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In-medium QCD forces for HQs at high T Yukinao Akamatsu Nagoya University, KMI Y.Akamatsu, A.Rothkopf, PRD85(2012),105011 (arXiv:1110.1203[hep-ph] ) Y.Akamatsu,

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Presentation on theme: "In-medium QCD forces for HQs at high T Yukinao Akamatsu Nagoya University, KMI Y.Akamatsu, A.Rothkopf, PRD85(2012),105011 (arXiv:1110.1203[hep-ph] ) Y.Akamatsu,"— Presentation transcript:

1 In-medium QCD forces for HQs at high T Yukinao Akamatsu Nagoya University, KMI Y.Akamatsu, A.Rothkopf, PRD85(2012),105011 (arXiv:1110.1203[hep-ph] ) Y.Akamatsu, PRD87(2013),045016 (arXiv:1209.5068[hep-ph]) arXiv:1303.2976[nuch-th] 12013/12/11NFQCD2013@YITP New Frontiers in QCD 2013

2 Contents 1.Introduction 2.In-medium QCD forces 3.Influence functional of QCD 4.Perturbative analysis 5.Summary & Outlook 22013/12/11NFQCD2013@YITP

3 1. INTRODUCTION 32013/12/11NFQCD2013@YITP

4 Confinement & Deconfinement HQ potential 4 R V(R) Coulomb + Linear String tension K ~ 0.9GeVfm -1 Singlet channel T=0 2013/12/11NFQCD2013@YITP Debye Screened High T>>T c The Schrödinger equation Existence of bound states (cc, bb)  J/Ψ suppression in heavy-ion collisions _ _ Matsui & Satz (86) Debye screened potential Debye mass ω D ~ gT (HTL)

5 Quarkonium Suppression at LHC Sequential melting of bottomonia 2013/12/11NFQCD2013@YITP5 p+p A+A CMS Time evolution of quarkonium states in medium is necessary

6 2. IN-MEDIUM QCD FORCES 62013/12/11NFQCD2013@YITP

7 In-medium Potential Definition 7 T>0, M=∞ r t R Long time dynamics i=0 i=1 … Lorentzian fit of lowest peak in SPF σ(ω;R,T) σ(ω;R,T) ω V(R,T)V(R,T) Γ(R,T)Γ(R,T) (0<τ<β) 2013/12/11NFQCD2013@YITP Complex potential ! Laine et al (07), Beraudo et al (08), Bramilla et al (10), Rothkopf et al (12).

8 In-medium Potential Stochastic potential 8 Noise correlation length ~ l corr Imaginary part = Local correlation only Phase of a wave function gets uncorrelated at large distance > l corr Decoherence  Melting (earlier for larger bound states) Akamatsu & Rothkopf (‘12) 2013/12/11NFQCD2013@YITP

9 In-medium Forces Whether M<∞ or M=∞ matters 9 Debye screened force + Fluctuating force Drag force Langevin dynamics M=∞M=∞ M<∞M<∞ (Stochastic) Potential force  Hamiltonian dynamics Non-potential force  Not Hamiltonian dynamics 2013/12/11NFQCD2013@YITP

10 3. INFLUENCE FUNCTIONAL OF QCD 102013/12/11NFQCD2013@YITP

11 Open Quantum System Basics 112013/12/11NFQCD2013@YITP Hilbert space von Neumann equation Trace out the environment Reduced density matrix Master equation (Markovian limit) sys = heavy quarks env = gluon, light quarks

12 Closed-time Path QCD on CTP 2013/12/11NFQCD2013@YITP12 Factorized initial density matrix Influence functional Feynman & Vernon (63)

13 Influence Functional Reduced density matrix 2013/12/11NFQCD2013@YITP13 1 2 s Path integrate until s, with boundary condition

14 Influence Functional Functional master equation 2013/12/11NFQCD2013@YITP14 Long-time behavior (Markovian limit) Analogy to the Schrödinger wave equation Effective initial wave function Effective action S 1+2  Single time integral Functional differential equation

15 Hamiltonian Formalism (skip) Order of operators = Time ordered Change of Variables (canonical transformation) 2013/12/11NFQCD2013@YITP15 Instantaneous interaction Kinetic term or Make 1 & 2 symmetric Remember the original order Determines without ambiguity Technical issue

16 Hamiltonian Formalism (skip) Variables of reduced density matrix Renormalization 2013/12/11NFQCD2013@YITP16 Convenient to move all the functional differential operators to the right in Latter is better (explained later) In this procedure, divergent contribution from e.g. Coulomb potential at the origin appears  needs to be renormalized Technical issue

17 Reduced Density Matrix Coherent state 2013/12/11NFQCD2013@YITP17 Source for HQs

18 Reduced Density Matrix A few HQs 2013/12/11NFQCD2013@YITP18 One HQ Similar for two HQs, …

19 Master Equation From fields to particles 2013/12/11NFQCD2013@YITP19 Functional differentiation Master equation Functional master equation For one HQ Similar for two HQs, …

20 4. PERTURBATIVE ANALYSIS 202013/12/11NFQCD2013@YITP

21 Approximation (I) Leading-order perturbation 2013/12/11NFQCD2013@YITP21 Leading-order result by HTL resummed perturbation theory Expansion up to 4-Fermi interactions Influence functional

22 Approximation (II) Heavy mass limit 2013/12/11NFQCD2013@YITP22 Non-relativistic kinetic term Non-relativistic 4-current (density, current) (quenched) Expansion up to

23 Approximation (III) Long-time behavior 2013/12/11NFQCD2013@YITP23 Low frequency expansion Time-retardation in interaction Scattering time ~ 1/q (q~gT, T) HQ time scale is slow: Color diffusion ~ 1/g 2 T Momentum diffusion ~ M/g 4 T 2

24 Effective Action LO pQCD, NR limit, slow dynamics 2013/12/11NFQCD2013@YITP24 Stochastic potential (finite in M  ∞) Drag force (vanishes in M  ∞)

25 Physical Process Scatterings in t-channel 2013/12/11NFQCD2013@YITP25 Scatterings with hard particles contribute to drag, fluctuation, and screening Q Q g q q g g... Independent scatterings...

26 Single HQ Master equation Ehrenfest equations 2013/12/11NFQCD2013@YITP26 Moore et al (05,08,09)

27 Complex Potential Forward propagator 2013/12/11NFQCD2013@YITP27 Time-evolution equation + Project on singlet state Laine et al (07), Beraudo et al (08), Brambilla et al (10)

28 Stochastic Potential Stochastic representation 2013/12/11NFQCD2013@YITP28 M=∞ : Stochastic potential D(x-y): Negative definite Debye screened potential Fluctuation M<∞ : Drag force Two complex noises c 1,c 2  Non-hermitian evolution

29 5. SUMMARY & OUTLOOK 292013/12/11NFQCD2013@YITP

30 Open quantum systems of HQs in medium – Stochastic potential, drag force, and fluctuation – Influence functional and closed-time path – Functional master equation, master equation, etc. Toward phenomenological application – Stochastic potential with color – Emission and absorption of real gluons More on theoretical aspects – Conform to Lindblad form – Non-perturbative definition 2013/12/11NFQCD2013@YITP30

31 2013/12/11NFQCD2013@YITP31 Backup

32 In-medium Potential Definition 32 T=0, M=∞ r t R σ(ω;R) ω V(R)V(R) Long time dynamics V(R) from large τ behavior 2013/12/11NFQCD2013@YITP

33 Closed-time Path 33 Basics 1 2 Partition function 2013/12/11NFQCD2013@YITP

34 Functional Master Equation Renormalized effective Hamiltonian 2013/12/11NFQCD2013@YITP34

35 Functional Master Equation Analogy to Schrödinger wave equation 2013/12/11NFQCD2013@YITP35 Anti-commutator in functional space

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