# ATHIC 2008 Tsukuba Kenji Morita Yonsei University Charmonium

- Slides: 25

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Charmonium dissociation temperatures from QCD sum rules Kenji Morita Institute of Physics and Applied Physics, Yonsei University in Collaboration with Su Houng Lee 10/13/2008

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Contents 1. Introduction : Charmonium in QGP 1. Lattice QCD 2. Other approaches 2. QCD sum rules 1. 2. 3. Foundation Borel transformation How to extract physics 3. Some preliminary results 1. Stability above Tc 2. Dissociation temperatures 3. Summary 10/13/2008 2

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Charmonium in QGP : lattice QCD Survival in the deconfined phase? Spectral function from MEM : Tdis ~ 1. 5 -2 Tc for S-wave (Asakawa-Hatsuda, Datta et al. , Umeda et al. , Aarts et al, . . . ) Full quench BS amplitude : unchanged above Tc? Even P-wave can survive? (Umeda et al. ) 10/13/2008 3

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Charmonium in QGP : Other approaches Potential models (Wong, Alberico et al. , Mocsy et al. ) Traditional/Intuitive method Decrease of string tension (Hashimoto et al. , ’ 86) Debye screening (Matsui-Satz ’ 86) Ambiguity in the choice of lattice-based potential for Schrödinger Eq. F or U or. . . G(t) agrees with lattice, but melting just above Tc (Mocsy et al) T-matrix (Rapp et al. ) Based on the lattice-based potential NRQCD at finite T (Brambilla et al) No quantitave results yet 10/13/2008 4

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Charmonium in QGP : Our approach QCD sum rules (Shifman et al. , ’ 79) Traditional method for bound states perturbative QCD + condensates + quark-hadron duality Temperature dependence of condensates from lattice QCD Summary of previous works (PRL 100, PRC 77, 0808. 1153) For pure gluonic matter Gluon condensates suddenly decrease across Tc Mass and/or width suddenly decreases/increases Larger mass shift for P-wave Applicability : up to T~1. 05 Tc 10/13/2008 5

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University QCD Sum Rules at Finite Temperature (Hatsuda-Koike-Lee ’ 93) Start with current-current correlation function Take spacelike momentum : q 2 = -Q 2 < 0 OPE and truncation valid for： 4 m 2+Q 2 > L 2 QCD, T 2 Both heat bath and meson at rest: q = (w, 0) Dispersion relation (w 2 < 0) Phenomenological side : Hadron spectral density OPE side : in terms of QCD Temperature through condensates 10/13/2008 Matching → Hadron properties 6

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Borel transformation Definition (Q 2=-w 2) Dispersion relation Physical meanings Validating perturbation by large Q 2 as well as “feeling” resonance at large n Exponential suppression of high-energy part of r(s) 10/13/2008 7

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University OPE side (Bertlmann, ’ 82) Borel-transformed correlation function T-dep Bare loop gluon condensates 10/13/2008 radiative correction 8

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba How to extract physics Modeling phen. side s 0 : threshold Moving continuum part to OPE side Taking ratio after derivative Fixing s 0, G, M 2, solve the equation for m 10/13/2008 9

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Borel Window : validating QCDSR Borel Window : M 2 range such that. . . Criterion 1 – OPE convergence in the Window Power correction is small enough S Criterion 2 – Pole should dominate P M 2 min M 2 max Criterion 3 – Mass should not depend on M 2, or must have local mininum/maximum 10/13/2008 10

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Pole only case 10/13/2008 No stability? 11

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Incorporating continuum & width No stable curve at 1. 2 Tc without continuum and width 10/13/2008 Possible to obtain stable mass! 12

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba How to choose the best solution? Evaluation of flatness Find s 0 and G giving the minimum Caveats Solution is not unique! Many combination can give similarly flat curve! Need to fix either G or s 0 Changing s 0→M 2 max changes We need to give s 0 (T) 10/13/2008 13

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Result : J/y for linearly decreasings 01/2 10/13/2008 14

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Result : hc for linearly decreasings 01/2 10/13/2008 15

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Result : cc 0 for linearly decreasings 01/2 10/13/2008 16

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Result : cc 1 for linearly decreasings 01/2 10/13/2008 17

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Summary and Discussion Extension to higher temperature using Borel sum sule Incorporating both continuum and width can remedy the breakdown in previous calculation Tdis : 1. 3 -1. 35 Tc for S-wave, 1. 1 -1. 15 Tc for P-wave Not conclusive Not the best solution, but stability holds even at higher temperatures S-wave : 1. 6 Tc , G > 300 Me. V P-wave : Borel window closes – Melting into continuum? Difference between J/y and hc as well as cc 0 and cc 1 ? How to specify the s 0(T)? 10/13/2008 18

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Backup 10/13/2008 19

ATHIC 2008, Tsukuba Kenji Morita, Yonsei University Behavior of mass as a function of M 2 Ideally, m should not depend on M 2 Power correction dominates ex：J/y w/o continuum Best approximated 10/13/2008 Continuum dominates 20

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Effect of Continuum Reducing high energy part Become flat at some s 0 10/13/2008 21

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Effect of Width (see Lee, Morita, Nielsen, 0808. 3168) Change of RHS with varying G Rise at small M 2 10/13/2008 22

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Borel curve at 1. 5 Tc 10/13/2008 23

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Mass-width relation. J/y 10/13/2008 24

Kenji Morita, Yonsei University ATHIC 2008, Tsukuba Mass-width relationhc 10/13/2008 May survive at high T if s 0 increases? 25