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Quarkonia from Lattice and Potential Models

Quarkonia from Lattice and Potential Models. Ágnes Mócsy. based on work with Péter Petreczky. Characterization of QGP with Heavy Quarks Bad Honnef Germany, June 25-28 2008. Confined Matter. Deconfined Matter. Deconfined Matter. Screening. Deconfined Matter. Screening. J/  melting.

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Quarkonia from Lattice and Potential Models

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  1. Quarkonia from Lattice and Potential Models Ágnes Mócsy based on work with Péter Petreczky Characterization of QGP with Heavy Quarks Bad Honnef Germany, June 25-28 2008

  2. Confined Matter

  3. Deconfined Matter

  4. Deconfined Matter Screening

  5. Deconfined Matter Screening J/ melting

  6. Deconfined Matter Screening J/ melting J/ yield suppressed

  7. T/TC 1/r [fm-1] (1S) J/(1S) b’(2P) c(1P) ’’(3S) ’(2S) Sequential suppression QGP thermometer

  8. no T effects strong screening Screening seen in lattice QCD Free energy of static Q-Qbar pair: F1 RBC-Bielefeld Coll. (2007) The range of interaction between Q and Qbar is strongly reduced. Need to quantify what this means for quarkonia.

  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

  10. Potential Models Lattice QCD Studies of quarkonium in-medium Matsui, Satz, PLB 178 (1986) 416 Digal, Petreczky, Satz, PRD 64 (2001) 094015 Wong PRC 72 (2005) 034906; PRC 76 (2007) 014902 Wong, Crater, PRD 75 (2007) 034505 Mannarelli, Rapp, PRC 72 (2005) 064905 Cabrera, Rapp, Eur Phys J A 31 (2007) 858; PRD 76 (2007) 114506 Alberico et al,PRD 72 (2005) 114011; PRD 75 (2007) 074009 PRD 77 (2008) 017502 Mócsy, Petreczky, Eur Phys J C 43 (2005) 77; PRD 73 (2006) 074007 PRD 77(2008) 014501; PRL 99 (2007) 211602 Umeda et al Eur. Phys. J C 39S1 (2005) 9 Asakawa, Hatsuda, PRL 92 (2004) 012001 Datta et al PRD 69 (2004) 094507 Jakovac et al PRD 75 (2007) 014506 Aarts et al Nucl Phys A785 (2007) 198 Iida et al PRD 74 (2006) 074502 Umeda PRD 75 (2007) 094502

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

  12. scalar c0b0 cb pseudoscalar vector J/ axialvector c1b1 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]

  13. c 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 Details cannot be resolved. Jakovac et al, PRD (2007) “..it is difficult to make any conclusive statement based on the shape of the spectral functions … ” Jakovác et al PRD (2007)

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

  15. Recently: Zero-mode contribution Low frequency contribution to spectral function at finite T, scattering states of single heavy quarks(commonly overlooked) Quasi-free heavy quarks interacting with the medium Bound and unbound Q-Qbar pairs (>2mQ) Gives constant contribution to correlator =>> Look at derivatives Umeda, PRD 75 (2007) 094502

  16. Ratio of correlator derivatives Datta, Petreczky, QM 2008, arXiv:0805.1174[hep-lat] All correlators are flat. • Flatness is not related to survival: no change in the derivative scalar up to 3Tc!csurvives until 3Tc??? • 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

  17. From the lattice Dramatic changes in spectral function are not reflected in the correlator

  18. 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 3Tc 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.

  19. Would really the J/survive in QGP up to 1.5-2Tc even though strong screening is seen in the medium?

  20. V(r) Confined heavy quark mass mQ>>QCD and velocity v<<1 r 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. V(r)

  21. V(r) Confined Deconfined T>Tc r 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)

  22. Potential Models Lattice QCD Quarkonium correlators Quarkonium correlators Spectral functions Spectral functions Free energy of static quarks Potential from pNRQCD Lattice & Potential models Reliable Not yet reliable

  23. First lattice-based potential Free energy of static Q-Qbar pair: F1 RBC-Bielefeld Coll. (2007) Free energy F1≠ Potential V Contains entropy F1=E1-ST Digal, Petreczky, Satz, PRD (2001)

  24. 1.2Tc 1.2Tc TS Lattice-based potentials Most confining potential Wong potential T=0 potential Our physical potential - upper limit Internal energy Free energy - lower limit r2 r1 Mócsy, Petreczky 2008 • Deeper potentials: stronger binding, higher Tdiss • Open charm (bottom) threshold = 2mQ+Vinf(T) • Explore uncertainty assuming the general features of F1 • r < r1(1/T): vacuum potential • r > r2(1/T): exponential screening Can we constrain them using correlator lattice data?

  25. 1.2Tc ~ 1-2% Pseudoscalar correlators with set of potentials within the allowed ranges Set of potentials all agree with lattice data; yield indistinguishable results. No, we cannot determine quarkonium properties from such comparisons; If no agreement found, model is ruled out; We can set upper limits.

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

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

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

  29. 1/r[fm-1] T/TC Broadening in agreement with: • pQCD calculation • QCD sum rule • Imaginary part in resummed pQCD • pNRQCD at finite T Park et al (1S) 2 Lee, Morita Laine,Philipsen b(1P) Brambilla et al 1.2 J/(1S) ’(2S) b’(2P) ’’(3S) TC c(1P) ’(2S) Upper limit melting temperatures Ebin = 2mQ+V∞(T)-MQQbar< T Estimate dissociation rate due to thermal activation (thermal width) Dissociation condition: Kharzeev, McLerran, Satz, PLB (1995) J/ melts before it bounds.

  30. 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. Decrease in binding energies with increasing temperature. Upper limit potential predicts that all bound states melt by 1.3Tc, except the upsilon, which survives until 2Tc. Lattice results are consistent with quarkonium melting. • Large threshold enhancement above free propagation even at high T • - compensates for melting of states (flat correlators) • - correlation between Q and Qbar persists

  31. Implications for RHICollisions Karsch et al J/ survival  survival   • Consequences: • J/ RAA: 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?

  32. 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

  33. QCD m NRQCD 1/r ~ mv pNRQCD Ebin~mv2 potential model Final note II The future is in: Effective field theories from QCD at finite T Hierarchy of energy scales NRQCDHTL T mD ~gT pNRQCDHTL Brambilla, Ghiglieri, Petreczky, Vairo, arXiv:0804.0993[hep-ph] Real and Imaginary part of potential derived r: distance between Q and Qbar Ebin: binding energy Also: Laine et al 2007, Blaizot et al 2007

  34. Quarkonium correlators Quarkonium correlators Spectral Functions Free energy of q-antiq Extracted Spectral Functions Potential Models Lattice QCD 1/r[fm-1] T/TC (1S) 2 b(1P) 1.2 J/(1S) ’(2S) b’(2P) ’’(3S) TC c(1P) ’(2S) The QGP thermometer

  35. ****The END****

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