Electron - Weber State University · 2004-03-26 · THE PERIODIC TABLE Particles like the electron...
34
Electron - Positron Annihilation D. Schroeder, 29 October 2002 µ h W − − − − − − − − − − − − − + + + + + + + + + + + + + π K ν γ Z
Transcript of Electron - Weber State University · 2004-03-26 · THE PERIODIC TABLE Particles like the electron...
Electron - Positron Annihilation
D. Schroeder, 29 October 2002
µ
hW
−−
−−
−
−
−−
−
−−
−
− +
++
+
+
+
+
+
+
+
+
+
+
π
K
ν
γ
Z
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
Stanford8 GeV30 GeV100 GeV12 GeV
Ithaca12 GeV
Hamburg11 GeV47 GeV
Geneva200 GeV
Beijing4 GeV
Novosibirsk12 GeV
Tokyo64 GeV12 GeV
Electron-Positron Colliders
$ = αR +β E4
R
0 =d $dR
= α − β E4
R2
=⇒ R =
√β
αE2, $ = 2
√αβ E
E
2
Size (R) and Cost ($) of an e+e− Storage Ring
( = beam energy)
Find minimum $:
SPEAR: E = 8 GeV, R = 40 m, $ = 5 million
LEP: E = 200 GeV, R = 4.3 km, $ = 1 billion
Example 1:
momentum = 0
total
total
energy = 2E
Probability(E,θ) =
E-dependence follows from dimensional analysis:
density = ρ−
−
A
+
density = ρ+
Probability = (ρ−ρ+ − +A) × (something with units of length2)
When E me, the only relevant length ish
p=hc
E
=⇒
e+e−
e+
e−
θ
︸ ︷︷ ︸ ︸ ︷︷ ︸
e+e− −→ e+e−
?
Probability ∝ 1E2
Num
ber
ofC
ounts
cos θ
−0.8 −0.4 0 0.4 0.80
1000
2000
3000
4000
5000
6000
at SPEAR
Ecm = 4.8 GeV
Theory
Augustin, et al., PRL 34, 233 (1975)
Prediction for e+e− −→ e+e− event rate (H. J. Bhabha, 1935):
(eventrate
)∝ dσ
dΩ=
e4
32π2E2cm
[1 + cos4 θ
2
sin4 θ2
− 2 cos4 θ2
sin2 θ2
+
+
1 + cos2 θ2
]
Interpretation of Bhabha’s formula (R. P. Feynman, 1949):
= (const.) ×
2
Each diagram represents a complex number that depends on E and θ.
Each vertex represents a factor of the electron’s charge, e = −0.303.
e− e+ e− e+
e− e+e− e+
x y
p1 p2
p3 p4
e−ip1·x e−ip2·y
eip3·x eip4·y
∫d4q
(2π)4eiq·(x−y)
q2
e e
Feynman Rules (neglecting spin, h = c = 1)
Multiply pieces together, integrate over x and y . . .
+
+ +++
+ + + +
Higher-Order Diagrams
Also:
More vertices =⇒ more factors of e =⇒ smaller value
any charged particle!
(“vacuum polarization”)
0.4 0.2 0 0.2 0.4 0.60
50
100
150
200
250
cos θ− −
sdσ/d
Ω(G
eV2
nb/s
r)
tree-levelno vacuum polarizationfull radiative corrections
It Works!M. Derrick, et al., Phys. Rev. D34, 3286 (1986)
HRS Collaboration (SLAC)
Ecm = 29 GeV
THE PERIODIC TABLE
Particles likethe electron
Particles likethe photon
(fermions, spin 1/2)
Leptons Quarks (each in 3 “colors”)
−1 0 −1/3 2/3
e
µ
τ
νe
νµ
ντ
ud
cs
tb
γ
g
W± Z0
0.511 MeV
106
1777
< 0.000003
< 0.2
< 20
7 3
1200120
175,0004300
0
0
80,420 91,188
(bosons, spin 1)
photon
gluon(8 “colors”)
“electromagnetism”
“strong interaction”
“weak interaction”
(Gravity is negligible.)
← charge
Example 2: e+e− −→ µ+µ−
Only one diagram:
= (const.)× e4
E2
(1 + cos2 θ
)
(Same as third term in Bhabha formula, provided that E mµ.)
2
e− e+
µ+µ−
e− e+
Example 3: e+e− −→ qq −→ hadrons
uu
d
d
uu d
d
s sπ+π0
π0
K0
K−
gluon
23 |e|
↑
↑
↑
↑ ↑ ↑ ↑ ↑
For 10 GeV< Ecm< 40 GeV,
e+e− → hadronse+e− → µ+µ−
= 3×[(1
3
)2
+(2
3
)2
+(1
3
)2
+(2
3
)2
+(1
3
)2]
colors d u s c b
3 4 5 6 7 8 9 10 20 30 400
1
2
3
4
5
6
7J/ψ ψ(2S)
Ecm (GeV)
R = σ(hadrons)/σ(µ+µ−)
Υ(1S, 2S, 3S)
d+ u+ s
c
b
e− e+
Example 3(b): e+e− −→ Z0 −→ qq
q q
Z01
E2cm −m2
Z
Higher-order diagrams turn ∞ into smooth resonance curve.
0
5
10
15
20
25
30
35
87 88 89 90 91 92 93 94 95 96
Center-of-Mass Energy (GeV)
Tot
al H
adro
nic
Cro
ss-S
ectio
n (n
barn
)
OPAL
+ +
e− e+ e− e+ e− e+
Example 4: e+e− −→W+W−
W− W+ W− W+ W− W+
νeγ Z0
Requires Ecm > 2mW = 160 GeV
0
5
10
15
20
160 170 180 190 200 210
Ecm [GeV]
[p
b]
LEP Preliminary08/07/2001
no ZWW vertex exchange
Full theory
• Direct measurement of mW can be compared to indirect measurements:
• Corrections from higher-order diagrams must be included,
especially:
• Results disagree, typically by ∼
∼
∼
1%!
• Simplest solution: new spin-0 “Higgs” particle, mh < 200 GeV
(Also needed to avoid nonsensical predictions at E > 1000 GeV)
µ−
µ−νµ
νµ
W
W
W
d
t
b
u e−νe
h0
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
e− e+e− e+
W W
νe
Z0
Z0 h0 h0
νe
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/
