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Lecture I: introduction to QCD

Lecture I: introduction to QCD

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Lecture I: introduction to QCD

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  1. Lecture I: introduction to QCD Marco van Leeuwen Utrecht University Jyväskylä Summer School 2008

  2. General QCD references • Particle Data Group topical reviews • QCD and jets: CTEQ web page and summer school lectures • Handbook of Perturbative QCD, Rev. Mod. Phys. 67, 157–248 (1995) • QCD and Collider Physics, R. K. Ellis, W. J. Sterling, D.R. Webber, Cambridge University Press (1996) • An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder, Addison Wesley (1995) • Introduction to High Energy Physics, D. E. Perkins, Cambridge University Press, Fourth Edition (2000)

  3. What is QCD? From: T. Schaefer, QM08 student talk

  4. QCD and hadrons Quarks and gluons are the fundamental particles of QCD (feature in the Lagrangian) However, in nature, we observe hadrons: Color-neutral combinations of quarks, anti-quarks Baryon multiplet Meson multiplet S strangeness I3 (u,d content) I3 (u,d content) Mesons: quark-anti-quark Baryons: 3 quarks

  5. Seeing quarks and gluons In high-energy collisions, observe traces of quarks, gluons (‘jets’)

  6. How does it fit together? S. Bethke, J Phys G 26, R27 Running coupling: as decreases with Q2 Pole at m = L LQCD ~ 200 MeV ~ 1 fm-1 Hadronic scale

  7. Asymptotic freedom and pQCD At high energies, quarks and gluons are manifest At large Q2, hard processes: calculate ‘free parton scattering’ + more subprocesses But need to add hadronisation (+initial state PDFs)

  8. Low Q2: confinement a large, perturbative techniques not suitable Bali, hep-lat/9311009 Lattice QCD: solve equations of motion (of the fields) on a space-time lattice by MC Lattice QCD potential String breaks, generate qq pair to reduce field energy

  9. Singularities in pQCD (massless case) Soft divergence Collinear divergence Closely related to hadronisation effects

  10. Singularities in phase space

  11. How to picture a QCD event Initial hard scattering high virtuality Q2generates high-pT partons Followed by angle-ordered gluonemissions: fragmentation At hadronic scale: hadronisation prescription (e.g. clustering in HERWIG) MC event generators use this picture

  12. QCD matter Energy density from Lattice QCD g: deg of freedom Nuclear matter Quark Gluon Plasma Bernard et al. hep-lat/0610017 Tc ~ 170 -190 MeV ec ~ 1 GeV/fm3 Deconfinement transition: sharp rise of energy density at Tc Increase in degrees of freedom: hadrons (3 pions) -> quarks+gluons (37)

  13. QCD phase diagram Quark Gluon Plasma (Quasi-)free quarks and gluons Temperature Critical Point Early universe Confined hadronic matter High-density phases? Elementary collisions (accelerator physics) Neutron stars Nuclear matter Bulk QCD matter: T and mB drive phases

  14. Heavy quarks Definition: heavy quarks, m >> LQCD Charm: m ~ 1.5 GeV Bottom: m ~ 4.5 GeV Top: m ~ 170 GeV ‘Perturbative’ hadronisation M. Cacciari, CTEQ-MCNet summer school 2008 Complications exist: QCD, EW corrections; quark mass defined in different ways

  15. Regimes of QCD Heavy ion physics Asymptotic freedom Dilute, hard scattering Deconfined matter Bulk matter, hot Bound states Hadrons/hadronic matter Baryon-dense matter (neutron stars) Bulk matter, cold

  16. Accelerators and colliders • p+p colliders (fixed target+ISR, SPPS, TevaTron, LHC) • Low-density QCD • Broad set of production mechanisms • Electron-positron colliders (SLC, LEP) • Electroweak physics • Clean, exclusive processes • Measure fragmentation functions • ep, mp accelerators (SLC, SPS, HERA) • Deeply Inelastic Scattering, proton structure • Parton density functions • Heavy ion accelerators/colliders (AGS, SPS, RHIC, LHC) • Bulk QCD and Quark Gluon Plasma Many decisive QCD measurements done

  17. The HERA Collider Zeus H1 The first and only ep collider in the world e± p 27.5 GeV 920 GeV Located in Hamburg √s = 318 GeV Equivalent to fixed target experiment with 50 TeV e±

  18. Example DIS events NC: CC: DIS: Measured electron/jet momentum fixes kinematics

  19. Proton structure F2 Q2: virtuality of the g x = Q2 / 2 p q ‘momentum fraction of the struck quark’

  20. Factorisation in DIS Integral over x is DGLAP evolution with splitting kernel Pqq

  21. Parton density distribution Low Q2: valence structure Q2 evolution (gluons) Gluon content of proton risesquickly with Q2 Soft gluons Valence quarks (p = uud) x ~ 1/3

  22. p+p  dijet at Tevatron Tevatron: p + p at √s = 1.9 TeV Jets produced with several 100 GeV

  23. Testing QCD at high energy small x x = partonic momentum fraction large x CDF, PRD75, 092006 Dominant ‘theory’ uncertainty: PDFs DIS to measure PDFs Theory matches data over many orders of magnitude Universality: PDFs from DIS used to calculate jet-production Note: can ignore fragmentation effects

  24. Testing QCD at RHIC with jets STAR, hep-ex/0608030 RHIC: p+p at √s = 200 GeV (recent run 500 GeV) Jets also measured at RHIC NLO pQCD also works at RHIC However: signficant uncertainties in energy scale, both ‘theory’ and experiment

  25. e+e-→ qq → jets Direct measurement of fragmentation functions

  26. pQCD illustrated fragmentation jet spectrum ~ parton spectrum CDF, PRD75, 092006

  27. Note: difference p+p, e++e- e+ + e- QCD events: jetshave p=1/2 √s Directly measure frag function p+p: steeply falling jet spectrum Hadron spectrum convolution of jet spectrum with fragmentation

  28. Fragmentation function uncertainties Hirai, Kumano, Nagai, Sudo, PRD75:094009 z=pT,h / 2√s z=pT,h / Ejet Full uncertainty analysis being pursuedUncertainties increase at small and large z

  29. Global analysis of FF proton anti-proton pions De Florian, Sassot, Stratmann, PRD 76:074033, PRD75:114010 ... or do a global fit, including p+p data Universality still holds

  30. Heavy quark fragmentation Heavy quarks Light quarks Heavy quark fragmentation: leading heavy meson carries large momentum fraction Less gluon radiation than for light quarks, due to ‘dead cone’

  31. Dead cone effect Radiated wave front cannot out-run source quark Heavy quark: b < 1 Result: minimum angle for radiation  Mass regulates collinear divergence

  32. Heavy Quark Fragmentation II Significant non-perturbative effects seen even in heavy quark fragmentation

  33. Factorisation in perturbative QCD Parton density function Non-perturbative: distribution of partons in proton Extracted from fits to DIS (ep) data Matrix element Perturbative component Fragmentation function Non-perturbative Measured/extracted from e+e- Factorisation: non-perturbative parts (long-distance physics) can be factored out in universal distributions (PDF, FF)

  34. Reminder: parton kinematics ep DIS: e+e- Know: incoming electron 4-mom Measure: scattered electon 4-mom Reconstruct: exchanged g 4-mom momentum fraction of struck quark Know: incoming electrons 4-mom Measure: scattered quark (jet) directions Reconstruct: exchanged g 4-mom = parton momenta • p+p: direct access to underlying kinematics only via • g, jet reconstruction • Exclusive measurements (e.g. di-leptons, di-hadrons)

  35. Differential kinematics in p+p Example: p0-pairs to probe low-x Forward pion p+p simulation Second pion hep-ex/0502040 Resulting x-range Need at least two hadrons to fix kinematics in p+p

  36. Direct photon basics direct fragment Small Rate: Yield aas LO: g does not fragment,direct measure of partonic kinematics Gordon and Vogelsang, PRD48, 3136 NLO: quarks radiate photons Direct and fragmentation contributionsame order of magnitude ‘fragmentation photons’

  37. Experimental challenge: p0gg Below pT=5 GeV: decays dominant at RHIC

  38. Direct photons: comparison to theory P. Aurenche et al, PRD73:094007 Good agreement theory-experimentFrom low energy (√s=20 GeV at CERN) to highest energies (1.96 TeV TevaTron) Exception: E706, fixed target FNAL deviates from trend: exp problem?

  39. Experimental access to fragmentation g Two Methods in p+p 200GeV Isolation cut ( 0.1*E > Econe(R=0.5) ): identifies non-fragmentation photons Photons associated with high-pT hadron: fragmentation Look at associated photons Triggering leading hadron R Eg g(Isolated)/g(all direct) g(fragment) / g(inclusive) PHENIX, PRL98, 012002 (2007) Only ~10% of g show significant associated hadronic activity

  40. Perturbative QCD processes • Hadron production • Heavy flavours • Jet production • e+e-→ jets • p(bar)+p → jets • Direct photon production Theory difficulty Measurement difficulty

  41. Summary • QCD is theory of strong interactions • Fundamental d.o.f quarks and gluons • Ground state: hadrons (bound states) • Perturbative QCD, asymptotic freedom at high Q2, small distances • Factorisation for pQCD at hadron colliders: • DIS to measure proton structure • e+ e- to measure fragmentation functions • Calculate jet, hadron spectra at hadron colliders More on bulk QCD next lecture

  42. QCD NLO resources • PHOX family (Aurenche et al) • MC@NLO (Frixione and Webber) You can use these codes yourself to generate the theory curves! And more: test your ideas on how to measure isolated photons or di-jets or...

  43. Extra slides

  44. DIS kinematics Leptonic tensor - calculable 2 Lμν Wμν dσ~ Hadronic tensor- constrained by Lorentz invariance Et q = k – k’, Q2 = -q2 Px = p + q , W2 = (p + q)2 s= (p + k)2 x = Q2 / (2p.q) y = (p.q)/(p.k) W2 = Q2 (1/x – 1) Q2 = s x y Ee Ep s = 4 Ee Ep Q2 = 4 Ee E’ sin2θe/2 y = (1 – E’/Ee cos2θe/2) x = Q2/sy The kinematic variables are measurable

  45. DIS kinematics

  46. QCD and quark parton model At low energies, quarks are confined in hadrons At high energies, quarks and gluons are manifest S. Bethke, J Phys G 26, R27 Asymptotic freedom Running coupling: as grows with decreasing Q2 Confinement, asymptotic freedom are unique to QCD Theory only cleanly describes certaint limits Study ‘emergent phenomena’ in QCD

  47. Resolved kinematics inDeep Inelastic Scattering small x x = partonic momentum fraction large x DIS: Measured electron momentum fixes kinematics