Ágnes Mócsy, Bad Honnef 08 1 Quarkonia from Lattice and Potential Models Characterization of QGP with Heavy Quarks Bad Honnef Germany, June Ágnes Mócsy based on work with Péter Petreczky

Ágnes Mócsy, Bad Honnef 08 2 Confined Matter

Ágnes Mócsy, Bad Honnef 08 3 Deconfined Matter

Ágnes Mócsy, Bad Honnef 08 4 Deconfined Matter Screening

Ágnes Mócsy, Bad Honnef 08 5 Deconfined Matter Screening J/  melting

Ágnes Mócsy, Bad Honnef 08 6 Deconfined Matter Screening J/  melting J/  yield suppressed

Ágnes Mócsy, Bad Honnef 08 7 T/T C 1/  r  [fm -1 ]  (1S) J/  (1S)  c (1P)  ’(2S)  b ’(2P)  ’’(3S) Sequential suppression QGP thermometer

Ágnes Mócsy, Bad Honnef 08 8 Screening seen in lattice QCD no T effects strong screening Free energy of static Q-Qbar pair: F 1 RBC-Bielefeld Coll. (2007) The range of interaction between Q and Qbar is strongly reduced. Need to quantify what this means for quarkonia.

Ágnes Mócsy, Bad Honnef 08 9 J/  suppression measured … but interpretation not understood Hot medium effects - screening? Must know dissociation temperature, in-medium properties Cold nuclear matter effects ? Recombination? PHENIX, QM 2008

Ágnes Mócsy, Bad Honnef Studies of quarkonium in-medium Potential Models Lattice QCD Matsui, Satz, PLB 178 (1986) 416 Digal, Petreczky, Satz, PRD 64 (2001) Wong PRC 72 (2005) ; PRC 76 (2007) Wong, Crater, PRD 75 (2007) Mannarelli, Rapp, PRC 72 (2005) Cabrera, Rapp, Eur Phys J A 31 (2007) 858; PRD 76 (2007) Alberico et al,PRD 72 (2005) ; PRD 75 (2007) PRD 77 (2008) Mócsy, Petreczky, Eur Phys J C 43 (2005) 77; PRD 73 (2006) PRD 77(2008) ; PRL 99 (2007) Umeda et al Eur. Phys. J C 39S1 (2005) 9 Asakawa, Hatsuda, PRL 92 (2004) Datta et al PRD 69 (2004) Jakovac et al PRD 75 (2007) Aarts et al Nucl Phys A785 (2007) 198 Iida et al PRD 74 (2006) Umeda PRD 75 (2007)

Ágnes Mócsy, Bad Honnef Studies of quarkonium in-medium Potential Models Lattice QCD Spectral functions Still inconclusive (discretization effects, statistical errors) Assume: medium effects can be understood in terms of a temperature- dependent screened potential Contains all info about a given channel. Melting of a state corresponds to disappearance of a peak.

Ágnes Mócsy, Bad Honnef Quarkonium from lattice Euclidean-time correlator measured on the lattice Spectral functions extracted from correlators inverting the integrals using Maximum Entropy Method Kernel cosh[  (  -1/2T)]/sinh[  /2T] scal ar pseudoscalar vector axialvector c bc b  c0  b0 J/   c1  b1

Ágnes Mócsy, Bad Honnef Spectral function from lattice Shows no large T-dependence Peak has been commonly interpreted as ground state Uncertainties are significant! limited # data points limited extent in tau systematic effects prior-dependence cc Details cannot be resolved. “..it is difficult to make any conclusive statement based on the shape of the spectral functions … ” Jakovác et al PRD (2007) Jakovac et al, PRD (2007)

Ágnes Mócsy, Bad Honnef Ratio of correlators Compare high T correlators to correlators “reconstructed” from spectral function at low T Pseudoscalar Scalar Datta et al PRD (2004) T-dependence of correlator ratio determines dissociation temperatures:  c survives to ~2T c &  c melts at 1.1T c Initial interpretation Seemingly in agreement with spectral function interpretation. 2004: “J/  melting” replaced by “J/  survival”

Ágnes Mócsy, Bad Honnef Recently: Zero-mode contribution Bound and unbound Q-Qbar pairs (  >2m Q ) Bound and unbound Q-Qbar pairs (  >2m Q ) Quasi-free heavy quarks interacting with the medium Low frequency contribution to spectral function at finite T, scattering states of single heavy quarks (commonly overlooked) Gives constant contribution to correlator =>> Look at derivatives Umeda, PRD 75 (2007)

Ágnes Mócsy, Bad Honnef Ratio of correlator derivatives Flatness is not related to survival: no change in the derivative scalar up to 3T c !  c survives until 3T c ??? Almost the entire T-dependence comes from zero-modes. Understood in terms of quasi-free quarks with some effective mass - indication of free heavy quarks in the deconfined phase All correlators are flat. Datta, Petreczky, QM 2008, arXiv: [hep-lat]

Ágnes Mócsy, Bad Honnef From the lattice Dramatic changes in spectral function are not reflected in the correlator

Ágnes Mócsy, Bad Honnef Lessons from Lattice QCD Small change in the ratio of correlators does not imply (un)modification of states. Dominant source of T-dependence of correlators comes from zero- modes (low energy part of spectral function). Understood in terms of free heavy quark gas. High energy part which carries info about bound states shows almost no T-dependence until 3T c in all channels. Although spectral functions obtained with MEM do not show much T-dependence, the details (like bound state peaks) are not resolved in the current lattice data.

Ágnes Mócsy, Bad Honnef Would really the J/  survive in QGP up to 1.5-2T c even though strong screening is seen in the medium?

Ágnes Mócsy, Bad Honnef Potential model at T=0 Interaction between heavy quark (Q=c,b) and its antiquark Qbar described by a potential: Cornell potential Non-relativistic treatment Solve Schrödinger equation - obtain properties, binding energies Describes well spectroscopy; Verified on the lattice; Derived from QCD. heavy quark mass m Q >>  QCD and velocity v<<1 V(r) Confined r V(r)

Ágnes Mócsy, Bad Honnef Potential model at finite T Matsui-Satz argument: Medium effects on the interaction between Q and Qbar described by a T-dependent screened potential Solve Schrödinger equation for non-relativistic Green’s function - obtain spectral function Utilize lattice data V(r,T) Confined Deconfined T>T c r V(r)

Ágnes Mócsy, Bad Honnef Lattice & Potential models Potential Models Lattice QCD Quarkonium correlators Reliable Spectral functions Free energy of static quarks Potential from pNRQCD Quarkonium correlators Spectral functions Not yet reliable

Ágnes Mócsy, Bad Honnef First lattice-based potential Free energy of static Q-Qbar pair: F 1 Digal, Petreczky, Satz, PRD (2001) RBC-Bielefeld Coll. (2007) Free energy F 1 ≠ Potential V Contains entropy F 1 =E 1 -ST

Ágnes Mócsy, Bad Honnef Lattice-based potentials Most confining potential Our physical potential –Deeper potentials: stronger binding, higher T diss –Open charm (bottom) threshold = 2m Q +V inf (T) –Explore uncertainty assuming the general features of F 1 r < r 1 (1/T): vacuum potential r > r 2 (1/T) : exponential screening Wong potential 1.2T c T=0 potential Internal energy TS - lower limit - upper limit Mócsy, Petreczky 2008 Free energy r1r1 r2r2 Can we constrain them using correlator lattice data?

Ágnes Mócsy, Bad Honnef Pseudoscalar correlators 1.2T c No, we cannot determine quarkonium properties from such comparisons; If no agreement found, model is ruled out; We can set upper limits. Set of potentials all agree with lattice data; yield indistinguishable results. with set of potentials within the allowed ranges ~ 1-2%

Ágnes Mócsy, Bad Honnef Pseudoscalar spectral function cc most confining potential using most confining potential Mocsy, Petreczky 08 Large threshold (rescattering) enhancement even at high T - indication of Q-Qbar correlation - compensates for melting of states keeping correlators flat ~ 1-2%

Ágnes Mócsy, Bad Honnef Pseudoscalar spectral function cc most confining potential using most confining potential Mocsy, Petreczky 08 State is dissociated when no peak structure is seen. At which T the peak structure disappears? E bin =0 ?! E bin = 2m q +V ∞ (T)-M Warning! Widths are not physical - broadening not included

Ágnes Mócsy, Bad Honnef Binding energies weak binding strong binding Binding energies decrease as T increases. True for all potential models. What’s the meaning of a J/  with 0.2 MeV binding? With E bin < T a state is weakly bound and thermal fluctuations can destroy it Mocsy, Petreczky, PRL 08 Do not need to reach E bin =0 to dissociate a state.

Ágnes Mócsy, Bad Honnef Upper limit melting temperatures Estimate dissociation rate due to thermal activation (thermal width) Dissociation condition: E bin = 2m Q +V ∞ (T)-M QQbar < T Kharzeev, McLerran, Satz, PLB (1995) Broadening in agreement with: pQCD calculation QCD sum rule Imaginary part in resummed pQCD pNRQCD at finite T Laine,Philipsen Lee, Morita Park et al Brambilla et al J/  melts before it bounds. T/T C 1/  r  [fm -1 ]  (1S) J/  (1S)  ’(2S)  c (1P)  ’(2S)  b ’(2P)  ’’(3S) TCTC  b (1P)

Ágnes Mócsy, Bad Honnef Lessons from potential models Set of potentials (between the lower and upper limit constrained by lattice free energy data) yield agreement with lattice data on correlators (S- and P-wave) Precise quarkonium properties cannot be determined this way, only upper limit. Set of potentials (between the lower and upper limit constrained by lattice free energy data) yield agreement with lattice data on correlators (S- and P-wave) Precise quarkonium properties cannot be determined this way, only upper limit. Large threshold enhancement above free propagation even at high T - compensates for melting of states (flat correlators) - correlation between Q and Qbar persists Large threshold enhancement above free propagation even at high T - compensates for melting of states (flat correlators) - correlation between Q and Qbar persists Upper limit potential predicts that all bound states melt by 1.3T c, except the upsilon, which survives until 2T c. Lattice results are consistent with quarkonium melting. Upper limit potential predicts that all bound states melt by 1.3T c, except the upsilon, which survives until 2T c. Lattice results are consistent with quarkonium melting. Decrease in binding energies with increasing temperature.

Ágnes Mócsy, Bad Honnef Implications for RHICollisions  survival  J/   survival   Karsch et al Consequences: J/  R AA : J/  should melt at SPS and RHIC  suppressed at RHIC (centrality dependent?); definitely at LHC expect correlations of heavy-quark pairs  DD correlations?  non-statistical recombination?

Ágnes Mócsy, Bad Honnef Final note All of the above discussion is for isotropic medium Anisotropic plasma: Q-Qbar might be more strongly bound in an anisotropic medium, especially if it is aligned along the anisotropy of the medium (beam direction) Dumitru, Guo, Strickland, PLB 62 (2008) 37

Ágnes Mócsy, Bad Honnef Final note II The future is in: Effective field theories from QCD at finite T QCD NRQCD pNRQCD potential model E bin ~mv 2 1/r ~ mv m Hierarchy of energy scales r: distance between Q and Qbar E bin : binding energy Brambilla, Ghiglieri, Petreczky, Vairo, arXiv: [hep-ph] T m D ~gT NRQCD HTL pNRQCD HTL Real and Imaginary part of potential derived Also: Laine et al 2007, Blaizot et al 2007

Ágnes Mócsy, Bad Honnef The QGP thermometer Potential Models Lattice QCD Extracted Spectral Functions Free energy of q-antiq Quarkonium correlators Quarkonium correlators Spectral Functions T/T C 1/  r  [fm -1 ]  (1S) J/  (1S)  ’(2S)  c (1P)  ’(2S)  b ’(2P)  ’’(3S) TCTC  b (1P)

Ágnes Mócsy, Bad Honnef ****The END****