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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

1

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.

Problem is that for most of the processes we'veS been interested in. However, 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.

S

sq

q q

qs

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What is the charge of a particle ?

.

+ve charged particle in a dielectric.

The material surrounding the particle is composed ofmolecules which become polarised by the electric field of Produce a dipole field which reduces theelectric

q

q

2 20 0

.

4 4

field from

(12.01)

Anyone making a measurement of in the dielectric

would see a screened charge . Screening reduced as

measurement is made closer to the particle than mole

r

r

qq

qEr r

qq

cular separation.

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q/r

qeff

r

Screening in a dielectric

The effective charge increases at small distances

Intermolecular separation

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Vacuum polarisation

+

e-

,

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 asin a polarised dielectric.

eg paie e

, .

2.43

rs (lightest and easiest to make).

Feynman diagram formalism shown as photon coupling to pairs

Screening reduced for distances shorter than (12.02)

= electron Compton wavelength=

ce

ce

e eh

mh

m

1210 m (12.03)

e-

e-e-

e- e-

e- e-

e+,e-

e+,e-

e+,e-

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Screened charges

Electromagnetic force (QED)Electric charge screened: distance > Compton wavelength

Strong force (QCD)Effective colour charge grows at larger distances.Small charge over distances < fm lead to asymp

c

totically freequarks in hadrons.

2

04

1

Implications: coupling between two electrons: (1.24)

If the charges are screened then coupling, changes according to interaction distance.

Alternatively interaction distance momentum

e

d

1 (12.04)

exchange

depends on interaction distance or momentum exchange.

Q

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The electromagnetic coupling

Interaction distance

(Momentum transfer=Q)2 /GeV2

Barely changes

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What about the strong force ?

q q

q q

q q

q q

q q

q qq q

q q

q,q

Similar story as for electromagnetism except that gluonscan self-interact (they carry colour - the photon carries no charge!)This turns out to be critical.....

q,q

q,q + other higher order diagrams

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Electromagnetic force (QED)Electric charge screened: distance > Compton wavelength

Strong force (Quantum chromodynamics: QCD)Effective colour charge grows at larger distances.Small charge over dist

c

ances < fm lead to quasi-freequarks in hadrons.Asymptotic freedom! Justifies Feynman's fast proton frame argument (lecture 11). Nobel prize (2004) for Gross, Politzer and Wilczek.

Asymptotic freedom

s

Momentum transfer, Q (GeV)

Interaction distance

133 2

1 ln6

0.118 0.002

(12.05)

number of quark flavours

(12.06)

Varies strongly with momentum!!

fs s Z s Z

Z

f

s Z

N QQ M MM

N

M

sQ

s

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Running of the coupling ”constants”

If interactions occur over distance scales which suppress screeningThe three forces would be of (roughly) the same size

MeasurementsPredicted behaviour (tested with measurements at lower energies)

Similar story for weak force.

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

22 .From lecture 11 : constant with at fixed

Quasi-free quark is struck by photon. Bjorken scaling.

QCD corrections imply scaling violations.

F Q x

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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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Use what we've learned from hadron properties and DIS on a totally different reaction:

hadrons.Study electomagnetic quark interactions (quark electrodynamics) and strong interactions..

Show (1)

e e

2 1 .3 3

3 colours

(2) Quarks (+ antiquarks) with charges and

(3) QCD makes precise predictions for short distance reactions.

Also discuss how long-distance effects produce the observed hadrons

e e

Testing what we know about the quarks and their interactions

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Ratio of hadronic to muonic production

2

2 2 2 2 2 1

hadrons (12.07)

Approximation hadrons (12.08)

number of colours.Data show: steps due to thresholds for producing heavier

C a

C

C u d s c b

e eR

e e

e e e e qq N e e e

Nqq

R N e e e e e

1 2 10 39

(12.09) for GeV colours.C CM b CN E m N

Centre-of-mass energy ECM (GeV)

R

R

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Taking a closer look

QCD demands a correction to (12.08) by taking into account an additional diagram (gluon emission)

w/o correction

with correction

Gluon momentum >> 1 GeV 1 GeV use QCD.

S

113

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”Observing” gluon emission Gluons and quarks carry colour so are never seen.

The process by which they convert into hadrons is known as hadronisation/fragmentation. Highenergy quarks and gluons convert into jets of hadrons.

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.

jetjet

jet

jet

jet

jetComputer visulation of 3 jets

reconstructed in an reaction at the PETRA collider (1979).First measurement of gluon-jets.

e e

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Summary

● Vacuum polarisation makes the couplings of the fundamental forces ”run” with energy 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.