Supersymmetry, Dark Matter, and Neutrinos

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1 Supersymmetry, Dark Matter, and Neutrinos The Standard Model and Supersymmetry Dark Matter Neutrino Physics and Astrophysics The Physics of Supersymmetry

2 Gauge Theories Gauge symmetry requires existence of (apparently) massless spin-1 (vector, gauge) bosons Interactions prescribed up to group, representations, gauge coupling Analogous to QED (U(1)), but gauge self interactions for nonabelian groups Standard model: SU(3) SU(2) U(1) Application to strong (short range) confinement Application to weak (short range) spontaneous symmetry breaking (Higgs or dynamical) Unique renormalizable field theory for spin-1

3 QED Free electron equation, ( iγ µ ) x m ψ = 0, µ is invariant under U(1) (phase) transformations, ( iγ µ ) x m ψ = 0, where ψ e iβ ψ µ Not invariant under local (gauge) transf., ψ ψ e iβ(x) ψ, x ( x, t)

4 Introduce vector field A µ ( A, φ): ( iγ µ ) x + µ gγµ A µ m ψ = 0, (g = e = gauge coupling) is invariant under ψ e iβ(x) ψ, A µ A µ 1 β g x µ Quantization of A µ massless gauge boson Gauge invariance γ, long range force, prescribed (up to g) amplitude for emission/absorption e e p γ p

5 Non-Abelian n non-interacting fermions of same mass m: ( iγ µ ) x m ψ µ a = 0, a = 1 n, invariant under (global) SU(n) group, ψ 1. ψ n exp( i N β i L i ) ψ 1. ψ n i=1. L i are n n generator matrices; β i are real parameters; N = n 2 1. Generalize to other groups, representations, chiral (L R)

6 Gauge (local) transformation: β i β i (x) ( iγ µ x µδ ab + g ) N γ µ A iµ (L i ) ab mδ ab ψ b = 0. i=1 Gauge invariance implies: N (apparently) massless gauge bosons A iµ Specified interactions (up to g, group, representations), including self interactions g g 2 ψ a A iµ ψ b ig(l i ) ab γ µ

7 The Standard Model Gauge group SU(3) SU(2) U(1); gauge couplings g s, g, g ( u d ) L ( u d ) L ( u d ) L ( νe e ) u R u R u R ν er (?) d R d R d R e R ( L = left-handed, R = right-handed) L SU(3): u u u, d d d (gluons) SU(2): u L d L, ν el e L (W ± ); phases (W 0 ) U(1): phases (B) Heavy families (c, s, ν µ, µ ), (t, b, ν τ, τ )

8 Strong Interactions (QCD) Group SU(3), gauge coupling g s 8 massless gluons (G) Emission/absorption amplitude g s = O(1) (α s = gs 2 /4π 0.12) λ i are 3 3 SU(3) (Gell-Mann) matrices Diagonal in flavor Off diagonal in color Purely vector (parity conserving) u β i g s G i µ uα 2 λi αβ γ µ

9 Strength + gluon self-interactions confinement Yukawa model dipole-dipole QCD now very well established Short distance behavior (asymptotic freedom) Confinement, light hadron spectrum (lattice) Approximate global SU(3) L SU(3) R symmetry and breaking (π, K, η are pseudogoldstone bosons) Unique field theory of strong interactions

10 Electroweak Interactions Group SU(2) U(1); gauge bosons (W ±, W 0 ), B Gauge couplings g, g tan θ W g /g; e = g sin θ W W i µ ( ) i g 2 τ i 1 γ5 γ µ 2 B µ ig yγ µ ( ) 1 γ5 2 L, R transform differently parity violation (γ 5 ) y = weak hypercharge (U(1)); electric charge: q = τ y

11 The Weak Charged Current Fermi theory + W ± incorporated in SM and made renormalizable (β decay) n pe ν e ν µ N µ + hadrons Fermi constant G F 2 g2 8M 2 W Muon lifetime τ 1 = G2 F m5 µ 192π 3 G F = (2) 10 5 GeV 2 W mass from Higgs mechanism

12 Maximal P and C violation; CP conserved except for phases associated with family mixing (Cabibbo-Kobashi-Maskawa matrix) Excellent description of β, K, hyperon, heavy quark, µ, and τ decays, ν µ e µ ν e, ν µ n µ p, ν µ N µ X

13 Quantum Electrodynamics (QED) Incorporated into standard model e p γ e V (r) = q 1q 2 r e = g sin θ W p Photon field (massless) Orthogonal Z field (massive) γ = +B cos θ W + W 0 sin θ W Z = B sin θ W + W 0 cos θ W

14 Positron electric charge: e = g sin θ W, where tan θ W g /g Flavor and color diagonal Purely vector (parity conserving): L and R fields have same charge Spectacularly successful Many low energy tests (e.g., cesium hfs, e anomalous magnetic moment, etc., to few 10 8 ) m γ < ev Muon g 2 sensitive to new physics. Anomaly? Running α(q 2 ) observed High energy well-measured

15 The Weak Neutral Current Prediction of SU(2) U(1) Neutral boson orthogonal to photon Z = B sin θ W + W 0 cos θ W Massive by Higgs mechanism Purely weak processes: ν µ p ν µ p

16 Parity-violating interference with electromagetic e e p γ p e e p Z p WNC discovered 1973: Gargamelle at CERN, HPW at FNAL Flavor and color diagonal Parity violated but not maximally Fermion couplings depend on sin 2 θ W Strength G F 2 = g2 + g 2 8M 2 Z = g2 8M 2 W Tested in many processes: νe νe, νn νn, νn νx; e D ex; atomic parity violation; e + e, Z-pole reactions

17 Gauge Self-Interactions Three and four-point interactions predicted by gauge invariance Indirectly verified by radiative corrections, α s running in QCD, etc. Strong cancellations in high energy amplitudes would be upset by anomalous couplings Tree-level diagrams contributing to e + e W + W

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19 Spontaneous Symmetry Breaking Gauge invariance implies massless gauge bosons and fermions Weak interactions short ranged spontaneous symmetry breaking for mass; also for fermions Color confinement for QCD gluons remain massless Allow classical (ground state) expectation value for spin-0 field v = 0 ϕ 0 = constant µ v 0 increases energy, but important for monopoles, strings, domain walls

20 SU(2) U(1): introduce Higgs doublet ϕ = ( ϕ + ϕ 0 ) Allow 0 ϕ 0 0 = ν/ 2 (ν = real) Minimize potential energy (from equations of motion) V (ν) = 1 2 µ2 ν λν4, with λ > 0, to find ν For µ 2 < 0, minimum at V (ν) = ν(µ 2 + λν 2 ) = 0 ν = ( µ 2 /λ ) 1/2

21 ϕ 0 is neutral, so U(1) Q unbroken SU(2) U(1) Y U(1) Q, where Q = L 3 + Y Interaction with classical field ν gives effective masses to W, Z, and fermions W g 2 W ν M W = gν 2 ν ψ L h ψ ψ R ν = 2 ϕ 0 m ψ = h ψ ν Fermi constant G F 2 g2 8M 2 W = 1 ν 246 GeV (electroweak scale) 2ν2 Muon lifetime τ 1 = G2 F m5 µ 192π 3 G F = (2) 10 5 GeV 2

22 g = e/ sin θ W, where α = e 2 /4π 1/ M W = M Z cos θ W (πα/ 2G F ) 1/2 sin θ W Weak neutral current: sin 2 θ W 0.23 M W 78 GeV, and M Z 89 GeV (increased by 2 GeV by loop corrections) Discovered at CERN: UA1 and UA2, 1983 Current: M Z = ± M W = ± 0.034

23 The Higgs Scalar H Quantize around classical value of ϕ ϕ 1 2 ( 0 ν + H ) Higgs potential: V µ4 4λ µ2 H 2 + λνh 3 + λ 4 H4 Fourth term: Quartic self-interaction Third: Induced cubic self-interaction Second: (Tree level) H mass-squared, M H = 2µ 2 = 2λν

24 No a priori constraint on λ except vacuum stability (λ > 0 0 < M H < ), but Theoretical constraints (SM): 115 GeV < M H < 750 GeV Experimental bound (LEP 2), e + e Z ZH M H GeV at 95% cl Hint of signal at 115 GeV Indirect (precision tests): M H < 215 GeV, 95% cl MSSM: much of parameter space has standard-like Higgs with M H < 130 GeV >

25 Γ, σ, R, R Z had l q asymmetries ν scattering M W m t 200 all data 90% CL M H [GeV] excluded m t [GeV]

26 First term in V : vacuum energy 0 V 0 = µ 4 /4λ No effect on microscopic interactions, contribution to cosmological constant but gives negative Λ SSB = 8πG N 0 V Λ obs Require fine-tuned cancellation Λ cosm = Λ bare + Λ SSB Also, QCD contribution from SSB of global chiral symmetry

27 Precision Electroweak Tests WNC, W, and Z are primary test/prediction of electroweak model

28 The Z Pole Observables: LEP and SLC (01/03) Quantity Group(s) Value Standard Model pull M Z [GeV] LEP ± ± Γ Z [GeV] LEP ± ± Γ(had) [GeV] LEP ± ± Γ(inv) [MeV] LEP ± ± 0.15 Γ(l + l ) [MeV] LEP ± ± σ had [nb] LEP ± ± R e LEP ± ± R µ LEP ± ± R τ LEP ± ± A F B (e) LEP ± ± A F B (µ) LEP ± A F B (τ ) LEP ±

29 Quantity Group(s) Value Standard Model pull R b LEP/SLD ± ± R c LEP/SLD ± ± R s,d /R (d+u+s) OPAL ± ± A F B (b) LEP ± ± A F B (c) LEP ± ± A F B (s) DELPHI/OPAL ± ± A b SLD ± ± A c SLD ± ± A s SLD ± ± A LR (hadrons) SLD ± ± A LR (leptons) SLD ± A µ SLD ± A τ SLD ± A e (Q LR ) SLD ± A τ (P τ ) LEP ± A e (P τ ) LEP ± Q F B LEP ± ±

30 Implications SM correct and unique to zeroth approx. (gauge principle, group, representations) SM correct at loop level (renorm gauge theory; m t, α s, M H ) TeV physics severely constrained (unification vs compositeness) Precise gauge couplings (gauge unification)

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32 Problems with the Standard Model Standard model: SU(2) U(1) (extended to include ν masses) + general relativity Mathematically consistent, renormalizable theory Correct to cm However, too much arbitrariness and fine-tuning (O(20) parameters, not including ν masses/mixings, which add at least 7 more, and electric charges)

33 Gauge Problem complicated gauge group with 3 couplings charge quantization ( q e = q p ) unexplained Possible solutions: strings; grand unification; magnetic monopoles (partial); anomaly constraints (partial) Fermion problem Fermion masses, mixings, families unexplained Neutrino masses, nature? CP violation inadequate to explain baryon asymmetry Possible solutions: strings; brane worlds; family symmetries; compositeness; radiative hierarchies. New sources of CP violation.

34 Higgs/hierarchy problem Expect M 2 H = O(M 2 W ) higher order corrections: δm 2 H /M 2 W 1034 Possible solutions: supersymmetry; dynamical symmetry breaking; large extra dimensions; Little Higgs Strong CP problem Can add θ 32π 2 g 2 s F F to QCD (breaks, P, T, CP) d N θ < 10 9 but δθ weak 10 3 Possible solutions: spontaneously broken global U(1) (Peccei- Quinn) axion; unbroken global U(1) (massless u quark); spontaneously broken CP + other symmetries

35 Graviton problem gravity not unified quantum gravity not renormalizable cosmological constant: Λ SSB = 8πG N V > Λ obs ( for GUTs, strings) Possible solutions: supergravity and Kaluza Klein unify strings yield finite gravity. Λ?

36 The Two Paths: Unification or Compositeness The Bang unification of interactions grand desert to unification (GUT) or Planck scale elementary Higgs, supersymmetry (SUSY), GUTs, strings possibility of probing to M P and very early universe hint from coupling constant unification tests light (< GeV) Higgs (LEP 2, TeV, LHC) absence of deviations in precision tests (usually) supersymmetry (LHC) possible: m b, proton decay, ν mass, rare decays SUSY-safe: Z ; seq/mirror/exotic fermions; singlets variant versions: large dimensions, low fundamental scale, brane worlds

37 The Whimper onion-like layers composite fermions, scalars (dynamical sym. breaking) not like to atom nucleus +e p + n quark at most one more layer accessible (LHC) rare decays (e.g., K µe) severe problem no realistic models effects (typically, few %) expected at LEP & other precision observables (4-f ops; Zb b; ρ 0 ; S, T, U) anomalous V V V, new particles, future W W W W recent variant: Little Higgs

38 Supersymmetry Fermion Boson symmetry Motivations stabilize weak scale M SUSY < O(1 TeV) supergravity (gauged supersymmetry): unification of gravity (non-renormalizable) string/m theory (finite TOE) coupling constants in supersymmetric grand unification decoupling of heavy particles (precision, CP, FCNC)

39 Consequences additional charged and neutral Higgs particles M 2 < cos 2 2βM 2 H 0 Z + H.O.T. (O(m4 t )) < (150 GeV)2 cf., standard model: M H 0 < 750 GeV superpartners q q, scalar quark (spin-0) l l, scalar lepton (spin-0) H H, Higgsino (spin-1/2) G g, gluino (spin-1/2) W w, wino (spin-1/2) γ γ, photino (spin-1/2) Z z, zino (spin-1/2) typical scale: several hundred GeV LSP: cold dark matter candidate SUSY breaking large m t