1. Alexander Rothkopf Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Heavy Quarkonia in the QGP from effective field theories and potentials Heavy Quarkonia in the QGP from effective field theories and potentials Hard Probes 2012, Cagliari, Italy May 30th 2012, 11:30 a.m.

2. May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Heavy Quarkonia suppression in the QGP A decade of QGP related J/Psi suppression from RHIC / now LHC CMS: JHEP 1205 (2012) 063 STAR: arXiv:1107.0532 ALICE: arXiv:1202.1383 PHENIX: PRL 98 (2007) 232301 CMS Collaboration PRL 107 (2011) 052302 Clean results for ϒ spectra at LHC Bottomonium in p+p collisions Bottomonium in Pb+Pb collisions 2

3. T>T C T C >T>0 Heavy Quarkonium melting May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS How does a heavy quark bound state react to the presence of a hot medium? T=0 Need to develop fully dynamical potential description of QQ melting Presence of large constituent masses: Non-relativistic description ? Goal: Derive the potential from first principles QCD Goal: Treat effects at finite T consistently, e.g. spatial decoherence J/ψ Classic argument: Debye screening in the QGP prevents J/Psi formation Matsui, Satz 1986 3

4. Ad-hoc choice: Free Energies or Internal Energies Towards a potential May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Nadkarni, 1986 i=x,y,z Δτ ΔxΔx τ Ω R LQCD: Monte Carlo Model potentials at T>0 Systematic approach: Separation of scales Kaczmarek, Zantow PoS(LAT2005)192 N f =2 No Schrödinger equation available, gauge dependent, handling of entropy? 4

5. Relativistic thermal field theory Quantum mechanics Brambilla et. al. Rev.Mod.Phys. 77 (2005) 1423 PRD 78 (2008) 014017 Appropriate degrees of freedom: Systematic expansion in 1/m Q and r The effective field theory (EFT) strategy May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS QCD Dirac fields NRQCD Pauli fields pNRQCD Singlet/Octet 5 Connection between QCD and pNRQCD in the static limit t x,y,z Q Q R

6. T=0.5- 2.2 GeV GeV fm Im[V(R)] Re[V(R)] Laine, Philipsen, Romatschke, Tassler JHEP03 (2007) 054; Beraudo et. al. NPA 806:312,2008 What we know from perturbation theory H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS At high T>>T C : Resummed perturbation theory “Hard thermal loops” Debye screening Landau damping Brambilla, Ghiglieri, Vairo and Petreczky PRD 78 (2008) 014017 EFT: Systematic improvement possible E singlet -> octet -> singlet Corrections to both Re[V] and Im[V] Improvement of the small r region May 30th, 2012 How to go to a non-perturbative setting? 6

7. Spectrum of the Wilson Loop May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Make time dependence of the Wilson loop explicit (connection to Lattice QCD) At each R, lowest lying peak determines the potential ρ(ω)ρ(ω) ω Γ0Γ0 ω0ω0 Analytically solvable cases: Breit-Wigner shape Y.Burnier, A.R in preparation A.R., T.Hatsuda & S.Sasaki PRL 108 (2012) 162001 Maximum Entropy Method see talk by O. Kaczmarek 7

8. Extracting the Potential from Lattice QCD May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS ω R ρ Re[V (0) ](R) Im[V (0) ](R) τ ∈ [0,β] x,y,z T>0 Maximum Entropy Method Wilson Loop Lattice QCD Fit lowest lying spectral peak 8

9. Lattice Results: Quenched QCD H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Scenario: Real part freezes, medium modification through imaginary part Below T C : Real Part coincides with Color Singlet Free Energies, Im[V]=0 Around T C : Real part unchanged, imaginary part grows T>>T C : Both real and imaginary part show same large slope May 30th, 2012 Should we be surprised about the existence of Im[V]? 9

10. Heavy Quarkonia as Open Quantum System May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Underlying theoretical framework: Open Quantum Systems Interaction with the medium induces a stochastic element into the dynamics (similar concepts are quantum state diffusion, quantum jumps, etc..) see also: N.Borghini, C.Gombeaud: arXiv:1103.2945 Eur.Phys.J. C72 (2012) 2000 Decoherence: Interaction between medium and QQbar select a basis of states in which σ QQ becomes diagonal over time see e.g. H.-P. Breuer, F. Petruccione, Theory of Open Quantum Systems σ(t) denotes density matrix of states unitary evolution: H=H † Interested in the dynamics of the QQbar system only 10

11. Stochastic evolution in the QGP May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS A new proposal: width in the Wilson loop spectra uncertainty in Re[V(R)] ω Γ=Im[V] Re[V] ρ(ω)ρ(ω) ω V(R) Γ=δ(V(R)) How to treat stochastic nature of the dynamics in the potential picture? 11

12. Stochastic evolution in real-time May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Evolution on the level of the wavefunction: Average wavefunction depends on diagonal noise correlations Construct unitary stochastic time evolution (neglects back reaction on medium) Y.Akamatsu, A.R. PRD 85, 105011 (2012) 12

13. Summary H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Effective Field Theory allows derivation of QQbar in-medium potential V 0 (R) Systematic improvements possible (expansion in 1/m Q and r) Perturbative evaluation of the static potential: Debye screening and Landau damping (imaginary part) First correction: Singlet to octet breakup Stochastic Evolution of Heavy Quarkonia in the QGP : Open Quantum System Instead of imaginary part: uncertainty in the real part of the potential Microscopic evolution fully unitary Im[V] obtained after ensemble average Next order in HTL? - Improve fit to spectral peaks - Use full QCD medium - Improve fit to spectral peaks - Use full QCD medium - Extract Γ (x,x‘) from LQCD? - Include back reaction - Extract Γ (x,x‘) from LQCD? - Include back reaction May 30th, 2012 Lattice Evaluation (quenched) of the static potential: Real part freezes around phase transition Im[V] grows with temperature and distance Below T C : Re[V] coincides with the Color Singlet Free Energies 13

14. The End H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Thank you for your attention May 30th, 201214

15. An alternative observable ? May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Derivation of V(R) remains the same Lattice data much less noisy Real part and width are smaller Possible tradeoff to ensure same physics outcome? x x y y R W  (R,τ) R x x y y remove Wilson lines fix Coulomb gauge W || (R, τ) 15

16. i=x,y,z Δτ ΔxΔx τ LQCD: Monte Carlo J†J† J Do we need a potential picture? May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Spectral function and suppression: Interpretation remains difficult In the end: Combine the clarity of the potential picture with non-perturbative capabilities of lattice QCD Cannot measure spectral function directly Infer from a measurable quantity instead: Maximum Entropy Method Asakawa, Hatsuda, Nakahara Prog.Part.Nucl.Phys. 46 (2001) 459-508 Ding et. al. PoS LAT2010 (2010) 180, arXiv:1204.4945 Judging the survival of J/ψ through an inspection by eye 16

17. R=0.1fm The Potential at T=0.78T C May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS R=0.4fm Prior dependence MEM ringing MEM ringing 17

18. The Potential at T=1.17T C May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS R=0.1fm R=0.4fm MEM ringing MEM ringing Only lowest peak stable At T>T C upward trend At T>T C upward trend 18

19. R=0.1fm The Potential at T=2.33T C May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS R=0.4fm MEM stable but individual peaks overlapping T=2.33T C 19

20. Generic features of the 1-d simulation May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Unitarity is preserved in each member of the stochastic ensemble =1 Imaginary part emerges after averaging | |<1 Diagonal noise: Correlation length l corr = dx << 2π/T 20

21. Heavy quarkonium in the QGP I May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Populating of higher states: Noise vs. mixing through h(x) Exponential suppression in P v (t): v(x) and Γ(x,x) determine speed Very different parameter sets give similar asymptotic P v (t) -> artificial Vacuum potential + linearly rising noise Debye screening + small noise 21

22. Heavy quarkonium in the QGP II May 30th, 2012 H EAVY Q UARKONIA IN THE QGP, FROM EFT' S AND POTENTIALS Mixing through h(x) with m D =5GeV Debye screening without noise Only parity even eigenstates are excited Observed suppression not exponential, not even monotonous 22