PHYS 5396 – Lecture #2
Wednesday, Jan. 15, 2003
Dr. Jae Yu
1.
2.
3.
4.
What is a neutrino?
History of neutrinos
Neutrino cross section
Neutrino experiments
Wednesday, Jan. 15, 2003
PHYS 5396, Spring 2003
Jae Yu
1
Reading Assignments
• S. Weinberg on Electroweak theory
– S. Weinberg, PRL 19, 1264 (1967)
• S. Weinberg paper on Standard Model:
– S. Weinberg, Rev. Mod. Phys. 52, 515 (1980)
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
2
What are neutrinos?
• Lepton species without electrical charge
• Only affected by weak interactions, no EM
• Have one helicity
– we have observed only left-handed neutrinos and
right-handed anti-neutrinos
– This property led Yang & Lee to parity violation and
eventually theory of weak interactions
• No mass prescription in the SM  Atmospheric and
solar neutrino experiments seem to have provided direct
evidence that challenges this hypothesis
•Measurements show
three species only
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
3
Properties of Neutrinos
X-sec
(cm2)
Flavor
Spin
Masses
Magnetic
Spin(MeV/T)
ne
½
<2.8 ev
<5.8x10-20
~10-38
nm
½
<16~70KeV <4.3x10-20
~10-38
nt
½
18.2 MeV <3.1x10-17
~10-38
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
4
History of neutrinos
• It was noticed at the end of 19th century by nuclear
physicists that beta decays do not seem to conserve
momentum and energy  BIG problem!!!
n  p n e  e

• 1931: W. Pauli postulates that the missing energy may be
carried by a neutral particle, as a “desperate remedy”.
• 1934: Fermi develops a theory of beta decay in which the
inclusion of a neutral particle (neutrino) explains many
experimentally observed results.
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
5
Neutrino history, cnt’d
• 1956: Cowen and Reines detects electron neutrinos from a
reactor experiment by detecting photons (a few from neutron
capture by Cd nucleus and the other from positron annihilation
with an electron) emitted as a result of an inverse beta decay,
with a several ms time separation
n e  p  n  e
• 1956: Yang and Lee develops theory of parity violation of weak
interactions  Existence of different types from lack of
experimental observation of reactions like
m  e 

Wednesday, Jan. 15, 2003

PHYS 5326, Spring 2003
Jae Yu
6
Neutrino history, cnt’d
• 1962: BNL accelerator experiment proves the existence of
muon neutrinos, by producing neutrinos from pion decays
and determining the product of interaction to be muons 
No electrons above the background observed
• Late 60’: Proposal of Electroweak theory based on
SU(2)xU(1) by Weinberg, Salam and Glashow (Weinberg,
PRL 19, 1264 (1967))
• 1970:GIM model (Glashow, PR D2, 1285 (1970)) of second
quark family, confirmed experimentally in 1974
•1973: Experimental observation of neutral current
interaction at the Gargamelle experiment (bubble
chamber neutrino experiment) Confirmation of
electroweak theory
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
7
Weak Interaction Formalism
n  p n e  e

• Fermi 4-fermion contact interaction to describe
nuclear b-decay (E. Fermi, Z. Physik 88, 161 (1934))
p
n
LFermi
4GF CC  CC 

J J
2
GF  1.16639 105 GeV 2
• The theory begins to violate unitarity at about the
momentum transfer scale 100GeV  Cross section
becomes larger than that from optical theorem
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
8
Introduction of IVB’s and EW Unification
• Inspired by the failure of Fermi contact
interaction and QED, Weinberg, Salam and
Glashow introduced IVB’s exchange to replace
Fermi contact interactions
p
n
W-
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
9
EW Formalism
• Lagrangian for EW interactions by GSW:
- LEW
g CC   CC  
g
 J W  J W  
JNC Z0  g cosW JEM A
2
cosW
Charged Weak
Neutral Weak
EM
• Leptonic currents (J’s) couple to vector bosons
`n, l
W+/-
l, `n
u, d
`u, `d
Wednesday, Jan. 15, 2003
CC 
J
J CC 
1  5
1  5
 n i 
li  u i 
di
2
2
1  5
1  5
 l i 
n i  d i 
ui
2
2
PHYS 5326, Spring 2003
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EW Formalism cnt’d
EM
J
• EM current   q j f i  f j
• Weak Neutral Current
J   f j 
NC
V j  A j 5
2
fj
• where Vector and axial-vector couplings are
V j  I j  2Q j sin 2 W
Aj  I j
• with propagator terms
W or Z propagator 
Wednesday, Jan. 15, 2003

 i g mn  qm qn / M 2

q2  M 2
PHYS 5326, Spring 2003
Jae Yu
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Some properties of GSW
• GSW model is SU(2)xU(1) gauge group theory
with the specified relative coupling strength in
the Lagrangian. EM coupling is g sin W  e .
• GSW Prediction of IVB mass from spontaneous
symmetry breaking mechanism, that gives
masses to IVB and leptons, is
2
M
sin 2 W  1  W2
rM Z
• SM Predicts one Higgs boson, giving r=1
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
12
Linking Fermi to GSW
• Using the two Lagrangians of Fermi and GSW
and CC propagator
4GF CC  CC 
J J
2
g CC   CC  
g
 J W  J W 
JNC Z0  g cosW JEM A
2
cosW
LFermi  
- LEW


• The coupling g can be written (q2<<M2)
W or Z propagator for q  M 
2
2
 ig mn
M2
• Effective coupling strengths can be related
4GF  g  1  g 

 2 

2  2  MW  2 
Wednesday, Jan. 15, 2003
g
GF 
4 2M W2
PHYS 5326, Spring 2003
Jae Yu
13
Neutrino Cross Sections
( 3)
coupling  I weak
 QEM sin 2 W
( 3)
coupling  I weak
2

Mxy 
y
2
2
1

y

F
x
,
Q

2
xF
x
,
Q


2
1

2E 
2
d 2 2GF ME 

  y
dxdy

2

y
1

xF
x
,
Q



3
2

 












 nN / En  0.68 10 38 cm2 / GeV
Wednesday, Jan. 15, 2003
 n N / En  0.35 10 38 cm2 / GeV
PHYS 5326, Spring 2003
Jae Yu
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Sources of Neutrinos: Solar Neutrinos
• Nuclear Fusion inside stars with the primary
2

p

p

H

e
n e
(85%) reaction
• Energy spectra
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
15
Sources of Neutrinos:Atm and other
• High energy cosmic-ray (He, p, n, etc) interactions in
the atmosphere
– Cosmic ray interacts with air molecules He  p   , K
– Secondary mesons decay   m  n m  n e
– Muons decay again in 2.6ms m  e  n m  n e
• Neutrinos from Big Bang (relic neutrinos)
• Neutrinos from star explosion
• Neutrinos from natural background, resulting from
radioactive decays of nucleus
• Neutrinos from nuclear reactors in power plants
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
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Accelerator Based Neutrino Experiments
p
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
17
Homework Assignment
• Find a method of distinguishing neutrino
signs (neutrinos from anti-neutrinos) in an
accelerator based neutrino experiment.
Wednesday, Jan. 15, 2003
PHYS 5326, Spring 2003
Jae Yu
18