lecture sm 12
TRANSCRIPT
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Schning/Rodejohann 1 Standard Model of Particle Physics SS 2013
Lecture:
Standard Model of Particle Physics
Heidelberg SS 2013
Weak Interactions II
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Schning/Rodejohann 2 Standard Model of Particle Physics SS 2013
Important Experiments
Wu-Experiment (1957): radioactive decay of Co60
Goldhaber-Experiment (1958): radioactive decay of Eu152
Muon Decay: Michel spectrum
Pion Decay: branching ratios
Nuclear Beta Decays
Neutrino-Nucleon Scattering (neutrino antineutrino)
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Schning/Rodejohann 3 Standard Model of Particle Physics SS 2013
Neutron Decay
L =G
2(d (15)u) (v (1
5) e)
Lagrangian d u:
Decay Width
=GF
2c1
2 5
153
with
c1
= cos C
= 782 keV
Note: the dand u mass eigenstates are not weak eigenstates the neutron decay is not a simple d u decay (quarks are not free)
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Test of Lorentz Structure?
+
vectorcoupling
0*helicity -1 +1
n p e-
+
n p e-
Fermi transition Gamov Teller transition
-1
Momentum
Spin
axialvectorcouplingMomentum
Spin
0*helicity - +1-1- -
?
What is the relative contribution of V and A couplings in nuclear decays?
L =G
2(n (15)p) ( v (1
5) e)
Use a more general Lagrangian:
=cA
cVwith
The strength of the axial-coupling is related to the neutron lifetime!
=cA
cV
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Measurement of the Neutron Lifetime
Techniques:
(ultra) cold neutron traps
in-beam decays
electron detectors
proton detectors
electron-proton coincidence method
n pe e
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Neutron Trap II
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Results Neutron Lifetime
Significant tensions between
experiments!
Best value (PDG 2010): n = 885.7 s
derived from this value: =cA
cV
= 1.26940.0028
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Prediction for cA/c
v
Valence quark wave function of the neutron :
Detailed calculation of vector/axial-vector contributions gives:
cA/c
v= 5/3
Mismatch between experimentand prediction due to:
Relativistic corrections
Neglected sea quarks in the neutron
QCD corrections
e-
e
W-
-p
n
QCD correctionsmodify axial-coupling
spin flip
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Prediction for cA/c
v
Valence quark wave function of the neutron :
Detailed calculation of vector/axial-vector contributions gives:
cA/c
v= 5/3
Mismatch between experimentand prediction due to:
Relativistic corrections
Neglected sea quarks in the neutron
QCD corrections
e-
e
W-
-u
d
gluon
QCD correctionsmodify axial-coupling
spin flip
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Overview Weak Decay Processes
leptonic decay
semileptonic decays
semileptonic decays (S=1)hadronic weak decays (S=1)
heavy quark decays (C=1, B=1, T=1)
Weak decays of quarks and leptons (fermions)
W-Boson decays:
n pe e
e e
p e
e p
Q qW
W l lW q q
Charged currents can mediateinteractions between differentlepton and quark generations(mixing)
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K-Meson Decays
GF2ms
5
Lifetime ~ 10-8
sms 150 MeV
K+ 0 0 +K+ 0 l+
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Schning/Rodejohann 14 Standard Model of Particle Physics SS 2013
Weak Decays of B-mesons
GF
2
mb
5
Lifetime ~ 1.5 psmb 4.5 GeV
B0 D+ B0 D0 0 B0 D+ l
l
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Decay of the Top quark
GF2 mt
5
Lifetime ~ 10-25 s
mt172GeV
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Schning/Rodejohann 16 Standard Model of Particle Physics SS 2013
Summary Weak Interaction
left handedfermions: (
ee
)L
( )L (
)L (
u
d )L (c
s)L (t
b )L(I3=+ 1 /2I3=1 /2 )
right handedfermions:
e , ReR
, RR
, RR
uRdR
cRsR
tRbR
I3=0
W-bosons couple only on fermions with weak isospin!
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Weak Scattering Experiments
Question:What is the difference between:
A) scattering experiments in classical mechanics
B) weak scattering experiments?
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Weak Scattering Experiments
Video of a classical scattering experiment
Question:What is the difference between:
A) scattering experiments in classical mechanics
B) weak scattering experiments?
Answer:
Despite the fact that em
=1/127 is much smaller
than weak
~1/30electromagnetic interactions
(A) is much more dangerous than (B)weak interactions
http://home/schoning/heidelberg/lehre/SM13/Material/Stupid.mp4http://home/schoning/heidelberg/lehre/SM13/Material/Stupid.mp4 -
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Strength of Weak InteractionQuestion:
Why is the weak interaction so weak if
weak~1/30 ismuch stronger than
em=1/127 ?
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Strength of Weak InteractionQuestion:
Why is the weak interaction so weak if
weak~1/30 ismuch stronger than
em=1/127 ?
Answer:
1. Coupling
elm. IA weak IA
e ( 0.3) g ( 0.65) (e , g=4 )
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Strength of Weak InteractionQuestion:
Why is the weak interaction so weak if
weak~1/30 ismuch stronger than
em=1/127 ?
Answer:
1. Coupling
2. Propagator
elm. IA weak IA
Q2=1 eV2
Q2=1 MeV2
Q2=1 TeV2
e ( 0.3) g ( 0.65) (e , g=4 )
i g
q2
i g + qq /mW2
q2mW
2
i g
mW2
=8GF
2
lowenergy
Ratio(elm./weak)
0.641022
0.641010
0.64102 (
1
q2
)/(1
mW2
)
mW
~ 80 GeV
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Strength of Weak Interaction
At high mass scales E~100 GeV the weak interaction is
stronger than the electromagnetic interaction
Neutrino-nucleon scattering experiments require neutrino beams
of about E
~100 GeV to test weak interactions at reasonable
rates ~O(1pb) because of the propagator effect
(
e e) G
F
2s
e
e
neutrino-electron scattering
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Production of (Myon) Neutrino Beams
Production reactions:
CHARM Detector
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CHARM Detector
CHARM Detector
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CHARM Detector
Why marble?
20
40Ca(CO
3) is an iso-scalar target (same amount ofdand u quarks)
CHARMII Detector
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CHARMII Detector
CHARMII Detector
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CHARMII Detector
Detection of Myon Neutrinos in CC
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Detection of Myon Neutrinos in CC
N
X
long track identified as muon(minimum ionising particle)
length of track is a measureof the muon energy
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(Anti-) Neutrino-Nucleon Scattering
dd
( d
u) =GF
2
42s
neutrino-nucleon scattering
d
d
( u +
d) =GF
2
42
t
antineutrino-nucleon scattering
u
+
d
-
d
u
W
W
Neutrino-Nucleon:
Anti-Neutrino-Nucleon:
t
(A i ) N i N l S i
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(Anti-) Neutrino-Nucleon Scattering
dd
( d
u) =GF
2
42s
neutrino-nucleon scattering
d
d
( u +
d) =GF
2
42
t
antineutrino-nucleon scattering
u
+
d
-
d
u
W
J=0
W
Neutrino-Nucleon:
Anti-Neutrino-Nucleon:
(A ti ) N t i N l S tt i
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(Anti-) Neutrino-Nucleon Scattering
dd
( d
u) =GF
2
42s
neutrino-nucleon scattering
d
d
( u +
d) =GF
2
42
t
antineutrino-nucleon scattering
u
+
d
-
d
u
W
J=0
W
J=1
Neutrino-Nucleon:
Anti-Neutrino-Nucleon:
(A ti ) N t i N l S tt i
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(Anti-) Neutrino-Nucleon Scattering
dd
( d
u) =GF
2
42s
neutrino-nucleon scattering
d
d
( u +
d) =GF
2
42
t
antineutrino-nucleon scattering
u
+
d
-
d
u
W
t/s = (1cos)2 = (1y)2
J=0
W
J=1
Neutrino-Nucleon:
Anti-Neutrino-Nucleon:
dd
(N
X) 1
2
GF2
42x S
dd
(N+
X) 1
2
GF2
42x
t
sS
isoscalar target
Lorentz Invariant Kinematics of the
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Deep Inelastic Scattering Process
The virtuality of the exchanged
photon is given by:
Q2 = q2 = ( p p ')2
q
p
p '
positron
nucleon
W-boson
1sin
4 / 2
N
x P
Relative energy loss (inelasticity):
y = E
= q Pp P
x = q2
2 q P= Q
2
S y
relative fraction of parton momentum:
S = 2 p Pwith cms energy:
neutrino
Measurement of the Differential
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N and anti-N Cross Section
CDHS
Neutrino-Nucleon:
Anti-Neutrino-Nucleon:
ddy
( N
X) 1
2
GF2
x S
d
dy(
N + X)
1
2
GF2
x S (1y)2
isoscalar target
small deviations from above equations due to x-dependence!
Measurement of the Total N and
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anti-N Cross Section
From simple quarkcounting:(isoscalar target)
(N)
(N)= 3
Parton dynamicsmore complex
Sea Quarks!
measured value ~2is significantly smaller!
Example: Proton Parton Densities
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Example: Proton Parton Densities
Significant component from sea quarks!
multiply by 20!
(Anti ) Neutrino Nucleon Scattering
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(Anti-) Neutrino-Nucleon Scattering
d
u
u +
d
u
+
d
-
d
u
W
W
u d
d +
u
+
-
d
uW
W
_
_
d
u
_
_
Unfolding the Valence Quark
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Distributions
dv + dsea + (usea) 2dv + dsea + (usea)
2uv
+ usea
+ (dsea
) uv
+ usea
+ (dsea
)
_ _
_ _
Structure Functions
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S uc u e u c o sRelations:
Measurement:
Extraction of parton densities:
F2
Results xF3
Results
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F2
Results xF3
Results
Comparison N versus lepton-N
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Scattering
Structure function results
obtained in weak interactions
agree well with result obtained
in electromagnetic interactions!
Due to different couplings:
Ratio of d /u
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Ratio of dv/u
v
Result: dV/u
V 0ifx 1
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