t found the Higgs... L e ff = L SM ( h 0 , A µ , W ± (unitary gauge) µ , Z µ , G µ , q, ℓ ) Equivalent to nonlinearly realized SU (2) W × U (1) Y → U (1) EM E E Expansion in powers of 4 π v ∼ TeV Example: WW scattering ∼ E 2 ∼ E 0 + + � �� � � �� � � �� � ∼ E 4 + E 2 + · · · ∼ E 4 + E 2 + · · · ∼ E 4 + E 2 + · · · ∼ E 4 + E 2 + · · · ∼ E 2 + · · ·
Higgs Sector Effective standard model breaks down at TeV scale ⇒ new physics below TeV! Higgs boson is only one possibility... Maybe the only appearance of Higgs at LHC
Naturalness Not a question of “canceling UV divergences...” Dependence of effective parameters on (more) fundamental ones L SM = − m 2 H H † H + · · · H † H invariant under all symmetries* ⇒ scale of new physics m H ∼ E.g. grand unification: H ∼ g 2 X X ∼ (10 15 GeV) 2 GUT ⇒ ∆ m 2 16 π 2 M 2 H H *Except supersymmetry
Is SUSY Natural? λ ∼ g 2 + 3 y 4 16 π 2 ln m ˜ Higgs quartic coupling: t t m t � �� � Z + 3 y 4 t v 2 16 π 2 ln m ˜ h 0 ∼ λ v 2 ∼ m 2 t ⇒ m 2 + m t t ˜ t h 0 > 114 GeV requires m ˜ m 2 ∼ 1 TeV t > ˜ H ∼ 3 y 2 t t ⇒ ∆ m 2 16 π 2 m 2 t ∼ (1 TeV) 2 ˜ ⇒ 1% tuning in MSSM Exactly the problem SUSY was meant to solve...
Naturalness Sector Naturalness breaks down at TeV scale ⇒ new physics at TeV scale? • SUSY? • Strong electroweak symmetry breaking? • Composite Higgs? All have problems... • Just the standard model?
Dark Matter Another hint for new physics at the TeV scale � − 1 � σ ann v Thermal weak-scale relic ⇒ Ω ∼ 0 . 1 pb Standard collider signature: missing energy Many models, wide range of predictions (including no collider signatures)
Summary Expect new physics at TeV colliders • Higgs sector Required • Naturalness sector Highly recommended • Dark matter Suggested Anything else is a welcome surprise...
Strong Higgs Sector
Classic Technicolor Weinberg 1976; Susskind 1976 Copy QCD... New gauge force strong at TeV scale SU ( N ) � U L � U R � � Y ( U R ) = Y ( Ψ L ) + 1 Ψ L = Ψ R = 2 D L D R Y ( D R ) = Y ( Ψ L ) − 1 2 � �� � � �� � SU (2) W SU (2) W doublet singlet � ¯ Ψ La Ψ b R � = Λ 3 TC δ ab Λ TC ∼ TeV ¯ Ψ L U R ∼ H ⇒ same symmetry breaking pattern as SM ¯ Ψ L D R ∼ H ∗
Is Technicolor Natural? L TC = − 1 4 H µ ν A H µ ν A +¯ Ψ i / D Ψ No singlet operator with dimension < 4 (c.f. ) L SM = − m 2 H H † H + · · · Technifermion mass forbidden by gauge invariance ¯ ΨΨ
Technicolor Signatures Higgs sector = strong TeV resonances E.g. WW scattering + + + · · · m ∼ TeV QCD suggests vector resonances most prominent Spin 0 “composite Higgs” may be absent or obscure f 0 (600) IG ( JPC ) = 0+(0 + +) or σ A REVIEW GOES HERE – Check our WWW List of Reviews f 0 (600) T-MATRIX POLE √ s f 0 (600) T-MATRIX POLE √ s f 0 (600) T-MATRIX POLE √ s f 0 (600) T-MATRIX POLE √ s Note that Γ ≈ 2 Im( � spole). VALUE (MeV) DOCUMENT ID TECN COMMENT (400–1200) − i (250–500) OUR ESTIMATE (400–1200) − i (250–500) OUR ESTIMATE (400–1200) − i (250–500) OUR ESTIMATE (400–1200) − i (250–500) OUR ESTIMATE PDG 2010
WW Scattering @ LHC Enhanced forward emission of W, Z A model-independent signal for strong Higgs sector (Chanowitz, Gaillard 1984) Cut Value for keeping events 5 σ discovery with 30 fb -1 for Leptonic W P T P T > 320 GeV Hadronic W P T P T > 320 GeV Hadronic W mass 66 . 09 < M < 101 . 89 GeV models with resonances Y-scale 1 . 55 < Y − scale < 2 . 0 Top veto 130 < M W+jet < 240 GeV Tag Jets P T > 20 GeV, E > 300 GeV, 2 . 0 < | η | < 4 . 5 E. Stefanidis ATLAS Thesis (2007) Hard Scatter P T P T < 50 GeV Number of mini-jets ( P T > 15 GeV with | η | < 2 . 0) 0
Problems with Technicolor • Top quark • Flavor mixing • Precision electroweak
Flavor in Technicolor Standard model → technicolor dim(¯ ( solves naturalness problem) H → ¯ ΨΨ ) = 3 ΨΨ 1 L SM = y t ¯ ( ¯ Q L t R )(¯ Q L Ht R + · · · → ΨΨ ) � + · · · Λ 2 � �� t dim = 6 Effective 4-fermion interaction can arise from heavy particle exchange (c.f. Fermi theory) scale where effective flavor theory breaks down Λ t = ∼ few TeV ⇒ must address flavor near TeV scale
Top in Technicolor Topcolor Walking/conformal technicolor Hill 1991
Conformal Technicolor H = operator in Higgs sector Consider general values of d = dim( H ) (unitarity) • d ≥ 1 dim( ¯ • Q L Ht R ) = 3 + d ⇒ want as small as possible d • Want dim( H † H ) ≥ 4 (naturalness) � �� � Not necessarily... ⇒ d ≤ 2 ? Possible in conformal (scale invariant) theories
Conformal Fixed Point β function in QCD with colors and flavors: N f N c g N f ∼ 1 ⇒ confining µ g N f ≃ 11 2 N c g ∗ ⇒ conformal µ Under active study by lattice community
Conformal Window a = N c g 2 perturbative expansion parameter 16 π 2 = x = N f = 11 continuous for large N c , N f 2 − ǫ N c β ( a ) ≃ − 3 ǫ a 2 + 3 4(75 − 26 ǫ ) a 3 + · · · a ∗ = 4 ǫ ⇒ perturbative fixed point at for ǫ ≪ 1 75 β ( a ) a a ∗ Expect “conformal window” for x c ≤ x < 11 2 Lattice studies suggest x c ≃ 4
Conformal Breaking g µ • Walking technicolor (Holdom 1985; Appelquist, Karabali, Wijewardhana 1986; Yamawaki, It “just does it” Bando, Matumoto 1986) Plausible at x = x c • Conformal technicolor: “forced out” (ML, Okui 2004) χ = sterile technifermion ∆ L = − m ¯ χχ Soft breaking of spacetime symmetry triggers electroweak symmetry breaking (c.f. SUSY)
Status of Flavor? 3 TeV dim( H ) = 3 � 1 / ( d − 1) � TeV Λ t ∼ TeV 10 TeV dim( H ) = 2 ∼ m t 50 TeV dim( H ) = 1 . 5 Still wanted: a complete theory of flavor without large flavor-changing neutral currents Complete theory still lacking (Something I’m working on...)
More Signals 1 ¯ L e ff = Q L Ht R + · · · Λ d − 1 t ⇒ production of strong resonances: J = 0 , CP = ± , I = 0 , 1 LHC Production Cross Section (fb) g 3 t 10 Pseudoscalar Scalar ϕ 0 Charged 2 10 g 10 g t t 1 ϕ ± b 1000 1500 2000 2500 3000 Resonance Mass (GeV) ϕ → WW suppressed for ⇒ can be narrow I = 1 Many interesting signals: ϕ 0 → ¯ tt, W + W − Z, ZZZ, . . . ϕ + → ¯ bt, W + W + W − , W + ZZ, . . . (Evans, ML 2009)
Precision Electroweak Effective theory below TeV contains gauge-violating terms 2 ∆ M 2 W µ ∆ L e ff = 1 3 W 3 µ − 1 2 ǫ W µ ν 3 B µ ν + · · · ⇒ leading corrections to γ , W, Z 0.5 Z lineshape V e G 0.4 asymmetries 0 0 0 W mass 1 = 0.3 V � scattering e G M H 0 : e scattering l 4 l 0.2 a 3 V = e APV G M H 7 ρ , T ∝ ∆ M 2 1 0.1 : l 1 l a = : M H y 0 g T V : r l e l e a G n e 7 w 1 -0.1 1 o S ∝ ǫ l = M H -0.2 -0.3 -0.4 -0.5 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 S Erler, Langacker 2010
Strong Higgs Sector 0.5 90% CL 0.4 m h, ref = 1 TeV 0.3 0.2 T 0.1 0 NDA QCD � 0.1 � 0.2 � 0.3 � 0.6 � 0.4 � 0.2 0 0.2 0.4 0.6 S QCD: assume scaled-up QCD dynamics, use QCD data NDA: all interactions → strong at TeV No reliable prediction for walking/conformal theories Not ruled out!
Summary Mandarin: crisis = danger + opportunity • A compelling solution to the naturalness problem dim( H † H ) ≥ 4 • Top quark Topcolor? dim( H ) < 3 ? • Flavor and precision electroweak do not rule it out • Distinctive signals at LHC
Experiment will Decide...
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