Particle Physics - High Energy Physics Group

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QED Running Coupling Constants • “bare” charge of electron screened by virtual e + e – pairs • behaves like a polarizable dielectric In terms of Feynman diagrams: -Q +Q + + +…… Some final state so add matrix element amplitudes: Giving an infinite series which can be summed and is equivalent to a single diagram with “running” coupling constant Note sign Prof. M.A. Thomson Michaelmas 2009 273 Might worry that coupling becomes infinite at OPAL Collaboration, Eur. Phys. J. C33 (2004) i.e. at • But quantum gravity effects would come in way below this energy and it is highly unlikely that QED “as is” would be valid in this regime In QED, running coupling increases very slowly •Atomic physics: •<strong>High</strong> energy physics: Prof. M.A. Thomson Michaelmas 2009 274
QCD Running of s Similar to QED but also have gluon loops + + + +… Fermion Loop Boson Loops Remembering adding amplitudes, so can get negative interference and the sum can be smaller than the original diagram alone Bosonic loops “interfere negatively” with = no. of colours = no. of quark flavours S decreases with Q 2 Nobel Prize for <strong>Physics</strong>, 2004 (Gross, Politzer, Wilczek) Prof. M.A. Thomson Michaelmas 2009 275 Measure S in many ways: • jet rates • DIS • tau decays • bottomonium decays • +… 0.4 0.3 α s (µ) 0.2 QCD Prediction As predicted by QCD, S decreases with Q 2 0.1 0.0 1 2 5 10 20 50 100 200 µ (GeV) At low : S is large, e.g. at find S ~ 1 •Can’t use perturbation theory ! This is the reason why QCD calculations at low energies are so difficult, e.g. properties hadrons, hadronisation of quarks to jets,… At high : S is rather small, e.g. at find S ~ 0.12 Asymptotic Freedom •Can use perturbation theory and this is the reason that in DIS at high quarks behave as if they are quasi-free (i.e. only weakly bound within hadrons) Prof. M.A. Thomson Michaelmas 2009 276
Page 1 and 2: Particle Physics Michaelmas Term 20
Page 3 and 4: Colour Singlets It is important to
Page 5 and 6: Gluons In QCD quarks interact by e
Page 7 and 8: Hadronisation and Jets Consider a q
Page 9 and 10: The Quark - Gluon Interaction •Re
Page 11 and 12: Evaluation of QCD Colour Factors
Page 13 and 14: • Consequently the colour factors
Page 15: Test QCD predictions by looking at
Page 19 and 20: Configurations involving a single c
Page 21: Combining the short-range QCD poten

Particle Physics - High Energy Physics Group

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