Charmonium in the QGP Debye screening a' la Matsui & Satz Steffen Hauf 17.01.2008 22. Januar 2008 Fachbereich nn Institut nn Prof. nn 1
Overview (1)Charmonium: an Introduction (2)Rehersion: Debye Screening (3)Charmonium in the QGP (4)Color Screening Models and Predictions (5)Summary /Outlook 22. Januar 2008 Steffen Hauf 2
Introduction - Charmonium Charmonium is a bound state of a charm quark antiquark pair: c c Stable states as long as strong decay is forbidden, i.e. Mass of charmonium is below mass of possible light-heavy mesons M 1.9GeV stable Charmonium states and the binding Energies [Satz2006] states above ' possible but not stable, will not be discussed of importance to us: Quarkonia-states a much more tightly bound than lighter hadrons because of heavy quark masses 22. Januar 2008 Steffen Hauf 3
Charmonium in the QGP Consider heavy quark Q and antiquark Q in a colorsinglet state (for this talk mainly charm-quarks, but bottom quarks are qualatively equal) Assume quarks are heavy and static so that any energy changes in the system indicate change in the binding energy. What happens as we increase Temperature T? 22. Januar 2008 Steffen Hauf 4
Charmonium below T c Start at T=0 and vacuum: Free energy has string form: F r ~ r resonance experiments determine 0.16GeV 2 Q Q -state breaks if F(r) high enough that two light quarks can be formed: F 0 =2 M D m c 1.2GeV r 0 1.2GeV/ 1.5fm String breaking [Satz2006] In vacuum Q Q break if they are seperated by more than 1.5 fm 22. Januar 2008 Steffen Hauf 5
Charmonium below T c T>0: Light mesons are in our system: Flip flop recoupling may occur, decreasing the large distance Q Q potential F,T with increasing T String breaking through recoupling [Satz2006] 22. Januar 2008 Steffen Hauf 6
Focus on Deconfinement QCD predicts that the strong interaction weakens at small distances, resulting in asymptotic freedom. Interesting implication: At very high pressures or temperatures quarks come close enough to each other and form a deconfined phase of matter. Simplified idea: At large distances overall color charge has to be neutral. We need a) three quarks of different color i.e rgb b) quarkonium state r r At very small distances one quark alway sees enough quarks of suitable colors so that overall charge cancels out: 22. Januar 2008 Steffen Hauf 7
Charmonium in QGP At T T c light quarks and gluons become deconfined which leads to color screening. Quarkonium can be used as temperature probe, ranging from vacuum string breaking, then dissociation through recoupling to colorscreening. This talk: Screening theory, later talks: experimental implications 22. Januar 2008 Steffen Hauf 8
Charmonium in the QGP Critical Temperatures obtained from differen lattice studies[petreczky] 22. Januar 2008 Steffen Hauf 9
Debye-Screening: Rehersion In order to unterstand Debye-Screening in QGP, first look at screening in classical Plasma Plasma: charged particles with added test charge: d 2 dx 2 = 0 relation of electrostatic potential and charge density (1-D) (2.1) thermal equilibrium, particle density distribution follows Boltzmanndistr.: U x /kt n x =n 0 e (2.2) U x : potential Energy k :Boltzmann constant 22. Januar 2008 Steffen Hauf 10
Debye Screening: Rehersion Now assume ions charge Z q e Potential Energy becomes U x =Zq e x (2.3) Eq. (2.2) yields: density of ions density of electrons n i x =n 0 e Zq e x / kt i n e x =n 0 e q e x / kt e (2.4a) (2.4b) total charge density is: =Zq e n i q e n e =q e n 0 e Zq e / kt e e q e /kt i (2.5) 22. Januar 2008 Steffen Hauf 11
Debye-Screening: Rehersion Eq: (2.5) in (2.1) must satisfy In plasma T d 2 dx 2 = q e n 0 0 e Zq e / kt i e q e /kt e (2.6) e ±q e / kt =1± q e kt 2 n 0 d 2 dx = q e 2 0 k Z 1 T i T e q 2 e n 0 0 k ZT e T i T e T i (2.7) 22. Januar 2008 Steffen Hauf 12
Debye Screening: Rehersion Solution of (2.7) is of type = Ae x / D x / Be D with B=0, elso potential would grow to infinity for large x = Ae x / D D= 0 k T i T e n 0 q e 2 T i ZT e Debye-Length for T i T e D= 0k T e n 0 q e 2 The Coulomb-potential of a test charge drops to 1/e at. Thus it is effectively screened from charges outside the Debye-sphere 22. Januar 2008 Steffen Hauf 13 D [Feynmann, Hofmann]
Color Screening in the QGP Similar to Debye-Screening discussed earlier. color charge instead of electrical charge Charge-carriers are now quarks and gluons Won't work if charge-carriers can't move freely Need for deconfined medium: QGP 22. Januar 2008 Steffen Hauf 14
Color Screening in the QGP Due to screening Charmonium will dissociate, if Debye sphere around one charm quark is smaller than the binding radius of the charmonium. ([Matsui] 0.5 r max J / 1.3fm for non-relativistic interaction) Screening radius is inversely proportional to the density and thus temperature. What does this imply? 22. Januar 2008 Steffen Hauf 15
Color Screening in QGP Expect that different Charmonium states will dissociate at different temperatures, depending on how tightly bound [Satz2006] To compare with experiments quantitive calculations required 22. Januar 2008 Steffen Hauf 16
Color Screening in QGP - Models Three approaches possible: V r,t 1) Model heavy quark potential as function of T and solve Schrödinger-equation 2)Use internal energy as potential and then solve Schrödinger-equation V r,t =U r,t model dependent model dependent U r,t = T 2 [ F r,t /T ] T =F r,t T 3)Directly calculate quarkonium spectrum from finite temperature lattice QCD F r,t T (3.1) still to complicated 22. Januar 2008 Steffen Hauf 17 [Satz2006]
Potential Model Approach-Schwinger Form Simplest confining potential for Q Q is Cornell-potential V r = r r added Debye-screening yields : string tension : gauge coupling constant V r,t r { 1 e r r } r e r = {1 e r } r e r (3.2) T :inverse Debye-radius, determined from Free Energy Fits 22. Januar 2008 Steffen Hauf 18
Potential Model Approach-Schwinger Form Input into Schrödinger-equation {2m e 1 m e 2 V r,t } i = E i i r (3.3) ' and c dissociate at T T c, J / holds until about 1.2T c Shortcomings: Schwinger Form is for 1-D, reality is 3-D Screening Mass is assumed in high energy form, but behaves different at T c 22. Januar 2008 Steffen Hauf 19
Internal Energy Model [Dixit1990] suggests screening can be evaluated for a given free Energy F r q in Cornell-potential q=1 for string term, q=-1 for gauge term, d dimensions. Assuming screening can be calculated seprately for each term yields total free energy of: F r,t =F s r,t F c r,t = r f s r,t r f c r,t (3.4) with boundry conditions f s r,t = f c r,t =1 f s r,t = f c r,t =1 for T 0 r 0 (3.5) 22. Januar 2008 Steffen Hauf 20
Internal Energy Model Through Debye-Hückel theory this results in gauge/coulomb -term F c r,t = r [e r r ] (3.6) string term F s r,t = [ 1/4 2 3/ 2 3/4 r 2 3/2 3/4 K 1/4[ r 2 ]] (3.7) large distance limit due to color screening gaussian cut-off K 1/ 4 x 2 exp x 2 22. Januar 2008 Steffen Hauf 21
Internal Energy Model Can now use (3.6) and (3.7) as expression for free energy. screening fits for free energy [Digal2005] screening mass T vs. T [Digal2005] 22. Januar 2008 Steffen Hauf 22
Internal Energy Model Can now use (3.6) and (3.7) as expression for free energy. Recall (3.1): U r,t = T 2 [ F r,t /T ] F r,t =F r,t T T T this gives us binding potential which we put into the Schrödinger equation We want to know temperature rewrite potential as T i at which state i dissociates V r,t =V,T V r,t 22. Januar 2008 Steffen Hauf 23
Internal Energy Model d V,T =c 1 T dt [c 1 2 ] with c 1 = 1/4 /2 3/2 3/4 describes energy of cloud of quarks and gluons in Debye-sphere around heavy quark relative to cloud without heavy quark V r,t vanishes for r 22. Januar 2008 Steffen Hauf 24
Internal Energy Model Results Schrödinger Equation rewritten in terms of binding Energy of state i { 1 m e 2 V r,t } i = E i T i r with E i T =V,T M i 2m c State i ceases to excist if E i T =0 each state, depending only on T giving us a critical temperature for 22. Januar 2008 Steffen Hauf 25
Internal Energy Model - Results Binding energy at different values of T for different Charmonium states [Satz] 22. Januar 2008 Steffen Hauf 26 Dissociation temperatures for Charmonium and Bottonium states [Satz]
Lattice QCD calculations Brief overview First two approaches are model dependent, direct calculation using only QCD favourable To date solving full QCD calculations not possible due to lack of computer power. Quenced QCD does not include dynamical quark loops => uncertainies are introduced. J / and 22. Januar 2008 Steffen Hauf 27 c spectral functions at different temperatures [Satz2006]
Summary/ Outlook Charmonium supression can be a useful probe for QGPs Screening models so far still include uncertainties, but near future will allow full lattice QCD calculations, which are truely model independent Models need to be experimentally verified. See future talks: 22. Januar 2008 Steffen Hauf 28 A. Marin - The experimental status of J/ψ measurements in nucleus-nucleus collisions (E) Jun Nian - J/ψ suppression and enhancement - the statistical hadronization model (T) M. Freudenberger - Quarkonium physics in nuclear collisions at the LHC (T)
References [Satz2006] Helmut Satz, Colour Deconfinement and Quarkonium Binding, hep-ph/0512217 v2, März 2006 [Digal2005] S. Digal et al., Eur Phys H. C 43 (2005) 71. [Dixit1990] V.V. Dixit, Mod Phys. Lett. A5 (1990) 227. [Feynmann] R. Feynmann, The Feynmann Lect. o. Phys. II (1963) 7.4 [Hoffmann] H.H Hoffmann, Lecture Notes Atoms a. Ions i. Plasma (2007) [Petreczky] P. Petreczky, hep-lat/0506012. [Matsui] T. Matsui, J/Psi Suppression by QGP Formation, Phys. Lett B, 178/4 416-421 22. Januar 2008 Steffen Hauf 29