Transcript Elementary Particle Physics

Lecture 14 – Neutral currents and
electroweak unification
●
Neutral currents
●
Electroweak unification
●
Number of neutrinos and fermion generation
●
The Standard Model
●
The Higgs boson
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Basic diagrams for weak neutral currents
Same quark flavour:
u,d,s,c,b,t
Flavour changing:
forbidden
u
c
u
c
Same quark flavour:
u,d,s,c,b,t
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Flavour changing:
forbidden
2
Using the mixed states
Discussed in lecture 13 that the weak force "saw" mixed states d ', s ' and this led to cross-generation
interactions.
d '  d cos C  s sin C ; s '  d sin C  s cos C (13.02)
instead of physical states d and s .(Simple two-doublet approximation.)
Show that it doesn't matter whether we use the physical or Cabibbo-rotated states.
+
=
+
Contributions to amplitude:
M 1  d ' d '   d cos C  s sin C   d cos C  s sin C   dd cos 2 C  ss sin 2 C   ds  sd  sin C cos C (14.01)
M 2  s ' s '   d sin C  s cos C   d sin C  s cos C   dd sin 2 C  ss cos 2 C   ds  sd  sin C cos C (14.02)
 M  M 1  M 2 (14.03)
 d ' d ' s ' s '
 dd cos 2 C  ss sin 2 C   ds  sd  sin C cos C  dd sin 2 C  ss cos 2 C   ds  sd  sin C cos C
 dd  ss (14.04)
Neutral currents don't change flavour.
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Question
Draw Feynman diagrams for K   e   e and K L0  e   e 
What are the decay rates for these processes ?
Are these results in agreement with the assertion that flavour changing
neutral currents are suppressed ?
eK-
s
u
Z0
K0
d
K L0  e   e  has not been observed.
Best limits on decay rates are:
  K L0  e   e  
  K   e  e 
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 3 105.
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Neutral currents
Evidence for charged current interactions via W  is readily available at low energies. In 1938
Klein proposed a heavy charged particle was responsible for weak processes. It was hard to
avoid observing their influence:
eg nuclear  -decay and   decays: n  p  e  + e        .


Until 1973 all weak interactions could be understood with the W  .
Evidence for the neutral partner of the W  , the Z 0 was more difficult to obtain:
(1) There's no flavour changing allowed eg K L0  e   e  is forbidden as a Z 0 -process.
(2) Any decays which would mediated by the heavy Z 0 would also be mediated by the
photon and the weak contribution would be unobservable.
Eg f  ss 
f ss
g,Z0
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Rare decays
The decay K L0  e   e  can take place but is predicted to be incredibly
rare since higher orders/internal loops are needed.
The search for rare decays is useful for
s
u
(1) testing our theories to high precision
(2) looking for evidence of "new physics".
Eg supersymmetry predicts many new heavy
particles which can also manifest themselves
W
u
d
in loops at low energy and which can thus change
decay rates.
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First evidence for neutral current weak processes

e-
Bubble chamber experiment at CERN, 1973.
Look for interaction:    e     e
Obs! We used neutrino to find about that the Z 0 exists.
Later in this lecture we'll use the Z 0 to tell us how many neutrinos exist.
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Electroweak theory
The existence of the Z 0 was not a great surprise. Electroweak theory predicted it would exist
(and the W  , Z masses). The Z 0 is necessary to ensure that calculations for certain processes
were not divergent.
Electroweak theory was developed by Glashow, Weinberg and Salam (Nobel prize 1979).
It unifies the the weak and electromagnetic forces in a single theoretical framework.
The details are very complex but it the achievement is on the same footing as the
unification of the electric and magnetic forces into a single electromagnetic force
with the Maxwell equations and special relativity.
What concerns us are the predictions and how they were confirmed by experiment.
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Electroweak unification
Electroweak theory states that the weak and electromagnetic forces look different at low
energies due to the masses of g , Z 0 , and W  . At high energies  combined electroweak force.
From lecture 13:
e
MW2
6400 GeV2
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Electroweak theory predictions
Unification condition links the electromagnetic and weak couplings:
=
e2
4 0

2

=electromagnetic coupling constant (1.24)
e
2  2 0 
1
2
 gW sin W  g Z cos W (14.05) g Z  neutral current coupling (14.06)
Weak mixing angle cosW 
MW
MZ


0



W

 (14.07)
2

Anomaly condition:
Q
 3 Qa  0
; sum over all leptons
 
and quarks  a  (14.08)
a
Q  lepton charge , Qa  quark charge
Also, each family individually satisfies the anomaly condition.
Eg first generation of lepton and quarks
1 
2
Qe  Q e  3  Qu  Qd   -e  3  e  e   0 (14.09)
3 
3
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For low energy charged current interactions, recall:
gW2
GF
 2 (2.39) 
2 MW
From (14.05) g 
2
W
2 gW2
M 
GF
2
W

2sin W
2
 M 
2
W

2GF sin W
2
(14.10)
GF  Fermi constant=1.166 105 GeV 2 (2.37)

Using (14.07)  M 
(14.11)
2
2
2GF sin W cos W
2
Z
GZ
g Z2
2 g Z2
2
Low energy Z weak interaction:
 2 (14.12)  M Z 
(14.13)
GZ
2 MZ
0
GZ g Z2 M W2

 2  2  sin 2 W (14.14)
GF gW M Z
 measure sin W from rates of low energy charged and neutral current processes.
Measurement (1981): sin 2 W  0.227  0.014 (14.15)
 Predicted W and Z 0 masses from the couplings.
 M W  78.3  2.4 GeV ; M Z  89.0  2.0 GeV (14.16)
Consistent with masses measured in 1983 (UA1, UA2 experiments).
Nobel prize (1983, Carlo Rubbia and
Simon Van der Meer).
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A small correction
Current measurement:
sin 2 W  0.2315  0.0001 (14.17)
 from (14.10) and (14.11) M W  77.5  0.03 GeV ; M Z  88.41  0.04 GeV (14.18)
Current direct mass measurements:
M W  80.4  0.02 GeV ; M Z  91.188  0.002 GeV (14.19)
gW2
GF
GZ
g Z2
We were wrong to use
 2 (2.39) and
 2 (14.12)
2 MW
2 MZ
This neglected loop contributions as below. More precise calculations take
these into account and obtain good agreement with the directly measured
masses†
† Hidden in this is an interesting principle - that the measured masses of particles
are sensitive to the existence and properties (eg mass) of other particles.
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Strategy for directly observing Z0
(1) Demonstrate how to measure the mass of the Z 0 .
(2) Demonstrate how the same experiments also allow us to answer an interesting question.
We know there are three lepton doublets. Each doublet has one charged lepton

with mass
and a (just about) massless neutrino  . Has nature only given us 3 families ?
Are there more families i.e. heavier charged leptons (> 200 GeV) that we can't
directly discover at current colliders which are associated with light neutrinos in a doublet ?
Eg when we turn on the LHC is it likely we'll extend our table of leptons with a new
lepton pair: Y  and  Y
Lepton
Charge (e)
Mass (GeV)
e-
-1
0.0005
e
0
0

-1
0.105

0
0
t
-1
1.8
t
0
0
Y-
-1
> 200
Y
0
0
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Measuring the mass and decays of a Z0
Z 0 -interactions reminder.
Any process in which a photon is exchanged can also take place with a Z 0 .
In addition, the Z 0 interacts with neutrinos.
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Energy dependence
Consider annihilation reaction e   e      
in centre-of-mass frame.
Can be mediated by photon or Z 0 .
mostly
When is the photon contribution big
and the Z 0 contribution small and
vice versa ?
Photon contribution:  g
2
E
2
(14.20)
mostly
Z 0  contribution:
Z
0
GZ2 E 2 (for E  M Z ) (14.21)
E  beam energy
ECM  2 E  mass of photon/Z 0 (14.22)
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M Z 0  91.2 GeV
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LEP
Large Electron-Positron Collider at CERN, Geneva.
Started 1989: 45 GeV + 45 GeV electrons and positrons.
Designed as a Z 0 factory. Similar facility at SLAC, California: SLC.
LEP was later upgraded to higher energies, eventually reaching 209 GeV
and almost finding (or finding depending on who you talk to) the Higgs boson.
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  e  e  hadrons  from LEP and other colliders
The Z0 resonance is
what concerns us.
What can we learn
from it ?
W W 
Lower energy
experiments
LEP
+ SLD (at Z0)
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Resonances reminder
From lecture 4
Short-lived particles simply don’t
have well-defined masses.
Their masses follow a BreitWigner distribution
 
1
 m  m0  
2

4
2
Measured mass fromdecay :
    
(4.11)
Mass reconstructed from
1 decay :

1
Γ   Δm (4.12)
τ
 Δmτ  1 (nu)  Δm  c 2 τ 
    t

 m   E
(MKS)
Consistent with uncertainty principle
E t  (1.27).
770 MeV – ”nominal” mass
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What an experiment observes
What is meant by e   e   X ? What is X ?
Eg OPAL experiment at LEP.
Observe and count , eg number of e   e   hadrons
events.
Similarly e   e 



could be observed and
counted - select events appropriate t o the lepton species:
 e,  ,t .
e   e      can't be observed in the detector.
The neutrinos interact so weakly that they
are never seen. We can still, however, work
out that they were produced and count how
many neutrino species exist!
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The Z0 resonance
m t  1 (4.12)
  e  e  hadrons 
 Z  m  2.495  0.002 GeV (14.23)
LEP
1
 0.4 GeV 1  1025 s (14.24)
2.5
Consider e  e   X
X  any chosen observed final states,
 t Z0 
m  2.5 GeV
   Z 0  e  e    Z 0  X  
12 M 
 (14.25)
  e  e  X  
2
2
2
2
2 2

ECM 
E

M

M



CM
Z
Z
Z


2
Z
  Z 0  e  e 
strength of Z 0 production (time reversal symmetry) (14.26)
  Z 0  X  = decay rate of Z 0 after production to specific final state X . (14.27)
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1
Recall: branching ratio for a given decay i Bi 
(2.11)
tot
B  Z 0  e  e  B  Z 0  X  
  Z 0  e  e    Z 0  X 
Z 0
Z0
(14.28)
Measure B  Z 0  e   e   , B  Z 0  X  ,  Z 0  measure   Z 0  e   e     Z 0  X 
Fits to observed data:
  Z 0  hadrons   1.744  0.002 GeV
Z 0 



 Z 0  hadrons  Z 0  qq  (14.29)
  0.0840  0.0009 GeV for each lepton species:
 e,  ,t . (14.30)
Make an assumption that Z 0 decays only via:
Z 0  hadrons, Z 0 



, Z 0    .
 Z 0    Z 0  hadrons   3  Z 0 



  N Z

0
  

(14.31)
N  number of neutrino species
 N   Z 0    
  0.499  0.004 GeV (14.32)
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There are three light neutrino species
  Z 0   
  0.166 GeV (calculated) (14.33)
 N  3.00  0.05 (14.34)
Combined data
from LEP
experiments
A stunning result demonstrating
the precision of particle physics
measurements and theory.
 there aren't any heavy charged
leptons with associated light neutrinos.
 from anomaly condition: if neutrinos are
massless there are only 3 generations of leptons
and quarks. We've already found the fundamental
fermions.
This is where we end the story.
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The Standard Model
Goal: a theory which describes all of the fundamental constituents of nature and their
interactions with the minimum of assumptions and free parameters. Ultimately describe
all interactions over small distance scales and cosmological observations.
The Standard Model is our best attempt at this - assess how successfult it is in lecture 15.
6 quarks, 6 leptons, 3 exchange bosons
+ antiparticles.
Two independent forces (electroweak and QCD).
19 free parameters: particle masses, mixing angles,
CP-violating term, couplings....
Consistent method of introducing interactions via
so-called gauge invariance and Feynam diagram
formalism (next lecture course).
The Standard Model assumes massless neutrinos
but this is easily fixed.
Barring neutrino oscillations, the Standard Model has never failed a single experimental test.
There is still one test left to pass - finding the Higgs boson.
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The most rigorous test of the Standard Model to date: g-2
From the Dirac equation :
Dipole moment and spin for a point-like fermion related by:
e
S ; g e  2 (1.23)
2m
This can be measured by experiments studying the response of an electron in a magnetic field.
Need to calculate higher orders:
   ge
Basic interaction
with B field photon
Next to leading order
correction
Precision experimental result:
g 2
 1159652180.7  0.3 10 12 (14.35)
2
Dirac prediction + quantum corrections:
g 2
 1159652153.5  28  10 12 (14.36)
2
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Higher order corrections
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Summary
●
Neutral currents

●
Flavour changing vertices
Electroweak unification and measurement of
the Z0 resonance

3 light neutrinos

3 fermion generations
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