Transcript Elementary Particle Physics

Lecture 12 – Asymptotic freedom and the
electrodynamics of quarks
●
●
Asymptotic freedom and the running of coupling
”constants”.
Testing the theory of the quarks and strong
force in e- e+ reactions.
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The theory of the strong force QCD
Its a bit embarrassing.
We talk about quarks and gluons but we haven't
even attempted a calculation/estimate for a process
using Feynman diagrams.
q
q
s
q
q
s
Problem is that  S  1 for most of the processes we've been interested
in. However,  S can be low depending on how close the quarks
are to each other.
Easiest to see how this all works by first considering electromagnetic interactions.
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What is the charge of a particle ?
+ve charged particle q in a dielectric.
The material surrounding the particle is composed of
molecules which become polarised by the electric
field of q. Produce a dipole field which reduces the
electric field from q.
q
E
q
4 0 r 2

r
(12.01)
4 0 r 2
Anyone making a measurement of q in the dielectric
would see a screened charge q
 r . Screening reduced as
measurement is made closer to the particle than molecular
separation.
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Screening in a dielectric
qeff
q/r
Intermolecular separation
r
The effective charge increases at small distances
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Vacuum polarisation
The "vacuum" consists of virtual particles fluctuating into and out of existence.
An electron is surrounded by virtual particles which act to shield the charge as
in a polarised dielectric.
eg e , e pairs (lightest and easiest to make).
Feynman diagram formalism shown as photon coupling to e , e pairs.
h
Screening reduced for distances shorter than c 
(12.02)
me
c 
h
= electron Compton wavelength=2.43 1012 m (12.03)
me
e-
e-
e-
e-
e+,e+
e+,e-
e-
e-
e+,ee-
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Screened charges
Electromagnetic force (QED)
Electric charge screened: distance > Compton wavelength c
Strong force (QCD)
Effective colour charge grows
e 2 at larger distances.
Implications: coupling between two electrons:  
(1.24)
Small charge over distances
4 0 < fm lead to asymptotically free
quarks
in hadrons.
If the charges are screened then
coupling,
 changes according to interaction distance.
1
1
Alternatively interaction distance d
(12.04)
momentum exchange Q
  depends on interaction distance or momentum exchange.
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The electromagnetic coupling
Barely changes
(Momentum transfer=Q)2 /GeV2
Interaction distance
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What about the strong force ?
q
q
q
q
q
q
q
q
q,q
+ other higher
order diagrams
q,q
q,q
q
q
q
q
q
q
q
q
Similar story as for electromagnetism except that gluons
can self-interact (they carry colour - the photon carries
no charge!)
This turns out to be critical.....
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Asymptotic freedom
Strong force (Quantum chromodynamics: QCD)
Effective colour charge grows at larger distances.
Small charge over distances < fm lead to quasi-free
quarks in hadrons.
Asymptotic freedom! Justifies Feynman's fast proton frame
argument (lecture 11).
Nobel prize (2004) for Gross, Politzer and Wilczek.
  33  2 N f 
 Q
 s  Q    s  M Z  1 
 s  M Z  ln 
6

 MZ
N f  number of quark flavours
s


 
1
(12.05)
 s  M Z   0.118  0.002 (12.06)
Varies strongly with momentum!!
s
Q
s
Momentum transfer, Q (GeV)
Interaction distance
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Running of the coupling ”constants”
Similar story for weak force.
If interactions occur over
distance scales which
suppress screening
The three forces would be
of (roughly) the same size
Measurements
Predicted behaviour (tested
with measurements at lower
energies)
The coupling strengths of the strong,electromagnetic, and
Weak forces converge at higher energies. Is this evidence that
they are part of a single force ? Later lecture.
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Consequences
2
From lecture 11 : F2 constant with Q at fixed x.
Quasi-free quark is struck by photon.
 Bjorken scaling.
QCD corrections imply scaling violations.
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Scaling violations
Described by QCD
over several orders
of magnitude in Q2.
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OZI suppression
In OZI-suppressed processes, the gluons carry all of the momenta
of some or all of the final particles and there is consequently a
lower probability of emitting such ”hard” gluons in comparison with
”soft” gluons in non-OZI suppressed reactions.
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Testing what we know about the quarks and their interactions
Use what we've learned from hadron properties and
DIS on a totally different reaction:
e  e  hadrons.
Study electomagnetic quark interactions
(quark electrodynamics) and strong interactions..
Show
(1) 3 colours
2
1
(2) Quarks (+ antiquarks) with charges  e and  e.
3
3
(3) QCD makes precise predictions for short distance reactions.
Also discuss how long-distance effects produce the observed hadrons
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Ratio of hadronic to muonic production
R
R
R
  e e  hadrons 
 e e   
 



Centre-of-mass energy ECM (GeV)
(12.07)
Approximation   e  e   hadrons     e  e   qq   N C ea2  e  e        (12.08)
N C  number of colours.
Data show: steps due to thresholds for producing heavier qq
R  N C  eu2  ed2  es2  ec2  eb2  
11
N C (12.09)  for ECM   2mb
9
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10 GeV   N C  3 colours.
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Taking a closer look
QCD demands a correction to (12.08) by taking into
account an additional diagram (gluon emission)
Gluon momentum >> 1 GeV
  S  1 GeV
 use QCD.
with correction
11
3
w/o correction
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”Observing” gluon emission
Gluons and quarks carry colour so are never seen.
jet
The process by which they convert into hadrons
is known as hadronisation/fragmentation. High
energy quarks and gluons convert into jets of hadrons.
jet
jet
Models of hadronisation exist but are simply very good
"best guesses". We don't yet understand the process
by which quarks are confined and therefore the process
through which jets are formed. An example of how we
think hadronisation is given in the next lecture when the
top quark discovery is discussed.
jet
Computer visulation of 3 jets
jet
jet
reconstructed in an e e reaction
at the PETRA collider (1979).
First measurement of gluon-jets.
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Summary
●
Vacuum polarisation makes the couplings of the
fundamental forces ”run” with energy

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●
Asymptotically free quarks!
At high energies QCD makes precise
calculations

Scaling violations

3 jet events
Tested our picture of quarks, gluons and the
strong force on e- e+ interactions.
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