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Electron - Positron Annihilation Electron - Positron Annihilation γ µ K Z − − − + + + − − − + + + − − − − + + + − − − + + + + W ν h π D. Schroeder, 29 October 2002 OUTLINE • Electron-positron storage rings • Detectors • Reaction examples e+e− −→ e+e− [Inventory of known particles] e+e− −→ µ+µ− e+e− −→ q q¯ e+e− −→ W +W − • The future:Linear colliders Electron-Positron Colliders Hamburg Novosibirsk 11 GeV 12 GeV 47 GeV Geneva 200 GeV Ithaca Tokyo Stanford 12 GeV 64 GeV 8 GeV 12 GeV 30 GeV 100 GeV Beijing 12 GeV 4 GeV Size (R) and Cost ($) of an e+e− Storage Ring βE4 $=αR + ( E = beam energy) R d $ βE4 Find minimum $: 0= = α − dR R2 β =⇒ R = E2, $=2 αβ E2 α SPEAR: E = 8 GeV, R = 40 m, $ = 5 million LEP: E = 200 GeV, R = 4.3 km, $ = 1 billion + − + − Example 1: e e −→ e e e− total momentum = 0 θ − total energy = 2E e e+ Probability(E,θ)=? e+ E-dependence follows from dimensional analysis: density = ρ− A density = ρ+ − + × 2 Probability = (ρ− ρ+ − + A) (something with units of length ) ¯h ¯hc When E m , the only relevant length is = e p E 1 =⇒ Probability ∝ E2 at SPEAR Augustin, et al., PRL 34, 233 (1975) 6000 5000 4000 Ecm = 4.8 GeV 3000 2000 Number of Counts 1000 Theory 0 −0.8 −0.40 0.40.8 cos θ Prediction for e+e− −→ e+e− event rate (H. J. Bhabha, 1935): event dσ e4 1 + cos4 θ 2 cos4 θ 1 + cos2 θ ∝ = 2 − 2 + rate dΩ 32π2E2 4 θ 2 θ 2 cm sin 2 sin 2 Interpretation of Bhabha’sformula (R. P. Feynman, 1949): − + e− e+ e e 2 = (const.) × + − e e+ e− e+ Each diagram representsa complex number that dependson E and θ. Each vertex representsa factor of the electron’scharge, e = −0.303. Feynman Rules (neglecting spin,h ¯ = c =1) p3 p4 · · eip3 x eip4 y e e xy · − d4q eiq (x y) − · 4 2 − · e ip1 x (2π) q e ip2 y p1 p2 Multiply pieces together, integrate over x and y ... Higher-Order Diagrams + ++ + + any charged particle! (“vacuum polarization”) Also: + + ++ More vertices =⇒ more factors of e =⇒ smaller value It Works! M. Derrick, et al., Phys. Rev. D34, 3286 (1986) 250 HRS Collaboration (SLAC) 200 Ecm = 29 GeV nb/sr) tree-level 2 150 no vacuum polarization full radiative corrections Ω (GeV 100 sdσ/d 50 0 −0.4− 0.2 0 0.2 0.4 0.6 cos θ THE PERIODIC TABLE Leptons Quarks (each in 3 “colors”) e νe d u 0.511 MeV < 0.000003 73 Particles like the electron µ νµ s c 106 < 0.2 120 1200 (fermions, spin 1/2) τ ντ b t 1777 < 20 4300 175,000 −1 0 −1/3 2/3 ← charge γ photon “electromagnetism” 0 Particles like gluon the photon g “strong interaction” (8 “colors”) 0 (bosons, spin 1) ± 0 W Z “weak interaction” 80,420 91,188 (Gravity is negligible.) + − + − Example 2: e e −→ µ µ Only one diagram: µ− µ+ 2 e4 = (const.) × 1 + cos2 θ E2 e− e+ (Same as third term in Bhabha formula, provided that E mµ.) + − Example 3: e e −→ qq¯ −→ hadrons 0 0 π K − π+ K u u¯ d¯ d s¯ s u u¯ 0 ↑ gluon d π d¯ ↑ 2 | | 3 e e− e+ For 10 GeV <Ecm < 40 GeV, e+e− → hadrons 1 2 2 2 1 2 2 2 1 2 =3× + + + + e+e− → µ+µ− 3 3 3 3 3 ↑ ↑↑↑↑↑ colors duscb R = σ(hadrons)/σ(µ+µ−) 7 J/ψ ψ(2S) Υ(1S, 2S, 3S) 6 5 4 b 3 c 2 1 d + u + s 0 345678910 203040 Ecm (GeV) − Example 3(b): e+e −→ Z0 −→ qq¯ q q¯ 0 1 Z 2 − 2 Ecm mZ e− e+ Higher-order diagrams turn ∞ into smooth resonance curve. 35 30 OPAL 25 20 15 10 Total Hadronic Cross-Section (nbarn) 5 0 87 88 89 90 91 92 93 94 95 96 Center-of-Mass Energy (GeV) + − + − Example 4: e e −→ W W − − W − W + W W + W W + ++γ Z0 νe e− e+ e− e+ e− e+ Requires Ecm > 2mW = 160 GeV 08/07/2001 LEP Preliminary 20 15 ] pb [ 10 Full theory no ZWW vertex 5 exchange 0 160 170 180 190 200 210 Ecm [GeV] • Direct measurement of mW can be compared to indirect measurements: − − µ u νµ ν¯e e W W − νµ d µ • Corrections from higher-order diagrams must be included, t especially: b • Results disagree, typically by ∼1%! • Simplest solution: new spin-0“Higgs” particle, mh ∼< 200 GeV h0 W (Also needed to avoid nonsensical predictions at E ∼> 1000 GeV) Looking for the Higgs Particle(s) • Tevatron (Fermilab, Chicago): pp¯, Ecm = 2000 GeV • Large Hadron Collider (CERN, Geneva): pp, Ecm =14, 000 GeV, 2007 Discovery likely! Detailed study difficult. + − • e e storage ring, Ecm = 500+ GeV? Too big, too expensive. • e+e− linear collider Z0 h0 h0 νe ν¯e Z0 WW e− e+ e− e+ The Next Linear Collider e+ e− 20 - 30 km Suggested Reading • Feynman, QED: The Strange Theory of Light and Matter • Barnett, et al., The Charm of Strange Quarks • Riordan, The Hunting of the Quark • ParticleAdventure.org • physics.weber.edu/schroeder/feynman/.
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