QGP and High p T Physics

Transcription

1 QGP and High p T Physics Lecture 1: The Physics of the QGP Helmholtz Graduate School of Fundamental Physics Winter School Obergurgl 2010 January 29 February 2, 2010 PD Dr. Klaus Reygers Physikalisches InsMtut Universität Heidelberg 1

2 Books/Paper Introduc*on to High Energy Heavy Ion Collisions Cheuk Yin Wong World ScienMfic Quark Gluon Plasma K. Yagi, T. Hatsuda, and Y. Miake, (Cambridge Monographs, ed. T. Ericson, P.V. Landshoff) ISBN Ultrarela*vis*c Heavy Ion Collisions (Elsevier) R. Vogt ISBN Quark Gluon Plasma 3 (World ScienMfic Publishing, ed. R.C. Hwa and X. N. Wang) ISBN The Large Hadron Collider, Nature 448 (2007) 269 Jet Quenching in Heavy Ion collisions, U. Wiedemann, arxiv

3 Introduc)on 3

4 Strong InteracMon Confinement: Isolated quarks and gluons cannot be observed, only color neutral hadrons Nobel prize in physics (2004) (work done in 1973 = Birth of QCD) David J. Gross H. David Politzer Frank Wilczek Asympto)c freedom: Coupling α s between color charges gets weaker for high momentum transfers, i.e., for small distances r (Perturba)ve methods applicable for r < 1/10 fm) Limit of low par)cle densi)es and weak coupling experimentally well tested ( QCD perturba)on theory) Nucleus Nucleus collisions: QCD at high temperatures and density ( QCD thermodynamics ) 4

5 UltrarelaMvisMc Heavy Ion Physics Basic, childlike ques)ons addressed in ultrarela)vis)c heavy ion physics: What happens to maser if you make it hoser and hoser? denser and denser? With increasing temperature T: solid liquid gas plasma QGP 5

6 Quark Gluon Plasma 6

7 Confinement Quark potential: V(r) = 4 3 QED: flux is not confined: 1/r potenmal Dominant at small distances (1 gluon exchange) α s (r) c r + k r quark potenmal Dominant at large distances (related to confinement) The long distance term k r is expected to disappear in the QGP QCD: flux is confined (flux tubes form): potenmal ~ r 7

8 Nucleus Nucleus Collisions: Mini Big Bang in the Laboratory Temperature (Kelvin) Time after Big Bang (seconds) Transi)on from the Quark Gluon Plasma to a gas of hadrons at ~ C hoser than the core of the sun Early universe: QGP hadron gas a few microseconds a[er the Big Bang 8

9 PredicMons from First Principles: Lamce QCD F. Karsch, E. Laermann, hep lat/ quark flavors: ε SB = g π2 30 T 4 with g = 37 only 20% deviation: qgp is an ideal gas not 9 T c = ( ) MeV ε c GeV/fm 3

10 Expected QCD Phase Diagram Early universe (t 10 6 s) RHIC, LHC (?) FAIR project at GSI ( ) 10 Measure of the net baryon density ρ

11 Ultra Rela)vis)sche Schwerionenkollision 11

12 Geometry Plays a Key Role in Ultra RelaMvisMc Heavy Ion Physics z Au + Au s NN = 200 GeV Uncorrected x Non-central Collision Number of produced charged parmcles N ch Number of par)cipants: number of nucleons in the overlap region Number of binary collisions: number of inelas)c nucleon nucleon collisions Small impact parameter b corresponds to large par)cle mul)plicity Reac)on plane: x z plane 12

13 Au+Au Collision at the Rela)vis)c Heavy Ion Collider (RHIC) in the USA gold nucleus E tot = 100 GeV/nucleon gold nucleus E tot = 100 GeV/nucleon LHC: E tot = 2750 GeV/nucleon for each beam 13

14 Au + Au Collisions at RHIC Peripheral Event STAR 14

15 Au + Au Collisions at RHIC Mid-Central Event STAR 15

16 Au + Au Collisions at RHIC Central Event about 5000 charged par)cles per central collisons STAR 16

17 Ultra RelaMvisMc Nucleus Nucleus Collisions *me Early hard parton parton scarerings (Q 2 >> Λ 2 QCD ) Time scales (RHIC, s NN = 200 GeV): Thermalized medium (QGP!?) (T 0 > T c, T c MeV) Thermalization: τ 0 < 1 fm/c TransiMon QGP hadron gas Freeze out Note: 1 fm/c = s QGP lifetime (center of a central Au+Au coll.): 5 fm/c 17

18 Brief History of Heavy Ion Physics Start Accelerator Projectile Energy ( s) per NN pair ~1985 AGS (BNL) Si ~5 GeV ~1985 SPS (CERN) O, S ~20 GeV 1994 SPS (CERN) Pb 17 GeV 2000 RHIC (BNL) Au 200 GeV 2010 LHC (CERN) Pb 5500 GeV 18

19 Important Results of the RHIC Heavy Ion Program Hadron suppression at high p T Medium is to large extent opaque for jets ( jet quenching ) Elliptic flow: Anisotropy in position space Ellip)c Flow at low p T Ideal hydro close to data Small viscosity: perfect liquid Evidence for early thermaliza)on (τ < 1 fm/c) All hadron species in chemical equillibrium (T 160 MeV, μ B 20 MeV) reaction plane Anisotropy in momentum space 19

20 Nucleus Nucleus Collisions: Freeze out Parameters MeV RHIC SPS Freeze out parameters T and μ B approximately at expected phase boundary 20

21 Points to Take Home Ultrarela)vis)c Heavy Ion Collisions: Study of QCD in the regime of extreme temperatures and densi)es Goal: Characteriza)on of the Quark Gluon Plasma Transi)on QGP hadrons about 10 6 s a[er the Big Bang QCD phase diagram: QGP reached at high temperature (about MeV [~ K]) and/or add high baryochemical poten)al μ B RHIC/LHC: μ B 0 Experiments at FAIR: μ B > 0 search for cri)cal point 21

22 Thermodynamics of the QGP 22

23 How to EsMmate the TransiMon Temperature for the QGP Hadron Gas TransiMon? Compute the pressure p in each phase The phase with the higher pressure wins 23

24 Bag Model Energy density in the bag is higher than in the vacuum: ε BAG ε vacuum =: B > 0 Hadron = bag filled with quarks Two kinds of vacuum Normal QCD Vacuum outside of the bag Perturba)ve QCD Vacuum within the bag Energy density: ε = E / V Energy of N quarks in a bag of radius R: E = 2.04N R + 4π 3 R3 B Condi)on for stability: de/dr = 0 (minimum): B 1/ 4 = 2.04N 1/ 4 4π 1 N = 3, R = 0,8 fm B 1/ 4 = 206 MeV ( = c = 1) R 24 normal QCD vacuum inward pressure perturba)ve QCD vacuum inside the proton kinetic energy of N particles in a spherical box of radius R

25 Quark AnMquark PotenMal in the QGP V (r) = 4 α(r) QCD vacuum: + kr 3 r V (r) = 4 α(r) QGP: exp r 3 r 25 λ d Within a QGP, the long range part of the poten)al of a quark an)quark pair vanishes Consequently, at high temperatures the J/Ψ cannot exist anymore Asympto)c freedom (α s (q 2 ) 0 for q 2 ): QGP is an ideal gas of quarks and gluons at very high temperatures Debye screening length, approx. 0,1 fm

26 Number of States Number of states between momentum p and p+dp (each state occupies a volume h 3 in phase space): number of states physical volume dn = V h 3 4π p2 dp volume of a spherical shell with radius p and thickness dp in momentum space 26

27 Fermi Dirac and Bose Einstein DistribuMon Number of par)cles with energy E... for fermions (half integer spin): g n(e) = ( E µ )/ kt 1 + e (Fermi Dirac distribu)on)... for bosons (integer spin): g n(e) = e ( E µ )/ kt 1 (Bose Einstein distribu)on) g : µ : T : # degrees of freedom (degeneracy) Chemical poten)al Temperature 27

28 Degeneracy QGP: g Bosons = 8 Color 2 Polarisation = 16 g Fermions = g Quarks + g Antiquarks = 2 g Quarks = 2 3 Color 2 Flavour 2 Spin = 24 assume only u and d quarks can be produced in the QGP, the rest too heavy Pion Gas: g Bosons = 3 Type g Fermions = 0 bosom line: ndf QGP 10 ndf Hadrons 28

29 Why Do We Consider Only Pions in the Hadronic Phase? Assume T << 500 MeV for the hadronic phase Then only pions should be relevant 29

30 IntegraMon Yields Total Quark Density in the Ideal (= non interacmng) QGP at Temperature T Massless quarks, Fermi Dirac distribu)on: degrees of freedom Quark density: dn q = g q V h 4π 1 3 p2 1 + e ( E µ q = k = c=1 p 2 V 1 = g q 2π e ( p µ q )/T n q (µ q ) = N q V = g q )/ kt dp dp 4π p 2 (2π ) e ( p µ q )/T d p holds for massless quarks An)quarks ( ): µ q = µ q 0 occupa)on factor n q (µ q ) = N q V = g q 4π p 2 (2π ) e ( p+ µ q )/T 0 d p 30

31 Quark Gluon Plasma with μ = 0: Quarks Quark density (μ q = 0): n q = n q = N q V = 3 2 ζ ( 3 ) g q π 2 2π 2 30 T 3 Total energy of the quarks: E q = 0 pdn q Calcula)ng the integral for vanishing energy density and pressure (μ q = 0) yields: ε q = E q V = 7 8 g π 2 q 30 T 4, p q = 1 3 ε q (iden)cal result for an)quarks (μ q = 0)) Example: T = 200 MeV, g q = 12 n q = n q = 1,71 / fm 3 31

32 Quark Gluon Plasma with µ = 0: Gluons Gluons, Bose Einstein distribu)on: dn g = Vg g 2π 2 p 2 e p/t 1 dp, n g = N g V = 1 V dn, E g g = pdn g 0 0 Solu)on: Energy density: Pressure: Par)cle density: ε g = E g V = g g π 2 30 T 4, p g = 1 3 ε g, n g = g g π 2 ζ (3)T Example: T = 200 MeV, g g = 16 n g = 2, 03 Gluons / fm 3 32

33 Quark Gluon Plasma with µ = 0: Pressure and Energy Density Pressure and energy density in a Quark Gluon Plasma at μ = 0 without par)cle interac)ons: p QGP = g g (g + g ) q q = 37 π 2 90 T 4 π 2 90 T 4 ε QGP = 3 p QGP = 37 π 2 30 T 4 Example: id. T = 200 MeV ε Gas QGP = 2,54GeV/fm 3 33

34 Quark Gluon Plasma with μ = 0: CriMcal Temperature (I) Accoun)ng for the QCD vacuum: QCD-Vac. ε QGP = ε QGP + B E = T S pv (µ = 0) QCD-Vac. p QGP = p QGP B p = Ts ε, s := S V So we have: p HG = 3aT 4 ε HG = 9aT 4 QCD-Vac. p QGP = 37aT 4 QCD-Vac. B ε QGP = 111aT 4 + B Gibbs criterion for the phase transi)on: p HG = p QCD-Vac. QGP, T HG = T QGP = T c T c = B 34a Phase transi)on in the bag model is of first order. Latent heat: ε QCD-Vac. QGP (T c ) ε HG (T c ) = 102aT 4 c + B = 4B 1/ 4 150MeV 34

35 Quark Gluon Plasma with µ = 0: CriMcal Temperature (II) QCD-Vac. p QGP = 37aT 4 B p HG = 3aT 4 35

36 Quark Gluon Plasma mit µ = 0: Entropy Entropy density for constant temperature and pressure: E = T S pv (µ = 0) S V = s = ε + p T = 4 p T Ra)o of entropy density (QGP / pion gas): s QGP = 148aT 3, s HG = 12aT 3 s QGP s HG 12, 3 Entropy per par)cle: Pion gas: s HG n π = 12π 2 / 90 T 3 g π 1, 202 / π 2 T 3 = 3.6 QGP: s q n q = 1,4 s g n g = 1, 2 36

37 Quark Gluon Plasma with µ = 0: QGP with parmcle interacmons (I) F. Karsch, E. Laermann, hep lat/ Upper limit: ideal gas 3 flavour Gitter-QCD für µ b = 0 37 T c 170 MeV ε c 0,7 GeV/fm 3 Different calcula)on yield results in the range T c = MeV

38 Quark Gluon Plasma with µ 0 Energy and ParMcle Number Density of the Quarks For µ q 0 but not for a solu)on in closed form can be found for and separately: ε q ε q 7π 2 ε q + ε q = g q 120 T µ 2 T q 8π µ 4 2 q Accordingly one finds for the quark density 1 n q n q = g q 6 µ T q 6π µ 3 2 q, g = 12 q ε q + ε q From this the net baryon density can be determined as: n B = n q n q 3 = 2 3 µ T q 3π µ 3 = 2 2 q 9 µ T B 81π µ 3 2 B (µ B = 3µ q ) 38

39 Quark Gluon Plasma with µ 0: CriMcal Temperature and CriMcal Quark PotenMal Energy density in a QGP with μ 0 (without par)cle interac)ons): ε QGP = π 2 T µ 2 q T π µ 4 2 q Condi)on for QGP stability: p QGP = 1! 3 ε = B T QGP c (µ q ) Cri)cal temperature / quark poten)al: Condi)on for QGP: QGP pressure pressure of the QCD vacuum (similar, but not iden)cal, to the previous condi)on p HG = p QGP ) T c (µ q = 0) = 90B 37π 2 1/ 4 µ c q (T = 0) = ( 2π 2 B) 1/ 4 = 0,43 GeV n B c (T = 0) = 2 3π 2 ( 2π 2 B) 3/ 4 = 0,72 fm -3 5 n nucleus Possibly reached in neutron stars 39

40 Quark Gluon Plasma with µ 0: Phase Diagram of the Non InteracMng QGP Quark-Gluon-Plasma Condition: ε c 0,7 GeV/fm 3 Hadron Gas µ B = 3 µ Quark 40

41 Quark Gluon Plasma with µ 0: Phase Diagram from Lamce QCD La~ce calcula)ons for μ b 0 Transi)on temperature for μ b = 0: T c = 164 MeV Cri)cal point: T = 162 MeV μ b = 340 MeV Z. Fodor, S.D. Katz, JHEP 404 (2004) 50 [hep lat/ ]. Normale Kernmaterie The existence and exact posi)on of the cri)cal point remains an open ques)on 41

42 Points to Take Home When treated as a rela)vis)c ideal gas, parameters for the transi)on Hadron Gas QGP are: T c (μ b =0) 150 MeV μ b (T=0) = 3 μ Quark (T=0) 1,3 GeV (this corresponds to approximately five )mes the density of normal nuclear maser) La~ce QCD calcula)ons show that for temperatures up to several )mes T c the assump)on of an ideal gas is a poor approxim)on Transi)on temperature from La~ce QCD: T c (μ b =0) = MeV 42