Introduction to Hard Probes in Heavy Ion Collisions. Sangyong Jeon

Transcription

1 Introduction to Hard Probes in Heavy Ion Collisions Sangyong Jeon Department of Physics McGill University Montréal, QC, CANADA NNSPP Stonybrook University, July 2013 Jeon (McGill) Hard Probes Stony Brook / 33

2 McGill is in Montréal, Québec, Canada Montreal QC Canada Jeon (McGill) Hard Probes Stony Brook / 33

3 McGill is in Montréal, Québec, Canada Jeon (McGill) Hard Probes Stony Brook / 33

4 McGill is in Montréal, Québec, Canada Jeon (McGill) Hard Probes Stony Brook / 33

5 McGill is in Montréal, Québec, Canada Mr. McGill going home after a hard day s work. Jeon (McGill) Hard Probes Stony Brook / 33

6 McGill is in Montréal, Québec, Canada Rutherford carried out his Nobel (1908) winning work at McGill ( ). His original equipments on display Jeon (McGill) Hard Probes Stony Brook / 33

7 McGill Team Charles Gale Sangyong Jeon Björn Schenke (Formerly McGill, now BNL) Clint Young (Formerly McGill, Now UMinn) Gabriel Denicol Matt Luzum Sangwook Ryu Gojko Vujanovic Jean-Francois Paquet Michael Richard Igor Kozlov Khadija El Berhoumi Jean-Bernard Rose Jeon (McGill) Hard Probes Stony Brook / 33

8 Relativistic Heavy Ion Collisions Why do it? To study QGP Most extreme environment ever created: T 1 GeV. This existed only at around 1 microsecond after the Big Bang How do we understand it? Theory: Many-body QCD Experimental probes: Soft Hard Jeon (McGill) Hard Probes Stony Brook / 33

9 Hard Probes are useful Hard Probes Large momentum/energy phenomena pqcd applies We know how to do this Produced before QGP is formed in the same way as in hadron-hadron collisions Difference between pp, pa and AA tells us about the medium. Caveat: How well do we know the nuclear initial state? Jeon (McGill) Hard Probes Stony Brook / 33

10 What do we want to learn? Medium properties What is it made of? Quarks? Gluons? Hadrons? Tools Jets Thermodynamic properties Temperature, Equation of state, etc. Transport properties Mean-free-path, transport coefficients, etc. Hard Photons Jeon (McGill) Hard Probes Stony Brook / 33

11 Outline 1 pqcd 2 Jet Quenching 3 Hard Photons My goal for these lectures: Qualitative understanding Jeon (McGill) Hard Probes Stony Brook / 33

12 What is a hard probe? Early hard probe experiments Jeon (McGill) Hard Probes Stony Brook / 33

13 What is a hard probe? Early hard probe experiments Signal System Detector Object identification Probe Jeon (McGill) Hard Probes Stony Brook / 33

14 What is a hard probe? Early hard probe experiments Rutherford s α scattering experiment (1911) dσ d cos θ = π 2 Z 2 α 2 EM ( c E kin 1 (1 cos θ) 2 ) 2 Small angle scattering dominates dσ/d cos θ 1/θ 4 But backscattering prob. is finite, favoring Rutherford s model over Thompson s (which causes no backscattering) Jeon (McGill) Hard Probes Stony Brook / 33

15 Fast-forward to the present ATLAS: Intact dijets in Pb+Pb ATLAS: One jet is fully quenched in Pb+Pb Simplest conclusion to draw: The medium is opaque. We want to know much more than that! Jeon (McGill) Hard Probes Stony Brook / 33

16 Hard Probe Requirements Must be known & calculable using pqcd. Must be created before QGP forms Both requirements satisfied if the energy scale is much large compared to Λ QCD 200 MeV and the length (time) scale is much shorter than 1 fm. Example: Jets (high energy partons) with E 1 GeV and Heavy quarks (c, b) with M 1 GeV Jeon (McGill) Hard Probes Stony Brook / 33

17 Hard Probes Probes Propagation of hard partons or Jets Quarkonium suppression High p T electromagnetic probes (real and virtual photons) Goal To characterize QGP To characterize initial state (npdf, CGC?) Jeon (McGill) Hard Probes Stony Brook / 33

18 (Very) Schematic view of heavy ion collisions Freeze out γ, dileptons, flow t background J/ψ, Jets Hadronic Phase Free streaming QGP Target trajectory Thermalization Projectile trajectory z Jeon (McGill) Hard Probes Stony Brook / 33

19 (Very) Schematic view of heavy ion collisions Static color charges Classical gluon field Jeon (McGill) Hard Probes Stony Brook / 33

20 (Very) Schematic view of heavy ion collisions High energy photons Hard Scatterings occur at this stage Jets are produced Nuclei are breaking up Gluon fields are grabbing each other Jeon (McGill) Hard Probes Stony Brook / 33

21 (Very) Schematic view of heavy ion collisions Jets propagating Photons are produced Nucleus remnant Entropy is produced. Pre equilibrium mix of streaming quarks, gluons and classical gluon field. Jeon (McGill) Hard Probes Stony Brook / 33

22 (Very) Schematic view of heavy ion collisions A jet can convert to photon Thermal photons Quenched jets come out High pressure flows develope Jeon (McGill) Hard Probes Stony Brook / 33

23 Review of some basic concepts - Feynman Rules ( ) G µν ba = iδ ba g µν + (1 1/λ) k µ k ν k 2 +iɛ k 2 +iɛ S βα ij δ ij = i k 2 m 2 +iɛ (k µγ µ + m) βα ig[t (F ) c ] β [γ µ ] βα gf a1 a 2 a 3 (g ν 1ν 2(p1 p 2 ) ν 3 + perm.) ig 2 (f ea1 a 2 f ea3 a 4 (g ν 1ν 3g ν 2 ν 4 g ν 1 ν 4g ν 2 ν 3) +perm. on 234) Jeon (McGill) Hard Probes Stony Brook / 33

24 Review of some basic concepts Basic unit: With = c = 1 Units Mass: GeV/c 2 Momentum: GeV/c Energy: GeV Length: c/gev 200 MeV 1/fm 1 fm 1/(200 MeV) c = MeV fm 0.2 GeV fm Thermal energy k B = evk 1 With k B = 1, 1 ev = 11, 605 K or 290 K 1 40 ev Jeon (McGill) Hard Probes Stony Brook / 33

25 Review of some basic concepts Spatial resolution: x p 1/2 Shorter the wavelength (larger the momentum) sees spatial details up to x λ. Jeon (McGill) Hard Probes Stony Brook / 33

26 Review of some basic concepts Energy-Time uncertainty: E t 1/2 E = p 0 p 2 + m 2. If E = 0, then p µ p µ = m 2 : On-shell If E 0, the p µ p µ m 2 : Off-shell Interpretation An off-shell state can exist only for t 1/ E. 2 k = 0 p = m 2 2 q = m 2 2 p = m k = 0 This interaction lasts t 1/ ( p + k (p + k) 2 ) Jeon (McGill) Hard Probes Stony Brook / 33

27 Hard Probe time scale p k Q p Off-shell scale with k = k + Q k Q 2 = (k k ) µ (k k ) µ = ( k k ) 2 ( k 0) 2 (0 k ) 2 s Time scale: τ 1/ (k k ) 2 1/ s Jeon (McGill) Hard Probes Stony Brook / 33

28 Perturbative QCD Jeon (McGill) Hard Probes Stony Brook / 33

29 Perturbative QCD (pqcd) q QCD Interaction of quarks and gluons g g g q g g g g g N f flavors of quarks N 2 c 1 gluons Jeon (McGill) Hard Probes Stony Brook / 33

30 Perturbative QCD (pqcd) Perturbation Theory when g << 1 q g q q g g g q O(g) g More important >> g O(g^3) Less so Calculate physical quantities as an expansion in the small coupling constant g Corrections to vertices Corrections to propagators Jeon (McGill) Hard Probes Stony Brook / 33

31 Perturbative QCD (pqcd) Calculate physical quantities as an expansion in the small coupling constant g Corrections to vertices Corrections to propagators Jeon (McGill) Hard Probes Stony Brook / 33

32 Perturbative QCD (pqcd) Perturbative expansion possible because of asymptotic freedom Q 2 α S Q 2 = β 0α 2 S β 1α 3 S + α S (Q 2 ) 1 ((33 2n f )/12π) ln(q 2 /Λ 2 QCD ) pqcd reliable for Q > 1 GeV S. Bethke, arxiv: Jeon (McGill) Hard Probes Stony Brook / 33

33 Intuitive understanding of asymptotic freedom q r rg QED QCD g rb bg +e e b gb q QED: Surrounded by virtual eē cloud Virtual e cloud drawn closer to q > 0 ==> Screening Larger Q ==> smaller distance ==> Sees less of the cloud ==> Closer to bare charge Possible because the original q never changes and photons do not carry charges Jeon (McGill) Hard Probes Stony Brook / 33

34 Intuitive understanding of asymptotic freedom q r rg QED QCD g rb bg +e e b gb q QCD: Can resolve more soft virtual gluons at larger Q The color of the real particle can change whenever a gluon is emitted. Larger Q ==> More frequent changes ==> Less average color charge ==> Asymptotic freedom Jeon (McGill) Hard Probes Stony Brook / 33

35 Difficulties with QCD As Q Λ QCD, α S (Q 2 ) Hadrons are O(Λ QCD ) objects. 1 ((33 2n f )/12π) ln(q 2 /Λ 2 QCD ) Anything that has to do with hadron properties such as color confinement and hadronization is non-perturbative. In the IR limit, perturbation theory does not work ==> Factorize what can be calculated with pqcd (UV) and what cannot be calculated (IR) Jeon (McGill) Hard Probes Stony Brook / 33

36 Factorization Theorem hadron Jet Hadron-Hadron Jet production scheme: hadron x 1 x 2 Q pqcd process Jet σ = abcd f a/a (x a, Q f )f b/b (x b, Q f ) σ ab cd D C/c (z C, Q) Jeon (McGill) Hard Probes Stony Brook / 33

37 Factorization Theorem How realistic pqcd calculations are done σ hh C+X = abcd dx 1 dx 2 f a/h (x 1, Q f )f b/h (x 2, Q f )σ ab cd (Q R )D C/c (z C, Q f ) f a/h (x 1, Q f ): Parton distribution function. Probability to have a parton type a with the momentum fraction x 1 in a hadron h. Depends on the factorization scale Q f. D C/c (z C, Q f ): Fragmentation function. Probability to create a hadron type C our of parton type c carrying the momentum fraction z c. σ ab cd (Q R ): Parton-parton scattering cross-section. Jeon (McGill) Hard Probes Stony Brook / 33

38 Factorization Theorem How realistic pqcd calculations are done σ hh C+X = abcd dx 1 dx 2 f a/h (x 1, Q f )f b/h (x 2, Q f )σ ab cd (Q R )D C/c (z C, Q f ) pqcd controls the evolutions of f a/h (x 1, Q f ) and D C/c (z C, Q f ). But pqcd cannot determine the initial data because this is dominated by IR processes. pqcd can calculate σ ab cd (Q R ) when the renormalization scale Q R can be set high (that is, when s is large) Jeon (McGill) Hard Probes Stony Brook / 33

39 How to think about the initial state factorization QED analogy Weizsäcker-Williams field Highly contracted in the z direction Q Coulomb potential in the rest frame of the charge ϕ = Q/ r Q v ~ c In the moving frame A µ (x ) = Λ µ ν A ν (x(x )) The coordinate in the moving frame x = (t, x, y, z). This corresponds to the rest frame position x = (tγ zγv, x, y, zγ tγv). Jeon (McGill) Hard Probes Stony Brook / 33

40 How to think about the initial state factorization QED analogy Weizsäcker-Williams field Highly contracted in the z direction Coulomb potential in the rest frame of the charge Q v ~ c Q ϕ = Q/ r In the moving frame A µ Q(γ, 0, 0, γv) = (z vt) 2 γ 2 + x 2 Pure gauge in the v 1 limit A µ Q(1, 0, 0, 1) z vt = Q µ ln z vt Jeon (McGill) Hard Probes Stony Brook / 33

41 How to think about the initial state factorization QED analogy Weizsäcker-Williams field Highly contracted in the z direction F µν 0 unless z vt Q v ~ c Q In the rest frame: Coulomb field is made up of space-like virtual photons q µ q µ = q 2 with q 0 = 0. In the Lab frame: q µ = (q z sinh η, q, q z cosh η) For large η, E = q q e η q 2 /q z ==> t 1/ E e η q z /q 2 ==> virtual photons look almost like real photons. Jeon (McGill) Hard Probes Stony Brook / 33

42 How to think about the initial state factorization QED analogy Weizsäcker-Williams field Highly contracted in the z direction F µν 0 unless z vt Q v ~ c Q To a first approximation, the approaching particles do not know about each other until they are on top of each other. Initial photon momentum distribution factorizes: F(x 1, x 2 ) = f (x 1 )f (x 2 ) but this is not exact. In QCD, color neutrality of hadrons help. Jeon (McGill) Hard Probes Stony Brook / 33

43 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. Q 0 : Coarse grained. You see one almost on-shell parton. Jeon (McGill) Hard Probes Stony Brook / 33

44 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. Q 0 < Q 1 : Start to resolve another parton Jeon (McGill) Hard Probes Stony Brook / 33

45 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. Q 0 < Q 1 < Q 2 : And another Jeon (McGill) Hard Probes Stony Brook / 33

46 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. Q 0 < Q 1 < Q 2 < Q 3 : And another Jeon (McGill) Hard Probes Stony Brook / 33

47 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. You get the idea Jeon (McGill) Hard Probes Stony Brook / 33

48 DGLAP Equation f (x, Q f ): Probability density of partons with the virtuality less than Q f. Q 2 ( q S Q 2 g ) = α S(Q 2 ) 2π ( Pqq 2n f P qg P gq P gg ) ( q S g ) where P ij : Splitting function Probability to end up with ij in the final state. Jeon (McGill) Hard Probes Stony Brook / 33

49 Splitting can cause IR divergence p is on-shell: p 2 = 0 Diverges when either k or l is on-shell p k l This happens either k is very soft so that l 2 = (p k) 2 p 2 or p and k are almost collinear l 2 = (p k) 2 = p 2 + k 2 2pk 0 Jeon (McGill) Hard Probes Stony Brook / 33

50 Splitting can cause IR divergence g q q and g q qg Only the sum is IR finite because soft and collinear divergences Splitting functions know about this Jeon (McGill) Hard Probes Stony Brook / 33

51 Splitting can cause IR divergence Observables must be IR safe. 3rd diagram must be treated as 2-jet when the radiation is soft or collinear ==> IR-safe Jet definitions Jeon (McGill) Hard Probes Stony Brook / 33

52 Factorization Theorem Fragmentation function similarly runs 3 different scales: Q f for the pdf, Q R for σ(q R ) and Q f for the fragmentation function In principle, physical observables should not depend on these scales. However, factorization theorem is only approximate. Lots of freedom to choose the scales. Usually something like Q f = Q R = Q f = #p T works OK where p T is the momentum of the final state particle. Jeon (McGill) Hard Probes Stony Brook / 33

53 pqcd & Factorization at work 2 HERA F 2 em F 2 -log10 (x) x=6.32e-5 x= x= x= x= x= x= x= x= x= x= x=0.005 x=0.008 x=0.013 ZEUS NLO QCD fit H1 PDF 2000 fit x=0.021 H H1 (prel.) 99/00 ZEUS 96/97 BCDMS E665 NMC 1/2π dσ/(dηdpt) [pb/gev] Combined MB STAR p+p g jet + X s=200 GeV midpoint-cone r cone= <η<0.8 (a) 2 x=0.032 x=0.05 x= Combined HT NLO QCD (Vogelsang) 1 x=0.13 x=0.18 x=0.25 x=0.4 x= Q 2 (GeV 2 ) data / theory Systematic Uncertainty Theory Scale Uncertainty (b) p T [GeV/c] Jeon (McGill) Hard Probes Stony Brook / 33

54 pqcd & Factorization at work CTEQ 06 Proton PDF s Larger Q ==> More soft partons Jeon (McGill) Hard Probes Stony Brook / 33

55 pqcd & Factorization at work Gluon distributions for Q 2 = 10 GeV 2 and Q 2 = 100 GeV 2. Jeon (McGill) Hard Probes Stony Brook / 33