Alexander Rothkopf Albert Einstein Center for Fundamental Physics

1. Heavy Quarkonia in the QGP fromeffectivefieldtheoriesandpotentials Alexander Rothkopf Albert Einstein Center for Fundamental Physics Institute forTheoreticalPhysics University of Bern Hard Probes 2012, Cagliari, Italy May 30th 2012, 11:30 a.m.

2. Heavy Quarkonia in the QGP, from EFT's and potentials Heavy Quarkoniasuppression in the QGP Bottomonium in p+pcollisions CMS: JHEP 1205 (2012) 063 STAR: arXiv:1107.0532 CMS Collaboration PRL 107(2011) 052302 Bottomonium in Pb+Pbcollisions ALICE: arXiv:1202.1383 PHENIX: PRL 98 (2007) 232301 Clean results for ϒ spectra at LHC A decade of QGP related J/Psi suppression from RHIC / now LHC

3. Heavy Quarkonia in the QGP, from EFT's and potentials Heavy Quarkoniummelting J/ψ T=0 TC>T>0 T>TC Matsui, Satz 1986 Goal: Derivethepotentialfromfirstprinciples QCD Need to develop fully dynamical potential description of QQ melting Presence of large constituent masses: Non-relativistic description ? How does a heavy quark bound state react to the presence of a hot medium? Classic argument: Debye screening in the QGP prevents J/Psi formation Goal: Treat effects at finite T consistently, e.g. spatial decoherence

4. Heavy Quarkonia in the QGP, from EFT's and potentials Towards a potential LQCD: Monte Carlo Ω Nf=2 R τ Δx Δτ i=x,y,z Nadkarni, 1986 Ad-hoc choice: Free Energies or Internal Energies Kaczmarek, Zantow PoS(LAT2005)192 No Schrödinger equation available, gauge dependent, handling of entropy? Systematic approach: Separation of scales Model potentials at T>0

5. Heavy Quarkonia in the QGP, from EFT's and potentials The effectivefieldtheory (EFT) strategy t R Relativistic thermal field theory Quantum mechanics Q Q Brambilla et. al. Rev.Mod.Phys. 77 (2005) 1423 PRD 78 (2008) 014017 x,y,z Appropriate degrees of freedom: Systematic expansion in 1/mQ and r Connection between QCD and pNRQCD in the static limit QCD Dirac fields NRQCD Pauli fields pNRQCD Singlet/Octet

6. Heavy Quarkonia in the QGP, from EFT's and potentials Whatweknowfromperturbationtheory Im[V(R)] GeV fm Re[V(R)] Laine, Philipsen, Romatschke, TasslerJHEP03 (2007) 054; Beraudo et. al. NPA 806:312,2008 T=0.5- 2.2 GeV How to go to a non-perturbative setting? EFT: Systematic improvement possible At high T>>TC: Resummed perturbation theory “Hard thermal loops” Brambilla, Ghiglieri, Vairo and Petreczky PRD 78 (2008) 014017 E Landau damping Debye screening singlet -> octet -> singlet Improvement of the small r region Corrections to both Re[V] and Im[V]

7. Heavy Quarkonia in the QGP, from EFT's and potentials Spectrum of the Wilson Loop Maximum EntropyMethod seetalkby O. Kaczmarek A.R., T.Hatsuda & S.Sasaki PRL 108 (2012) 162001 ω0 ρ(ω) Make time dependence of the Wilson loop explicit (connection to Lattice QCD) At each R, lowest lying peak determines the potential Analytically solvable cases: Breit-Wigner shape Γ0 Y.Burnier, A.R in preparation ω

8. Heavy Quarkonia in the QGP, from EFT's and potentials Extractingthe Potential fromLattice QCD Fit lowestlying spectralpeak Wilson Loop Lattice QCD Maximum Entropy Method τ∈[0,β] ρ x,y,z T>0 ω Re[V(0)](R) Im[V(0)](R) R

9. Heavy Quarkonia in the QGP, from EFT's and potentials LatticeResults: Quenched QCD Scenario: Real part freezes, medium modification through imaginary part Below TC: Real Part coincides with Color Singlet Free Energies, Im[V]=0 Around TC: Real part unchanged, imaginary part grows T>>TC: Both real and imaginary part show same large slope Should we be surprised about the existence of Im[V]?

10. Heavy Quarkonia in the QGP, from EFT's and potentials Heavy Quarkoniaas Open Quantum System see e.g. H.-P. Breuer, F. Petruccione, Theory of Open Quantum Systems unitaryevolution: H=H† see also: N.Borghini, C.Gombeaud: arXiv:1103.2945 Eur.Phys.J. C72 (2012) 2000 Interaction with the medium induces a stochastic element into the dynamics (similar concepts are quantum state diffusion, quantum jumps, etc..) Decoherence: Interaction between medium and QQbar select a basis of states in which σQQ becomes diagonal over time σ(t) denotes density matrix of states Interested in the dynamics of the QQbar system only Underlying theoretical framework: Open Quantum Systems

11. Heavy Quarkonia in the QGP, from EFT's and potentials Stochasticevolution in the QGP ρ(ω) ω ω Re[V] V(R) A new proposal: width in the Wilson loop spectra uncertainty in Re[V(R)] How to treat stochastic nature of the dynamics in the potential picture? Γ=Im[V] Γ=δ(V(R))

12. Heavy Quarkonia in the QGP, from EFT's and potentials Stochasticevolution in real-time Y.Akamatsu, A.R. PRD 85, 105011 (2012) Average wavefunction depends on diagonal noise correlations Evolution on the level of the wavefunction: Construct unitary stochastic time evolution (neglects back reaction on medium)

13. Heavy Quarkonia in the QGP, from EFT's and potentials Summary Next order in HTL? Below TC: Re[V] coincides with the Color Singlet Free Energies - Improve fit tospectralpeaks - Usefull QCD medium First correction: Singlet to octet breakup Systematic improvements possible (expansion in 1/mQ and r) Debye screening and Landau damping (imaginary part) Instead of imaginary part: uncertainty in the real part of the potential Microscopic evolution fully unitary Im[V] obtained after ensemble average Effective Field Theory allows derivation of QQbar in-medium potential V0(R) Perturbative evaluation of the static potential: Stochastic Evolution of Heavy Quarkonia in the QGP : Open Quantum System Lattice Evaluation (quenched) of the static potential: - ExtractΓ (x,x‘) fromLQCD? - Include back reaction Real part freezes around phase transition Im[V] grows with temperature and distance

14. Heavy Quarkonia in the QGP, from EFT's and potentials The End Thankyouforyourattention

15. Heavy Quarkonia in the QGP, from EFT's and potentials An alternative observable ? R R y y x x remove Wilson lines fix Coulomb gauge W(R,τ) W||(R,τ) y y x x Real part and width are smaller Lattice data much less noisy Derivation of V(R) remains the same Possible tradeoff to ensure same physics outcome?

16. Heavy Quarkonia in the QGP, from EFT's and potentials Do weneed a potential picture? LQCD: Monte Carlo τ J† Δx Δτ J Cannot measure spectral function directly Asakawa, Hatsuda, Nakahara Prog.Part.Nucl.Phys. 46 (2001) 459-508 Ding et. al. PoSLAT2010 (2010) 180, arXiv:1204.4945 Judging the survival of J/ψthrough an inspection by eye i=x,y,z Infer from a measurable quantity instead: Maximum Entropy Method In the end: Combine the clarity of the potential picture with non-perturbative capabilities of lattice QCD Spectral function and suppression: Interpretation remains difficult

17. Heavy Quarkonia in the QGP, from EFT's and potentials The Potential at T=0.78TC Prior dependence MEM ringing R=0.4fm R=0.1fm

18. Heavy Quarkonia in the QGP, from EFT's and potentials The Potential at T=1.17TC Onlylowestpeakstable At T>TC upwardtrend MEM ringing R=0.4fm R=0.1fm

19. Heavy Quarkonia in the QGP, from EFT's and potentials The Potential at T=2.33TC T=2.33TC T=2.33TC MEM stable but individualpeaksoverlapping R=0.4fm R=0.1fm

20. Heavy Quarkonia in the QGP, from EFT's and potentials Genericfeatures of the 1-d simulation Unitarity is preserved in each member of the stochastic ensemble <|ΨQQ|>=1 Imaginary part emerges after averaging |<ΨQQ>|<1 Diagonal noise: Correlation length lcorr= dx << 2π/T

21. Heavy Quarkonia in the QGP, from EFT's and potentials Heavy quarkonium in the QGP I Debye screening + smallnoise Vacuum potential + linearlyrisingnoise Very different parameter sets give similar asymptotic Pv(t) -> artificial Populating of higher states: Noise vs. mixing through h(x) Exponential suppression in Pv(t): v(x) and Γ(x,x) determine speed

22. Heavy Quarkonia in the QGP, from EFT's and potentials Heavy quarkonium in the QGP II Debye screeningwithoutnoise Mixing through h(x) with mD=5GeV Only parity even eigenstates are excited Observed suppression not exponential, not even monotonous