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