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ECT Trento 2013 – 5/04/2013

Quantum and semi-Classical Approaches to J/ ψ SUPPRESSION. Roland Katz. 1 st year PhD student at Subatech (France). Advisor : P.B. Gossiaux. ECT Trento 2013 – 5/04/2013. Summary. Introduction Quantum formalism Quantum results Semi-classical formalism Semi-classical results

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ECT Trento 2013 – 5/04/2013

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  1. Quantum and semi-Classical Approaches to J/ψ SUPPRESSION Roland Katz 1st year PhD student at Subatech (France) Advisor: P.B. Gossiaux ECT Trento 2013 – 5/04/2013

  2. Summary • Introduction • Quantum formalism • Quantum results • Semi-classical formalism • Semi-classical results • Comparison • Conclusion Roland Katz – 5/04/2013

  3. IntroductionQuantumSemi-classicalComparison Conclusion Introduction Background? • Quarkonia suppression was predicted by Matsui and Satz as a sign of Quark-Gluon Plasma production in heavy-ion collisions. • Quarkonia suppression has been observed but is still poorly understood. PhD thesis goal ? • Study the evolution of a pair in the QGP by different means. • Explain the observed suppression of the J/ψ suppression as the collision energy increases. Roland Katz – 5/04/2013

  4. IntroductionQuantumSemi-classicalComparison Conclusion This project goal ? • Study the wavefunction of a pair in an isotropic QGP at thermal equilibrium through: … thenprojection onto the J/ψstate. • Resultscomparison to validate/unvalidate Young and Shuryak* semi-classicalapproach to J/ψ survival with stochastic Langevin equation. * Phys.Rev.C79:034907,2009 Roland Katz – 5/04/2013

  5. IntroductionQuantumSemi-classicalComparison Conclusion • The color potentials V(Tred, r) • “Weak potential F<V<U” • “Strong potential V=U” The commontools F<V<U V=U • Evaluated by Mócsy & Petreczky* and Kaczmarek & Zantow** from some lQCD results and reparametrized by Gossiaux * Phys.Rev.D77:014501,2008 **arXiv:hep-lat/0512031v1 Roland Katz – 5/04/2013

  6. IntroductionQuantumSemi-classicalComparison Conclusion The commontools • The temperature scenarios • At fixed temperatures • where • Time dependent temperature • Cooling of the QGP over time by Kolb and Heinz* (hydrodynamic evolution and entropy conservation) • At LHC ( ) and RHIC ( ) energies Instantaneous transition from QGP at to hadronisation phase at . Roland Katz – 5/04/2013 * arXiv:nucl-th/0305084v2

  7. IntroductionQuantumSemi-classicalComparison Conclusion Quantum formalism • Schrödinger equation for the cc pair evolution • then expanded to the 1st degree in . • Where: c r QGP c reduced radial wave-function with Roland Katz – 5/04/2013

  8. IntroductionQuantumSemi-classicalComparison Conclusion Quantum results • Projection onto the J/ψ state With no color potential: V=0 Roland Katz – 5/04/2013

  9. IntroductionQuantumSemi-classicalComparison Conclusion Tred=0.4 Tred=0.6 With the weak color potential (F<V<U) at fixed temperatures Tred=0.8 Tred=1 Tred=1.4 RHIC With the weak color potential (F<V<U) and a time-dependent temperature LHC Roland Katz – 5/04/2013

  10. IntroductionQuantumSemi-classicalComparison Conclusion With the strong color potential (V=U) at fixed temperatures Tred=1 Tred=0.8 Tred=1.2 Tred=0.4 Tred=1.4 Oscillations between 2 or 3 eigenstates for U(0.4<Tred <1.2) Roland Katz – 5/04/2013

  11. IntroductionQuantumSemi-classicalComparison Conclusion With the strong color potential (V=U) and a time-dependent temperature RHIC LHC Roland Katz – 5/04/2013

  12. IntroductionQuantumSemi-classicalComparison Conclusion Semi-classicalformalism • The“Quantum” Wigner distribution of the cc pair: • … is evolved with the “classical”, 1st order in ħ, Wigner-Moyal equation: • Finally the projection onto the J/ψ state isgiven by: Roland Katz – 5/04/2013

  13. IntroductionQuantumSemi-classicalComparison Conclusion Semi-classicalresults • But in practice: N test particles (initiallydistributedwith the samegaussian distribution in (r, p) as in the quantum case), thatevolvewithNewton’slaws, and give the J/ψweightat t with: With no color potential: V=0 Roland Katz – 5/04/2013

  14. IntroductionQuantumSemi-classicalComparison Conclusion With the weak color potential (F<V<U) at fixed temperatures With the strong color potential (V=U) at fixed temperatures Roland Katz – 5/04/2013

  15. IntroductionQuantumSemi-classicalComparison Conclusion • From observing the distribution of test particles in the phase space over time: • The increase of Surv(J/ψ) for t < 0.5 fm/c <= some particles loose momentum while climbing the potential • And decrease of Surv(J/ψ) for t < 1 fm/c <= the particles with sufficient momentum go out the « J/ψ zone » by climbing the potential • Finally Surv(J/ψ) remains constant for t > 1 fm/c <= the latter particles reach the continuum Roland Katz – 5/04/2013

  16. IntroductionQuantumSemi-classicalComparison Conclusion Relativistic 2 bodies dynamics instead of the previous non-relativistic relative one Relativistic 2 bodies dynamics Gives around 20 % lower J/ψ survival than the previous dynamics Roland Katz – 5/04/2013

  17. IntroductionQuantumSemi-classicalComparison Conclusion With additional stochastic and drag forces The Langevin forces are added in Newton’s laws. • From observing the distribution of test particles in the phase space over time: • The increase of Surv(J/ψ) for t < … fm/c <= usual effect + an increased rate due to the drag force that keeps the particles to quit the “J/ψ zone” • And decrease of Surv(J/ψ) for t > … fm/c <= usual effects + with an increased rate, and during a longer time, effect due to the stochastic forces that continuously push the particles out of the “J/ψ zone” Roland Katz – 5/04/2013

  18. IntroductionQuantumSemi-classicalComparison Conclusion Comparison Comparison of Surv[J/ψ](t->∞) average values function of Tred Quantum approach Semi-classical approach (no stochastic forces, relative dynamics) Roland Katz – 5/04/2013

  19. IntroductionQuantumSemi-classicalComparison Conclusion Quantum Semi-classical V=0 Same fast damping of the J/ψ state The mean values of Surv[J/ψ](t->∞) are quite different especially at large Tred F<V<U Has troubles to quit the interval around 1 of Surv[J/ψ] Same remarks than for F<V<U V=U Oscillationsbetween 2 or 3 eigenstates for U(0.4<Tred <1.2) No damping of the oscillations The oscillations are damped Additionnal stochastic and drag forces Close result for both potentials Future work Roland Katz – 5/04/2013

  20. IntroductionQuantumSemi-classicalComparisonConclusion Conclusion • This project • The J/ψ survival in a screening medium -> studied with two different temperature dependent potentials and with two different approaches. • Strong discrepancies between the two approaches => • the semi-classic approach proposed by Young and Shuryak may not be relevant when quarkonia are studied in a color screened medium. • Future work • The quantum approach should then be pursued -> • Bottomonia • Different additional stochastic and drag forces (<=> taking into account the direct interactions with the medium particles) Roland Katz – 5/04/2013

  21. Backup 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

  22. Backup Additional stochastic forces

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