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## Lecture I: introduction to QCD

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**Lecture I: introduction to QCD**Marco van Leeuwen Utrecht University Jyväskylä Summer School 2008**General QCD references**• Particle Data Group topical reviews http://pdg.lbl.gov/2004/reviews/contents_sports.html • QCD and jets: CTEQ web page and summer school lectures http://www.phys.psu.edu/~cteq/ • Handbook of Perturbative QCD, Rev. Mod. Phys. 67, 157–248 (1995)http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.ps.gz • 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)**What is QCD?**From: T. Schaefer, QM08 student talk**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**Seeing quarks and gluons**In high-energy collisions, observe traces of quarks, gluons (‘jets’)**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**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)**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**Singularities in pQCD**(massless case) Soft divergence Collinear divergence Closely related to hadronisation effects**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**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)**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**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**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**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**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±**Example DIS events**NC: CC: DIS: Measured electron/jet momentum fixes kinematics**Proton structure F2**Q2: virtuality of the g x = Q2 / 2 p q ‘momentum fraction of the struck quark’**Factorisation in DIS**Integral over x is DGLAP evolution with splitting kernel Pqq**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**p+p dijet at Tevatron**Tevatron: p + p at √s = 1.9 TeV Jets produced with several 100 GeV**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**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**e+e-→ qq → jets**Direct measurement of fragmentation functions**pQCD illustrated**fragmentation jet spectrum ~ parton spectrum CDF, PRD75, 092006**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**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**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**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’**Dead cone effect**Radiated wave front cannot out-run source quark Heavy quark: b < 1 Result: minimum angle for radiation Mass regulates collinear divergence**Heavy Quark Fragmentation II**Significant non-perturbative effects seen even in heavy quark fragmentation**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)**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)**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**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’**Experimental challenge: p0gg**Below pT=5 GeV: decays dominant at RHIC**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?**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**Perturbative QCD processes**• Hadron production • Heavy flavours • Jet production • e+e-→ jets • p(bar)+p → jets • Direct photon production Theory difficulty Measurement difficulty**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**QCD NLO resources**• PHOX family (Aurenche et al)http://wwwlapp.in2p3.fr/lapth/PHOX_FAMILY/main.html • MC@NLO (Frixione and Webber)http://www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/ 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...**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**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**Resolved kinematics inDeep Inelastic Scattering**small x x = partonic momentum fraction large x DIS: Measured electron momentum fixes kinematics