Lecture 2 Theory concepts and leptons

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Lecture 2 Theory concepts and leptons

• Units
• Scattering and decays
• Leptons and the weak force
• Lepton universality.

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Units
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Conversion
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Dimensions and units
Quantity MKS Natural
Time T E-1
Distance L E-1
Momentum EMLT-1 E
Energy EML2T-2 E
Mass M E
Fermi constant GF (this lecture) M 1L5T-2 E-2
? (angular momentum) M L2T-1 E0?1
c (speed) LT-1 E0?1
Natural units are derived from a base unit of
energy.
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Question
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Question
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Theoretical concepts amplitude and golden rule
Target particles
Beam particles
A
A
C
B
C
D
Decay
Scattering
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Density of states
Quantum
px
Classical
px
.
.
.
.
p
p
.
.
.
L
L
x
x
Particle states in 2 space and momentum dimensions
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Density of states cont.
p
p
dp
dp
p
2-D (ring) or 3-D (spherical shell)
1-D (line)
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Fast
Slow
E
Eg atomic energy levels
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Question
potential well
L
px
p
L
x
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Yukawa potential
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Born approximation
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Short range force
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Summary putting things together
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Understanding better the Feynman diagrams
(a)
e-
e-
a
e-
e-
aW
Mg0
g
Suppressed MZ? 80 GeV
a
aW
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Particles in nature
Mass
171000
?
?
?
More information available from the Review of
Particle Physics http//pdg.lbl.gov/2008/listings
/contents_listings.html
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The charged leptons

• Three types of charged lepton
• Electron,muon,tau
• e-, e, m-, m , t-, t
• Charged leptons interact via the weak and
  electromagnetic forces

Lepton Charge (e) Mass (GeV)
e- -1 0.0005
m- -1 0.105
t- -1 1.8
antiparticles
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Heavier leptons

• Muon m- (Stevenson and Street, 1936)
• Measurements of energy loss of cosmic-ray
  particles.
• New particle with mass between e- and p (106
  MeV/c2)
• Interacts like a heavy electron

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Evidence for neutrinos
n
n ? p e- n

• Electrons produced by beta decay do not all have
  the same energy.
• Pauli proposed the existence of an unseen neutral
  particle to explain the observed electron
  spectrum.

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The lepton family
Spin 1/2
Lepton (antilepton) Charge (e) Mass (GeV)
e- (e) -1 (1) 0.0005
ne,(ne) 0 ?0
m- (m) -1 (1) 0.105
nm (nm) 0 ?0
t- (t) -1 (1) 1.8
nt (nt) 0 ?0
Charged leptons interact via the electromagnetic
and weak forces. Neutrinos interact only via the
weak force.
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Lepton number conservation
Lepton Le Lm Lt
e- 1 0 0
ne 1 0 0
m- 0 1 0
nm 0 1 0
t- 0 0 1
nt 0 0 1
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Evidence for more than one neutrino species

• Neutrinos produced with muons produce muons
  n nm
• Neutrinos produced with electrons produce
  electrons n ne
• Neutrinos produced with tau leptons produce tau
  leptons n nt
• - Neutrino oscillations (next lecture modify
  very slightly this picture).

X
p
n
m
m
X
n
n
e
e
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Limits on lepton number violation in charged
lepton decays
Decay Violates Limit on branching ratio





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Interactions of leptons
Neutral current
Leading order
Charged current
t-
nt
Higher order
suppressed.
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Lepton universality
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Summary

• Amplitudes, couplings and rates defined.
• Leptons
• Charged leptons and neutrinos
• Lepton number conservation
• Lepton universality in the weak force