Beyond the Standard Model

Transcription

1 Beyond the Standard Model The Standard Model Problems New Physics Supersymmetry Extended Gauge Structures Grand Unification Based on The Standard Model and Beyond, CRC Press, 12/09

2 The Standard Model Standard model: SU(2) U(1) (extended to include ν masses) + QCD + general relativity Mathematically consistent, renormalizable theory Correct to cm QCD: short distance, long distance symmetries QED, WCC, WNC, W, Z Gauge self-interactions Missing: Higgs (or alternative), dark matter, dark energy

3 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 (8 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 )

4 Quantum Chromodynamics (QCD) QCD now very well established Short distance behavior (asymptotic freedom) Confinement, light hadron spectrum (lattice) g s = O(1) (α s (M Z ) = gs 2 /4π 0.12) Strength + gluon self-interactions confinement Yukawa model dipole-dipole Approximate global SU(3) L SU(3) R (π, K, η are pseudo-goldstone bosons) symmetry and breaking Unique field theory of strong interactions

5 Quantum Chromodynamics (QCD) Modern theory of the strong interactions Average Hadronic Jets e + e - rates Photo-production Fragmentation Z width ep event shapes Polarized DIS Deep Inelastic Scattering (DIS)! decays Spectroscopy (Lattice) " decay # s (M Z )! s (µ) µ GeV 22nd Henry Primakoff Lecture Paul Langacker (3/1/2006)

6 Quantum Electrodynamics (QED) Experiment Value of α 1 Precision e ae = (ge 2)/ (94) [ ] h/m (Rb, Cs) (69) [ ] 0.33 ± 0.69 Quantum Hall (25) [ ] 3.3 ± 2.5 h/m (neutron) (28) [ ] 8.0 ± 2.8 γ p, 3 He (J. J.) (43) [ ] 12.2 ± 4.3 µ + e hyperfine (80) [ ] 2.0 ± 8.0 Spectacularly successful: Most precise: e anomalous magnetic moment α Many low energy tests to few 10 8 m γ < ev, Running α(q 2 ) observed q γ < e Muon g 2 sensitive to new physics. Anomaly?

7 The Electroweak Theory QED and weak charged current unified f f u i Weak neutral current (Z) predicted (νn νx, atomic parity violation) f ieq f γ µ γ Z f g i γ 2 cos θ µ (g f W V gf A γ5 ) W + d j i g 2 2 γµ (1 γ 5 )V qij Stringent tests of WCC, CP - violation, WNC, Z-pole, beyond Fermion gauge and gauge self interactions ig 2 J ν 2 W W ig 2 2 J µ W ig 2 cos θ W J ν Z Z ig 2 cos θ W J µ Z W W + W W + W W + ν e γ Z e e + e e + e e + Typeset by FoilTEX 1

8 Cross-section (pb) Z e + e hadrons 10 2 CESR DORIS PEP W + W - 10 KEKB PEP-II PETRA TRISTAN SLC LEP I LEP II Centre-of-mass energy (GeV) η excluded area has CL > 0.95 α γ sin 2β ε K γ m d α & m s m d ρ V ub ε K β CKM f i t t e r ICHEP 08 sol. w/ cos 2β < 0 (excl. at CL > 0.95) α " WW (pb) LEP PRELIMINARY YFSWW/RacoonWW no ZWW vertex (Gentle) only # e exchange (Gentle) /02/2005!s (GeV)

9 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) Consistent with light elementary Higgs Precise gauge couplings (SUSY gauge unification) Measurement Fit O meas O fit /σ meas α (5) had (m Z ) ± m Z [GeV] ± Γ Z [GeV] ± σ 0 had [nb] ± R l ± A 0,l fb ± A l (P τ ) ± R b ± R c ± A 0,b fb ± A 0,c fb ± A b ± A c ± A l (SLD) ± sin 2 θ lept eff (Q fb ) ± m W [GeV] ± Γ W [GeV] ± m t [GeV] ± August

10 The Higgs Mechanism Gauge symmetry forbids elementary masses for W, Z, fermions Introduce Higgs field H, with classical value ν and potential energy V (ν) = 1 2 µ2 ν λν4 W, Z, fermions acquire effective masses by coupling to H (transparent to photon) V (φ) W W ν ν e L e L g 2 g 2 h e h e ν ν ν ν φ W W ν ν e R e R

11 Higgs mass M H = 2µ 2 = 2λν (ν 246 GeV, λ unknown) all data (90% CL) LEP search e + e Z ZH: M H > GeV M H [GeV] Γ Ζ, σ had, R l, R q asymmetries M W low-energy m t excluded Indirect (electroweak radiative corrections)) + direct: M H < 167 GeV (95%) Tevatron searches now sensitive enough for higher masses LHC will cover full range for standard model Higgs % CL Limit/SM m t [GeV] 10 1 Tevatron Run II Preliminary, L= fb -1 LEP Exclusion SM Expected Observed ±1σ Expected ±2σ Expected Tevatron Exclusion March 5, m H (GeV/c 2 )

12 Problems with the Standard Model Lagrangian after symmetry breaking: L = L QCD + L gauge + L Higgs + i g ( ) 2 J µ W 2 W µ + J µ W W + µ ej µ Q A µ ( ψ i i m i m ) ih ψ i ν g 2 cos θ W J µ Z Z µ Standard model: SU(2) U(1) (extended to include ν masses) + QCD + general relativity Mathematically consistent, renormalizable theory Correct to cm

13 However, too much arbitrariness and fine-tuning: O(27) parameters (+ 2 for Majorana ν) and electric charges Gauge Problem complicated gauge group with 3 couplings (only EW chiral) 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? Probe of Planck/GUT scale? CP violation inadequate to explain baryon asymmetry Possible solutions: strings; brane worlds; family symmetries; compositeness; radiative hierarchies. New sources of CP violation.

14 Higgs/hierarchy problem H H λ H H W g 2 H Expect M 2 H = O(M 2 W ) higher order corrections: δm 2 H /M 2 W 1034 H g W W g H H h f f h H Possible solutions: supersymmetry; dynamical symmetry breaking; large and/or warped extra dimensions; Little Higgs; anthropically motivated fine-tuning (split supersymmetry) (landscape) Strong CP problem Typeset by FoilTEX Can add θ 32π 2 g 2 s F F to QCD (breaks, P, T, CP) d N θ < 10 11, 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

15 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 cosm = Λ bare + Λ SSB. Anthropically motivated fine-tuning (landscape)?

16 Necessary new ingredients Mechanism for small neutrino masses Planck/GUT scale? Small Dirac (intermediate scale)? Mechanism for baryon asymmetry? Electroweak transition (Z or extended Higgs?) Heavy Majorana neutrino decay (seesaw)? Decay of coherent field? CPT violation? What is the dark energy? Cosmological Constant? Quintessence? Related to inflation? Time variation of couplings?

17 What is the dark matter? Lightest supersymmetric particle? Axion? Suppression of flavor changing neutral currents? Electric dipole moments? Proton decay? Automatic in standard model, but not in extensions

18 New Physics A new layer at the TeV scale Compositeness, Little Higgs, twin Higgs, Higgless, dynamical symmetry breaking, strong dynamics Precision electroweak constraints, FCNC, UV completions? Large and/or warped extra dimensions; possible low fundamental scale Unification at the Planck scale, M P = G 1/2 N GeV Supersymmetry (between fermions and bosons), grand unification, strings? Top-down remnants: Z, W, extended Higgs, exotic fermions,

19 Supersymmetry Implications Formalism The MSSM Further Aspects -1! i ! i Standard Model! 1 "1! 2 "1! 3 " log 10 µ (GeV) Supersymmetric Standard Model M SUSY = M Z! 1 "1! 2 "1! 3 " log 10 µ (GeV)

20 Motivations for Supersymmetry Incorporation of gravity (but M SUSY could be very large) Stabilization of electroweak scale But landscape ideas (anthropically-motivated fine tuning); variants (e.g., split supersymmetry) Alternatives: LED, DSB, Little Higgs Gauge unification Cold dark matter (LSP) if R P conserved Z-pole: any new physics decouples Radiative electroweak breaking (large m t m 2 Hu < 0)

21 Stabilization of Electroweak Scale H h t t L t R h t H H φ r λ r H H κ r φ r κ r H Top quark contribution: M 2 H t = in c ( ih t ) 2 Z d 4 k (2π) 4 Tr N c(h t ) 2 Λ 2 4π 2 Λ M P GeV φ r i k m t i k m t GeV 2 «Introduce two complex scalars, L = λ r H 2 φ r φ r M 2 H φr λ rn c 8π 2 Typeset by FoilTEX 1 Finite for λ 1 = λ 2 = h 2 t. Corrections O(ln m t/m r ). Λ2

22 The Spectrum Use L-chiral fermions/antifermions, u L, u c L (u R {z} u c L and uc R CP {z} u L not independent) CP (Weyl spinors) Each particle requires new S = ± 1 sparticle 2 No known particles can be partners Chiral supermultiplets (spin- 1 Weyl spinor, spin-0 complex scalar) 2 q L, q L (squark); q c L, qc L ; l L, l L (slepton); l c L, l c L h + «u h 0 Two Higgs doublets h u = h 0 d, h d = u h d «and Higgsinos: h u, h d Two needed for anomaly cancellation and fermion masses λ replaced by gauge couplings M 2 h 0 < cos 2 2β M 2 Z at tree level

23 Vector supermultiplets (spin-1 gauge boson and spin- 1 2 Weyl spinor: gauge bosons G i, W i, B and gauginos G i, W i, B Gauginos and Higgsinos mix: Dirac charginos ( χ ± 1,2 ), Majorana neutralinos ( χ 0 1,2,3,4 ) Gravity supermultiplet (spin-2 graviton and spin- 3 2 gravitino) spin-0 spin- 1 2 ũl d L «ul d L «ũ c L d c L u c L dc L νl ẽ L νl e L ««ν c L ẽc L ν c L ec L G h +! 0 1 u h h0 d u h A d W i h B +! 0 u h h 0 1 d u h A {z d } χ 0, χ ± spin-1 G W {z i B} W ±,Z,γ spin- 3 2 spin-2 g 3/2 g

24 Mass splitting due to SUSY breaking in hidden sector (need mediation mechanism) Sparticle masses do not require electroweak breaking Typical predicted spectrum 800 m [GeV] g t ũ L, d R ũ R, d L b2 b1 400 H 0, A 0 H± χ 0 χ χ ± 2 t ll ν l τ 2 χ 0 2 χ ± h 0 lr τ 1 χ 0 1 0

25 Formalism Extend space-time x = (t, x ) to include (anticommuting) Grassmann coordinates θ and θ θ (spinor indices suppressed) Left-chiral superfield: Φ(x, θ, θ) = φ(y) + 2θξ(y) + θθf (y) φ = complex scalar, ξ = Weyl spinor, F = auxiliary field, y µ x µ iθσ µ θ Vector superfield (Wess-Zumino gauge): V (x, θ, θ) = θσ µ θa µ (x) + θθ θ λ(x) + θ θθλ(x) + 1 2θθ θ θd(x) A µ = gauge field, λ = gaugino, D = auxiliary field

26 Superpotential: W (Φ a ) contains supersymmetric mass terms, Yukawa couplings, and scalar self-interactions e.g., W = µ ab Φ a Φ b + h abc Φ a Φ b Φ c (holomorphic: no Φ ) L W = 1 2 V (φ) = X a X ξ a ξ b a,b 2 W Φ a Φ b {z θ= θ=0 } W ab (φ) V (φ) F a 2, with F a = W Φ a θ= θ=0 [W a (φ)] (Φ a = φ a + 2θξ a + θθf a )

27 Up quark U + U c and Higgs H, with W = muu c + h u UU c H for h u = 0: L = L KE m (ū R u L + ū L u R ) m 2 ` ũ 2 + ũ c 2 for h u 0: L = L KE L u V (ũ, ũ c, h), V = mũ c + h u ũ c h 2 + mũ + h u ũh 2 + hu ũũ c 2 L u = m (ū R u L + ū L u R ) h u ū R u L h + ū L u R h h u h c R u Lũ c + ū L h c Rũc h u ū R h L ũ + h L u R ũ u R h c R u R ih u h ih u ũ c ih u ũ u L u L h L

28 Kähler potential (Hermitian): K(Φ, Φ, V ) contains (matter) kinetic energy, gauge interactions e.g., K = P a Φ a Φ a or P a Φ a e2gq av Φ a Abelian U(1), single chiral field, q = 1 W = 0 L = 1 4 F µνf µν + i λ σ µ µ λ + ( µ + iga µ )φ + i ξ σ µ ( µ + iga µ )ξ 2g( ξ λφ + φ λ ξ) V (φ) V (φ) = 1 2 D 2 = 1 κ + gφ φ (V = θσ µ θaµ + θθ θ λ + θ θθλ + 1 θθ θ θd) 2 κ = Fayet-Iliopoulos term; absent for non-abelian

29 Non-abelian case L = 1 4 F i µν F iµν + i λ σ µ D λµ λ 1 X ξ a ξ b W ab (φ) + ξ ξ a b W ab (φ) 2 a,b + h(d Φµ φ) D µφ φ + i ξ σ µ D Φµ ξ 2g( ξ λ i i L i Φ φ + φ λ i L i Φ ξ V (φ) V (φ) = V F + D D = X F a a λ j ψ M al X D i 2, D i = gφ L i Φ φ i φa A i µ A i µ A i µ λ k M g γ µ c ijk ψ al ψ bl ig γ µ P L L i Φ ab φa φ b ig ( pa + p b ) µ L i Φ ab λ i M λ i M φ b i 2gP R L i Φ ab ψ bl i 2gP L L i Φ ab Supersymmetry breaking soft terms (Majorana gaugino masses, scalar masses, scalar trilinears)

30 The Minimal Supersymmetric Standard Model (MSSM) Chiral superfields: Q H u = H + u H 0 u ««U D H 0 «d H d = H d U c D c ; L N E «N c E c ; Superpotential (assuming R P conservation): W = µh u H d Γ d QH d D c + Γ u QH u U c Γ e LH d E c + Γ ν LH u N c = µ H + u H d H0 u H0 d Γ d UH d DH0 d D c + Γ u UH 0 u DH+ u U c Γ e NH d EH0 d E c + Γ ν NH 0 u EH+ u N c µ is supersymmetric mass for Higgs/Higgsino. Must be comparable to SUSY breaking (they jointly set EW scale). Why? (µ problem)

31 Soft breaking L soft = X r m G 2 m 2 r φ r φ r m B 2 B B + 8X G i G i + G i G i + i=1 B B m W 2 3X W i W i + i=1 h Bµh u h d + A d Γ d qh d d c A u Γ u qh u ũ c + A e Γ e lh d ẽ c A ν Γ ν lh i u ν c + h.c. W i W General MSSM (with R P ): 128 parameters (+N c ), severe problems with FCNC, EDMs

32 Minimal supergravity: SUGRA mediation: five new (real) parameters (4 at M P ) m 0, M 1/2, A 0, B, µ }{{} universal soft breaking }{{} Why small? m 0, M 1/2, A 0, tan β ν u /ν d, M Z, sign(µ) Specific models (e.g., dilaton) further relations RGE to electroweak scale Many other models: gauge mediation, anomaly, gaugino, Z,

33 The Higgs Sector Higgs doublets: h u = h + u h 0 u «, h d = h 0 d h d «V (h u, h d ) =V F + V D + V soft V F = µ 2 h u 2 + h d 2 V D = g2 8 h u τ h u + h d τ h d = g2 + g g 2 8 h u 2 h d 2 2 g V soft =m 2 hu h u 2 + m 2 h d h d 2 h Bµ h u 2 h d 2 2 h + u h0 d h0 u h d h 0 u h0 d h+ u h d 2 i + h.c., Charge, CP conservation automatic at tree level (but possible charge/color breaking from squarks at large A)

34 Let h 0 u,d ν u,d 2, tan β ν u νd, ν 2 ν 2 u + ν2 d V (ν u, ν d ) = 1 2 m2 u ν2 u m2 d ν2 d Bµν uν d + g2 + g 2 = 1 2 (ν u ν d ) M 2 νu ν d «+ g2 + g 2 32 (246 GeV)2 2 ν 2 u 32 ν2 d 2 ν 2 u ν2 d where m 2 u µ 2 +m 2 h u, m 2 d µ 2 +m 2 h d, M 2 ( m 2 u Bµ Bµ m 2 d ) For m 2 u + m2 d > 2Bµ and m2 u m2 d < (Bµ)2 µ 2 = M 2 Z 2 + m 2 hu tan2 β m 2 h d tan 2 β 1 sin 2β = 2Bµ m 2 u + m2 d = 2Bµ M 2 A

35 Scalars h, H, pseudoscalar A, charged Higgs H ±. At tree level M 2 A = m2 u + m2 d, M 2 H ± = M 2 A + M 2 W M 2 h,h = 1» M 2 A 2 + M 2 Z q`m 2 A + MZ 2 2 4M 2 Z MA 2 cos2 2β M 2 h M 2 Z cos2 2β M 2 Z Large loop corrections: "!!# M 2 h < M 2 Z + 3g2 m 4 t 8π 2 M 2 W ln M 2 S m 2 t + X2 t M 2 S 1 X2 t 12M 2 S M 2 S = 1 2 (m2 t 1 + m 2 t 2 ), X t = stop mixing M h 130 GeV (need tan β 5 10)

36 h is SM-like in decoupling limit M A M Z M h > GeV Z Zh limit weaker for small M A, but Z ha experimental errors 95% CL: LEP2/Tevatron (today) LEP2/Tevatron (8 fb -1 ) 8 fb -1 :!m t = 1.2 GeV,!M W = 20 MeV light SUSY M W [GeV] M H = 114 GeV SM M H = 400 GeV MSSM SM MSSM both models heavy SUSY Heinemeyer, Hollik, Stockinger, Weber, Weiglein m t [GeV]

37 Enhanced Yukawa couplings to b, τ m t L Y uk = ν sin β tt (cos αh + sin αh) + m t m b ν cos β bb ( sin αh + cos αh) i ν tan β tγ 5 t A i m b ν tan β bγ 5 b A h 2m t ν tan β t R b L H + 2mb + tan β b i R t L H + + h.c. ν

38 Squarks and Sleptons Mass matrix Lũ = ũ L ũ R δũl,r = cos 2βM 2 Z m 2 ũ + m 2 L u + δ ũ L X u m! «u ũl X u m u m 2 ũ + m 2 R u + δ ũ R ũ R i ht 3 ũl,r sin 2 θ W qũl,r, X u A u µ cot β Usually little mixing between families Usually squarks heavier ( t 1 lightest) than sleptons Typical decays ũ u χ 0 i, ũ d χ+ i

39 Gluinos Soft Majorana masses m G Strong QCD gluino pair production Cascade decays, e.g., G qqe ν e + χ 0 1 G G l + l, l ± l ± at same rate Danger of strong FCNC vertices from quark-squark mixing mismatch (unless degenerate squarks, alignment, heavy G); (also χ 0 i ) s K 0 G d γ, Z, G d, s, b d, s, b d, s, b d, s, b G G d K 0 s b s

40 4 Majorana neutralinos L χ 0 = 1 B W 3 h 0 h 0 d u 2 Neutralinos, and Charginos 0 m B 0 g ν d 2 0 m W g ν d 2 g νu 2 gν d 2 gν u 2 gν d 2 0 µ g νu 2 gν u 2 µ C B B W 3 h 0 d h 0 u 1 C A +h.c. 2 Dirac charginos L χ ± = W + h + u m W gν d 2 gνu 2 µ! W h d! + h.c. Some mediation schemes: gaugino unification: m G : m W : m B α 3 : α 2 : α 1 7 : 2 : 1

41 Supersymmetry Breaking and Mediation Spectral sum rules: supersymmetry broken in hidden sector F term breaking: (Φ = φ + 2θξ + θθf ) φ = 0 gauge symmetry broken (Higgs) F = 0 supersymmetry broken Can also be dynamical F term, e.g., gaugino condensate λλ = 0, where λ is gaugino of hidden sector group m 3/2 F/M P Alternative: D-term breaking Supergravity: mediation by higher-dimensional operators suppressed by M P K X XΦ Φ M 2 P m φ F X /M P = O(m 3/2 ) O(TeV)

42 Gauge mediation: some direct coupling between sectors Example: W XΨΨ c, Ψ charged under SM m ψ = m ψ c = φ X M, m 2 ψ = M 2 Scalar eigenvalues M 2 ± F X Transmitted to SM by gauge interactions m G m q = O( α s F XM 4π ) Typically, F X M GeV Light gravitino LSP (e.g., ev-kev) NLSP decay, e.g., χ 0 1 γg 3/2 or τ τ g 3/2 F X F X M 2 «ψ G G G q q ψ q

43 Tevatron, LHC Signatures Squarks, gluinos pair-produced at large rate by QCD Sleptons, charginos, neutralinos: smaller direct rate (Drell-Yan and t-channel squark), but occur in squark decay chains q Missing transverse energy: end in LSP (e.g., χ 0 1 in supergravity) decay chains Cascade decays multiple jets and leptons (same/opposite sign dileptons, trileptons); kinematic edges (mass eigenstates); some spin information Same sign leptons Majorana fermions q L χ 0 2 R χ 0 1

44 Effective 4-jet mass: E T + Σ 4 i=1 pi T Ú ÒØ ¼ Î ½¼ ½ Å «Îµ

45 OS-SF l + l mass from χ 0 2 l+ l χ Events/1 GeV/100 fb (GeV) m ll

46 M 1/2 (GeV) g(2500) L dt = 10 fb -1 tan(β) = 10, µ > 0, A 0 = CMS g(3000) ~ miss E T (100 fb -1 ) L dt = 1, 10, 100, 300 fb -1 A 0 = 0, tanβ= 35, µ > 0 miss E T (300 fb -1 ) h(123) g(2500) ~ l 2l OS 3l g(1500) g(2000) E T miss 0l 2l SS q(2000) q(2500) m 1/2 (GeV) TH q(2000) ~ g(2000) ~ miss E T (10 fb -1 ) q(2500) ~ g(1500) ~ q(1500) Ωh 2 = 0.4 Ωh 2 = 1 q(1500) ~ miss E T (1 fb -1 ) 400 g(1000) 400 g(1000) ~ q(1000) q(1000) ~ 200 g(500) q(500) 200 q(500) ~ h(110) Ωh 2 = 0.15 g(500) ~ EX DD_ M 0 (GeV) m 0 (GeV)

47 The Anomalous Magnetic Moment of the Muon Possible discrepancy a exp µ = (5.4)(3.3) a SM µ = (58) a µ = a exp µ a SM µ = 292(86) (3.4σ) Smaller (0.9σ) effect using hadronic τ decays SUSY loops for low scale? (m SUSY 67 tan β GeV) γ γ µ µ χ χ χ 0 µ µ ν µ µ

48 R-Parity Usually impose R p = ( 1) 3(B L)+2S conservation Lightest superpartner (LSP) stable (CDM candidate) Supergravity: χ 0 1 Gauge mediation: gravitino (g 3/2 ). NLSP may decay promptly, with displaced vertex, or outside the detector (e.g., χ 0 1 γg 3/2 or l lg 3/2 ) R P violation L violating: W LH u, LLĒ, LQ D B violating: W ŪŪ D (cannot have both) No missing energy signature Multi jets or leptons No CDM candidate (axion?)

49 Gauge Unification Precise gauge couplings (Z-pole, QCD) 1 α i (Q 2 ) = 1 α i (MZ 2 ) 4πb i ln Q B A = 1 10 B 16π 19 C 6 A 7 b 1 b 2 b 3 = 1 16π 2 0 GUT normalization: α 3 = α s, C A SM M 2 Z MSSM α 2 = g2 4π, α 1 = 5 3 g 2-1! i ! i Standard Model! 1 "1! 2 "1! 3 " log 10 µ (GeV) Supersymmetric Standard Model M SUSY = M Z! 1 "1! 2 "1! 3 "1 4π log 10 µ (GeV)

50 Supersymmetry Conclusions Advantages Incorporation of gravity (but M SUSY could be very large) Stabilization of electroweak scale (but not unique) Gauge unification Cold dark matter (LSP) if R P conserved Elegant and simple in principles Drawbacks Potential large FCNC and EDM effects Complicated in practice, especially supersymmetry breaking µ problem