1. New observables in Quarkonium Production Trento (Italy) 29/02/2016 – 4/03/2016 Pol B Gossiaux & Roland Katz and TOGETHER Pays de la Loire (www.rolandkatz.com)

2. In few words ? 2 Initial quasi stationary Sequential Suppression assumption (Matsui & Satz 86) Final quasi stationary Statistical Hadronisation assumption (Andronic, Braun-Munzinger & Stachel) Dynamical Models (implicit hope to measure T above Tc); often relies on some hypothesis not fully justified: (In medium) dissociation cross-section (how valid in dense medium ?) Prob survival … ??? Motivation Dynamical model Application to bottomoniaConclusion ???

3. In few words ? 3 a more dynamical point of view : QGP genuine time dependent scenario quantum description of the QQ screening, thermalisation Initial quasi stationary Sequential Suppression assumption (Matsui & Satz 86) Final quasi stationary Statistical Hadronisation assumption (Andronic, Braun-Munzinger & Stachel) Dynamical Models implicit hope to measure T above Tc ??? Motivation Dynamical model Application to bottomonia Conclusion ???

4. Motivation 4 Quarkonium formation and Q-Qbar evolution in URHIC is a deeply quantum and dynamical problem requiring QGP genuine time-dependent scenario quantum description of the QQ interaction between the 2 systems (screening, « thermalisation ») A priori: Nothing is instantaneous, nothing is adiabatic, nothing is stationnary and nothing is decoupled Motivation Dynamical model Application to bottomonia Conclusion

5. Q Q QGP hadronization Motivation 5 Whether the QQ pair emerges as a quarkonia or as open mesons is only resolved at the end of the evolution Beware of quantum coherence during the evolution ! Very complicated QFT problem at finite T(t) !!! Need for full quantum treatment Dating back to Blaizot & Ollitrault, Thews, Cugnon and Gossiaux; early 90’s No independent Y(1S), Y(2S),.. evolution during QGP history Motivation Dynamical model Application to bottomonia Conclusion

6. Ingredients for a generic model 6 Direct interactions with the thermal bath Thermalisation and diffusion Mean field: color screened binding potential V(r,T) + QGP temperature scenarios T(t,x) polarization due to color charges Cooling QGP Initial QQ state QGP(t) Q Q Ψ QQ (r,t) V(r,T) + Dynamical scheme p cm Motivation Dynamical model Application to bottomonia Conclusion

7. 7 The common open quantum approach  Idea: density matrix and {quarkonia + bath} => bath integrated out  non unitary evolution + decoherence effects  But defining the bath is complicated and the calculation entangled… Akamatsu* -> complex potential Borghini** -> a master equation * Y. Akamatsu Phys.Rev. D87 (2013) 045016 ; ** N. Borghini et al., Eur. Phys. J. C 72 (2012) 2000 Partonic approaches Very complicated QFT at finite T problem ! NOT EFFECTIVE (1) Q Q QGP Dynamical scheme ? Motivation Dynamical model Application to bottomoniaConclusion (1) See however Jean-Paul Blaizot et al: Nucl.Phys. A946 (2016)

8. 8 Effective: Langevin-like approaches Quarkonia are Brownian particles (M QQ >> T) + Drag A(T) => need for a Langevin-like eq. (A(T) from single heavy quark observables or lQCD calculations)  Idea: Effective equations to unravel/mock the open quantum approach ✓ Semi-classical See our SQM 2013 proceeding *** Schrödinger-Langevin equation Others Failed at low/medium temperatures Akamatsu and Rothkopf ** -> stochastic and complex potential * C. Young and Shuryak E 2009 Phys. Rev. C 79: 034907 ; ** Y. Akamatsu and A. Rothkopf. Phys. Rev. D 85, 105011 (2012) ; *** R. Katz and P.B. Gossiaux J.Phys.Conf.Ser. 509 (2014) 012095 Effective thermalisation from fluctuation/dissipation Young and Shuryak * -> semi-classical Langevin Dynamical scheme ? Motivation Dynamical model Application to bottomoniaConclusion

9. Important feature of Langevin Dynamics 9 InitialAsymptotic Classical Quantum x p p x Need for Einstein relation aka fluctuation-dissipation theorem: challenge for effective approaches n pnpn n pnpn Dynamics Motivation Dynamical model Application to bottomoniaConclusion

10. Schrödinger-Langevin (SL) equation 10 * Kostin The J. of Chem. Phys. 57(9):3589–3590, (1972) ** Garashchuk et al. J. of Chem. Phys. 138, 054107 (2013) Derived from the Heisenberg-Langevin equation*, in Bohmian mechanics** … Hamiltonian includes the Mean Field (color binding potential) Motivation Dynamical model Application to bottomoniaConclusion

11. Schrödinger-Langevin (SL) equation 11 Derived from the Heisenberg-Langevin equation, in Bohmian mechanics… Dissipation non-linearly dependent on Ψ QQ real and ohmic A = drag coefficient (inverse relaxation time) Brings the system to the lowest state Motivation Dynamical model Application to bottomoniaConclusion

12. Schrödinger-Langevin (SL) equation 12 * I. R. Senitzky, Phys. Rev. 119, 670 (1960); 124}, 642 (1961). ** G. W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965). Derived from the Heisenberg-Langevin equation, in Bohmian mechanics … Fluctuations taken as a « classical » stochastic force White quantum noise * Color quantum noise ** Motivation Dynamical model Application to bottomoniaConclusion

13.  2 parameters : A (Drag) and T (temperature)  Unitarity (no decay of the norm as with imaginary potentials)  Heisenberg principle satisfied at any T  Non linear => Violation of the superposition principle (=> decoherence)  Gradual evolution from pure to mixed states ( large statistics)  Mixed state observables:  Easy to implement numerically (especially in Monte-Carlo event by event generator) Properties of the SL equation 13 Motivation Dynamical model Application to bottomoniaConclusion

14. Equilibration with SL equation 14 See R. Katz and P. B. Gossiaux, arXiv:1504.08087 [quant-ph]. Accepted for publication in Annals of Physics Leads the subsystem to thermal equilibrium (Boltzmann distributions) for at least the low lying states Harmonic state weights p n (t) Motivation Dynamical model Application to bottomoniaConclusion

15. Ingredients for a dynamical model based on Schroedinger-Langevin Equation 15 Direct interactions with the thermal bath Thermalisation and diffusion:  need A(T,p cm ) Mean field: color screened binding potential V(r,T) + QGP temperature scenarios T(t,x) polarization due to color charges Cooling QGP Initial QQ state QGP(t) Q Q Ψ QQ (r,t) V(r,T) + Dynamical scheme  p cm Motivation Dynamical model Application to bottomoniaConclusion

16. 16 * Mócsy & Petreczky Phys.Rev.D77:014501,2008 ** Kaczmarek & Zantow arXiv:hep-lat/0512031v1 Mean color field : screened V(T red, r) binding the QQ F : free energy S : entropy Static lQCD calculations (maximum heat exchange with the medium): T U=F+TS : internal energy (no heat exchange) “Weak potential” F some heat exchange “Strong potential” V=U ** => adiabatic evolution F<V weak [GeV]<U r [fm] K chosen such that: E 2 -E 0 = E( Υ (2S ) )-E( Υ (1S) ) K|x| T=0 Linear approx T=  Screening(T) as V weak T=0 T=  1D simplification Motivation Dynamical model Application to bottomoniaConclusion

17. 17 p  Obtained within our running  s approach* Drag coefficient A b Initial QQ wavefunction  We assume either a formed state ( Υ(1S) or Υ(2S) ) OR a more realistic Gaussian wavefunction with parameter (from Heisenberg principle )  Produced at the very beginning : Arxiv:1506_03981 A b (fm -1 ) p(GeV/c) T=400 MeV K=1.5 * P.B. Gossiaux and J. Aichelin 2008 Phys. Rev. C 78 014904 Motivation Dynamical model Application to bottomoniaConclusion

18. Dynamics of QQ with SL equation 18  Simplified Potential but contains the essential physics  Observables: Weight Linear approxScreening(T) Stochastic forces => feed up of higher states and continuum => Leakage of bound component 1) Evolutions at constant T Motivation Dynamical model Application to bottomoniaConclusion

19. 19 Common decay law at large t (leakage+internal equilibration)  increases with T Starting from Y(1S), higher states are asymptotically more populated at large T. Naïve exp(-  t) Evolutions with V(T=cst) + F stocha Motivation Dynamical model Application to bottomoniaConclusion

20. 20 Evolutions with V(T=cst) + F stocha Υ(1S): The stochastic forces leads to larger suppressions Υ(2S): ……… for T≥0.3 only The screening also leads to larger suppression Motivation Dynamical model Application to bottomoniaConclusion

21. 21 Asymptotics with V(T=0) + F stocha Local equilibrium -> ! This sanity check is a unique feature of our approach Motivation Dynamical model Application to bottomoniaConclusion

22. 22  Very good model for AA URHIC  Glauber model for initial position of the b-bar pairs (assumed to be color singlets and then moving straight line with no Elos)  In general, initial internal bbar state chosen as a gaussian  Observables:  No CNM effects  NOT AIMED to reproduce exp. Data (just grasp the global trends) Weight : Survivance : 2) Evolution in EPOS2* * K. Werner, I. Karpenko, T. Pierog, M. Bleicher and K. Mikhailov, Phys. Rev. C 82 (2010) 044904. K. Werner, I. Karpenko, M. Bleicher, T. Pierog and S. Porteboeuf-Houssais, Phys. Rev. C 85 (2012) 064907  R AA Motivation Dynamical model Application to bottomoniaConclusion

23. 23 Density with V(T LHC (t,0) ) and initial Υ(1S) (at large t) Trapped bb Diffusive + screening Ballistic Case of bbar at hottest QGP point and at rest Motivation Dynamical model Application to bottomoniaConclusion

24. 24 Full EPOS2 evolutions with initial Gaussian Strong suppression of Y(2S), Taking place on longer times Initial suppression Saturation at large time (V closer to V vac ) Y(1S) Y(2S) NO STRONG p T DEPENDENCE We even observe a slight Y(1S) repopulation at large impact parameter Motivation Dynamical model Application to bottomoniaConclusion

25. 25 Final suppression (1) R AA Y(1S) Y(2S) Indeed, flatish R AA (p T ), except for the Y(2S) in peripheral collisions Motivation Dynamical model Application to bottomoniaConclusion

26. 26 Final suppression (2) R AA of N part Y(1S) Y(2S) From this first investigation, V=U is not favored by the CMS data Y(1S) Y(2S) F<V<U V=U Motivation Dynamical model Application to bottomoniaConclusion

27. 27 With feed down With feed downs => V weak favored by CMS data V weak U ϒ (1S) ϒ (2S) With feed dows Motivation Dynamical model Application to bottomoniaConclusion

28. 28 Refined analysis: Role of initial bbar state Y(1S) Y(2S)  (t=0): gaussian  (t=0): Y(1S) pure state  (t=0): Y(2S) pure state In actual life  init ≈ Gaussian => Y(2S) found at the end of QGP evolution are mostly the ones regenerated from the Y(1S)  (t=0): gaussian  (t=0): Y(1S) pure state  (t=0): gaussian Original Y(2S) would survive with a probability less then 2% Motivation Dynamical model Application to bottomoniaConclusion

29. 29 V(T=0)+stocha Y(1S) Y(2S) V(T=0) + stocha V weak (no stocha) V weak + stocha Refined analysis: Role of the various contributions in the SLE Strong suppression in Mean Field only Continuous repopulation from stochastic forces V weak (no stocha) V weak + stocha Slight depopulation from stochastic forces Init: gaussian Motivation Dynamical model Application to bottomoniaConclusion

30. 30 Conclusion  SLE: Framework satisfying all the fundamental properties of quantum evolution in contact with a heat bath, “Easy” to implement numerically  Rich suppression patterns of bbar and bottomonia states  First implementation in “state of the art background” (EPOS)  Reproduces experimental trends  Future:  3D internal dof and use of genuine potential extracted from the lattice => more reliable comparison with experiments  Identify the limiting cases and make contact with the other models (a possible link between statistical hadronization and dynamical models)  Pre-QGP and post-QGP evolution ? Motivation Dynamical model Application to bottomoniaConclusion

31. 31 New observables ?  Application to quarkonia production in pA  Polarization in AA ?  Correlation between D-Dbar and B-Bbar with small invariant mass: Motivation Dynamical model Application to bottomoniaConclusion QGP(t) Q Q Ψ QQ (r,t) V(r,T) p cm Entangled with QGP(t) Q Q Ψ QQ (r,t) V(r,T) B Bbar

32. BACK UP SLIDES

33. Some plots of the potentials With weak potential F<V<U with Tred from 0.4 to 1.4 With strong potential V=U with Tred from 0.4 to 1.4

34. Only mean field + T(t) 34 V=U at LHC Already an actual evolution => the scenario can not be reduced to its very beginning T ̴ T c F<V<U at LHC S i (t) « Weight : » « Survivance : »

35. 35 Semi-classical approach The“Quantum” Wigner distribution of the cc pair: … is evolved with the “classical”, 1 st order in ħ, Wigner-Moyal equation + FP: Finally the projection onto the J/ψ state is given by: But in practice: N test particles (initially distributed with the same gaussian distribution in (r, p) as in the quantum case), that evolve with Newton’s laws, and give the J/ψ weight at t with:

36. SL: numerical test of thermalisation 36 Harmonic potential V(x) Harmonic state weights (t) Boltzmann distribution line Asymptotic Boltzmann distributions ? YES for any (A,B,σ) and from any initial state (t >> )

37. Equilibration with SL equation 37 See R. Katz and P. B. Gossiaux, arXiv:1504.08087 [quant-ph] Leads the subsystem to thermal equilibrium (Boltzmann distributions) for at least the low lying states

38. T=400 MeV Naïve exp(-  t)  J/  Transient phase: reequilibration of the bound eigenstates 38 T=600 MeV J/   Naïve exp(-  t): NOT valid ! J/   T=600 MeV “Universal” decay Evolution with V(T=0) + F stocha Results for charmonia (equivalent behaviour for bottomonia) Decay of the global cc system with a common half-life V(T=0) => NO Debye screening

39. 39 Evolution with V(T=cst) and initial Gaussian

40. 40  S quite depends on the initial quantum state ! => Kills the assumption of quantum decoherence at t=0 Evolutions with V(T=cst) + F stocha

41. 41 Evolutions with V(T LHC (t,0) ) and initial Υ(1S) Fast suppression in MF only Continuous repopulation from stochastic forces Initial suppression Continuous depopulation from stochastic forces

42. 42 Evolutions with V(T LHC (t,0) ) and initial Υ(1S) Υ(2S) strongly suppressed while Υ(1S) partially survives Thermal forces lead to a larger suppression for Υ(1S) and a smaller for Υ(2S)

43. 43 Evolutions with V(T LHC (t,0) ) and initial Gaussian Initial weights have no big influence on large time weights