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

2 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) General QCD references

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 Baryons: 3 quarks I 3 (u,d content) S strangeness I 3 (u,d content) Mesons: quark-anti-quark

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:  s decreases with Q 2 Pole at  =   QCD ~ 200 MeV ~ 1 fm -1 Hadronic scale

7 Asymptotic freedom and pQCD At large Q 2, hard processes: calculate ‘free parton scattering’ At high energies, quarks and gluons are manifest But need to add hadronisation (+initial state PDFs) + more subprocesses

8 Low Q 2 : confinement Lattice QCD potential  large, perturbative techniques not suitable Lattice QCD: solve equations of motion (of the fields) on a space-time lattice by MC String breaks, generate qq pair to reduce field energy Bali, hep-lat/

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

10 Singularities in phase space

11 How to picture a QCD event MC event generators use this picture Initial hard scattering high virtuality Q 2 generates high-p T partons Followed by angle-ordered gluon emissions: fragmentation At hadronic scale: hadronisation prescription (e.g. clustering in HERWIG)

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

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

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

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

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

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

19 Proton structure F 2 Q 2 : virtuality of the  x = Q 2 / 2 p q ‘momentum fraction of the struck quark’

20 Factorisation in DIS Integral over x is DGLAP evolution with splitting kernel P qq

21 Parton density distribution Low Q 2 : valence structure Valence quarks (p = uud) x ~ 1/3 Soft gluons Q 2 evolution (gluons) Gluon content of proton rises quickly with Q 2

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

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

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

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

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

28 Fragmentation function uncertainties Hirai, Kumano, Nagai, Sudo, PRD75: z=p T,h / 2√sz=p T,h / E jet Full uncertainty analysis being pursued Uncertainties increase at small and large z

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

30 Heavy quark fragmentation Light quarks Heavy 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:  < 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: Know: incoming electron 4-mom Measure: scattered electon 4-mom Reconstruct: exchanged  4-mom momentum fraction of struck quark e+e-e+e- Know: incoming electrons 4-mom Measure: scattered quark (jet) directions Reconstruct: exchanged  4-mom = parton momenta p+p: direct access to underlying kinematics only via , jet reconstruction Exclusive measurements (e.g. di-leptons, di-hadrons)

35 Differential kinematics in p+p Example:  0 -pairs to probe low-x p+p simulation hep-ex/ Forward pion Second pion Resulting x-range Need at least two hadrons to fix kinematics in p+p

36 Direct photon basics direct fragment Gordon and Vogelsang, PRD48, 3136 Small Rate: Yield  s NLO: quarks radiate photons LO:  does not fragment, direct measure of partonic kinematics ‘fragmentation photons’ Direct and fragmentation contribution same order of magnitude

37 Experimental challenge:  0   Below p T =5 GeV: decays dominant at RHIC

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

39  (fragment) /  (inclusive) Experimental access to fragmentation  Two Methods in p+p 200GeV –Isolation cut ( 0.1*E  > E cone (R=0.5) ): identifies non-fragmentation photons –Photons associated with high-p T hadron: fragmentation PHENIX, PRL98, (2007) R EE Triggering leading hadron Look at associated photons  (Isolated)/  (all direct) Only ~10% of  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 Measurement difficulty Theory 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 Q 2, 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) (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 dσ~dσ~ 2 L μν W μν EeEe EtEt EpEp q = k – k’, Q 2 = -q 2 P x = p + q, W 2 = (p + q) 2 s= (p + k) 2 x = Q 2 / (2p.q) y = (p.q)/(p.k) W 2 = Q 2 (1/x – 1) Q 2 = s x y s = 4 E e E p Q 2 = 4 E e E’ sin 2 θ e /2 y = (1 – E’/E e cos 2 θ e /2) x = Q 2 /sy The kinematic variables are measurable Leptonic tensor - calculable Hadronic tensor- constrained by Lorentz invariance

45 DIS kinematics

46 QCD and quark parton model S. Bethke, J Phys G 26, R27 Running coupling:  s grows with decreasing Q 2 Asymptotic freedom At low energies, quarks are confined in hadrons Confinement, asymptotic freedom are unique to QCD At high energies, quarks and gluons are manifest Theory only cleanly describes certaint limits Study ‘emergent phenomena’ in QCD

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