Beyond the Standard Model

Transcription

1 Beyond the Standard Model The Standard Model Problems with the Standard Model New Physics Supersymmetry Extended Electroweak Symmetry Grand Unification References: 2008 TASI lectures: arxiv: [hep-ph] and The Standard Model and Beyond, CRC Press

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) sin 2! W (µ) Q W (APV) Q W (e) "-DIS Tevatron SM correct at loop level (renorm gauge theory; m t, α s, M H ) TeV physics severely constrained (unification versus compositeness) Consistent with light elementary Higgs Precise gauge couplings (SUSY gauge unification) MOLLER Qweak e-dis LEP 1 SLC µ [GeV] 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) Γ Z, σ had, R l, R q Z pole asymmetries M W low energy m t LEP search e + e Z ZH: M H > GeV Indirect (electroweak radiative corrections)) + direct: M H < 149 GeV (95%) M H [GeV] 200 Tevatron excluded 100 all data (90% CL) 50 LEP 2 excluded m t [GeV] Tevatron searches now sensitive enough for higher masses LHC will cover full range for standard model Higgs 95% CL Limit/SM 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,