Stochastic Dynamics of Heavy Quarkonium in Quark-Gluon Plasma

1. Stochastic Dynamics of Heavy Quarkonium in Quark-Gluon Plasma Yukinao Akamatsu (KMI,Nagoya) In collaboration with Alexander Rothkopf (Bielefeld) Reference: arXiv:1110.1203[hep-ph] QHEC11

2. Contents • Introduction • Complex potential from lattice QCD • Stochastic dynamics of heavy quarkonium • Bound states in the medium • Conclusion and discussion QHEC11

3. Introduction • Matsui and Satz (‘86) “Plasma formation thus prevents J/Ψ formation already just above Tc.”  Propose J/Ψ suppression as a signal for QGP formation No solution rJ/Ψ at T>1.2Tc • Underlying physics: Debye screening • Sensitive to color deconfinement • All the discussion based on the potential V(r) QHEC11

4. Introduction CMS • New data from LHC ALICE Y(1S) Y(2S,3S) QHEC11

5. Introduction • Potential Model Approaches • Provide clear physical picture! • Potential from QQ free energy, or internal energy, or linear combination of both? Relation to first principle? • Spectral Function of Current Correlator • Relation to first principle is clear! • How to discuss more than the shape of peak? How to define the potential from first principle? QHEC11

6. Complex potential from lattice QCD • Rothkopf, et al. (‘11) Proper potential from first principle Meson operator (J/Ψ,ηc, …) Forward correlator In heavy quark limit,ω~2MQ describes 2-HQs physics ≈ described by Schroedinger equation In MQ=∞ limit, Fourier transformation (t⇔ω) of D>NR(r,t) =Spectral decomposition of thermal Wilson loop V□(r) (Lorentzian fit) QHEC11

7. Complex potential from lattice QCD • Rothkopf, et al. (‘11) cont’d Complex potential also found by perturbation theory [Laine, et al. (07’)] V□(r) =Complex potential !! In Coulomb gauge What happened to unitarity? QHEC11

8. Stochastic dynamics of heavy quarkonium • Heavy quark(s) as an open quantum system Non-relativistic, Q and Q separately conserved Due to this hierarchy, we expect unitary evolution of the reduced system Heavy quarks k MQ fluctuation ~(MQT)1/2 Gluons, light quarks k ~T Stochastic unitary evolution of QQ? Can stochastic unitary evolution explain V□(r)? Integrated out QHEC11

9. Stochastic dynamics of heavy quarkonium • Unitary evolution by stochastic Hamiltonian  manifestly unitary  stochastic decays when |X-X’| > lcorr Θ1 Θ2 Stochastic term Θ3 lcorr~ thermal wavelength of medium particles QHEC11

10. Stochastic dynamics of heavy quarkonium • Stochastic differential equation QHEC11

11. Stochastic dynamics of heavy quarkonium • Relation to complex potential D>NR is ensemble average of wave functionΨ!  Evolution of D>NR needs not be unitary. In MQ＝∞ limit, complex potential = [real potential] + i[noise strength] QHEC11

12. Stochastic dynamics of heavy quarknoium • Remark1 : SPF of current correlator Can be calculated only from the complex potential.  no reference to lcorr • Remark2 : the observables of J/Ψ suppression Dilepton spectrum If charms are (chemically and kinetically) equilibrated, SPF of current correlator is enough to give dilepton spectrum. If not (and is not in heavy ion collisions), the stochastic dynamics is necessary. ① ② initial evolved J/Ψ J J J/Ψ QHEC11

13. Bound states in the medium Argument here can be made more quantitative in terms of master equation. • Fate of bound states Real potential : energy levels and sizes of bound states Noise : excites modes with k~1/lcorr (spatial decoherence) Low temperature High temperature Θ Bound state Θ1 Θ2 Bound state Θ3 Θ4 noise gives a nearly global phase does not change physics noises excite the bound state bound state disappears QHEC11

14. Bound states in the medium • 1d simulation – set up (Relative motion) Initial condition lcorr~dx=0.1  very(too) high temperature QHEC11

15. Bound states in the medium • 1d simulation – bound state probability P(t) Probability of occupying bound states decays, but saturatesat later time. QHEC11

16. Bound states in the medium • 1d simulation – norms, etc. Norm of each trajectory = 1 (unitary) Norm of average wave function decays. (noise  imaginary part) Energy average ~ 100! (due to high temperature) QHEC11

17. Conclusion and discussion • Conclusion • Stochastic unitary evolution can explain complex potential obtained by lattice simulation. • Noise correlation length lcorr plays a crucial role in determining the fate of bound states. • Discussion • What is the first principle definition of lcorr? • Gauge dependence in introducing the color • Quantum Brownian motion of single heavy quark • Thermodynamic quantities (free energy, entropy, …) • Relation to heavy quark effective field theories QHEC11

18. BACK UP QHEC11

19. Master equation • Master equation Reduced density matrix Master equation • Equivalent master equation: • proposed as a modified quantum mechanics (Ghirardi, et al. ‘86) • derived in scattering model (Gallis & Fleming ‘90) • in random potential in Feynman-Vernon approach (Gallis ‘92) QHEC11

20. Master equation • Extracting relative motion QHEC11