ECT Trento 2013 – 5/04/2013

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ECT Trento 2013 – 5/04/2013 1 st year PhD student at Subatech (France) Advisor : P.B. Gossiaux QUANTUM AND SEMI-CLASSICAL APPROACHES TO J/ψ SUPPRESSION Roland Katz

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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 - PowerPoint PPT Presentation

Transcript of ECT Trento 2013 – 5/04/2013

Page 1: ECT Trento 2013 – 5/04/2013

ECT Trento 2013 – 5/04/2013

1st year PhD student at Subatech (France)Advisor: P.B. Gossiaux

QUANTUM AND SEMI-CLASSICAL APPROACHES TO J/ψ SUPPRESSION

Roland Katz

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• Introduction• Quantum formalism• Quantum results• Semi-classical formalism• Semi-classical results• Comparison• Conclusion

Summary

Roland Katz – 5/04/2013

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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.

Introduction Quantum Semi-classical Comparison Conclusion

Introduction

Roland Katz – 5/04/2013

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

This project goal ?

Study the wavefunction of a pair in an isotropic QGP at thermal equilibrium through:

… then projection onto the J/ψ state.

Results comparison to validate/unvalidate Young and Shuryak* semi-classical approach to J/ψ survival with stochastic Langevin equation.

Quantum approach• Non relativistic Schrödinger equation

Semi-classical approach• Quantum Wigner distribution• Classical, 1st order in ħ, Wigner-Moyal equation

* Phys.Rev.C79:034907,2009

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

The common tools

• “Weak potential F<V<U”

• “Strong potential V=U”

* Phys.Rev.D77:014501,2008 **arXiv:hep-lat/0512031v1

Evaluated by Mócsy & Petreczky* and Kaczmarek & Zantow** from some lQCD results and reparametrized by Gossiaux

The color potentials V(Tred, r)

F<V<UV=U

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The common tools

Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013 * arXiv:nucl-th/0305084v2

• 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

The temperature scenarios

Instantaneous transition from QGP at to hadronisation phase at .

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Introduction Quantum Semi-classical Comparison Conclusion

Quantum formalism

Roland Katz – 5/04/2013

• Schrödinger equation for the cc pair evolution

then expanded to the 1st degree in .

Where:

rc

c

QGP

reduced radial wave-function

with

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Introduction Quantum Semi-classical Comparison Conclusion

Quantum results

Roland Katz – 5/04/2013

With no color potential: V=0

• Projection onto the J/ψ state

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

Tred=0.4

With the weak color potential

(F<V<U) at fixed temperatures

Tred=0.6

Tred=0.8

Tred=1

Tred=1.4

With the weak color potential (F<V<U) and a

time-dependent temperature

RHICLHC

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

With the strong color potential (V=U) at fixed temperatures

Tred=0.4

Tred=0.8

Tred=1.2

Tred=1

Tred=1.4

Oscillations between 2 or 3 eigenstates for U(0.4<Tred <1.2)

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

With the strong color potential (V=U) and a time-dependent temperature

LHC

RHIC

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Introduction Quantum Semi-classical Comparison Conclusion

Semi-classical formalism

Roland Katz – 5/04/2013

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 is given by:

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

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:

Semi-classical results

With no color potential: V=0

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

With the weak color potential

(F<V<U) at fixed temperatures

With the strong color potential (V=U) at fixed temperatures

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

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

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

Relativistic 2 bodies dynamics instead of the previous non-relativistic relative one

Gives around 20 % lower J/ψ survival than the previous dynamics

Relativistic 2 bodies

dynamics

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

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”

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

ComparisonComparison of Surv[J/ψ](t->∞) average values function of Tred

Quantum approachSemi-classical approach

(no stochastic forces, relative dynamics)

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

Quantum Semi-classical

V=0 Same fast damping of the J/ψ state

Additionnal stochastic and

drag forcesFuture work

F<V<U

V=U Oscillations between 2 or 3 eigenstates for U(0.4<Tred <1.2)

The oscillations are damped No damping of the oscillations

Same remarks than for F<V<U

The mean values of Surv[J/ψ](t->∞) are quite different especially at large Tred

Has troubles to quit the interval around 1 of Surv[J/ψ]

Close result for both potentials

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Introduction Quantum Semi-classical Comparison Conclusion

Roland Katz – 5/04/2013

ConclusionThis 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)

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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

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BackupAdditional stochastic forces