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 Su Houng Lee

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Contents  Introduction : Charmonium in QGP 1.Lattice QCD 2.Other approaches  QCD sum rules 1.Foundation 2.Borel transformation 3.How to extract physics  Some preliminary results 1.Stability above T c 2.Dissociation temperatures 3.Summary

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Charmonium in QGP : lattice QCD Survival in the deconfined phase? Spectral function from MEM : T dis ~ T c for S-wave (Asakawa-Hatsuda, Datta et al., Umeda et al., Aarts et al,...) BS amplitude : unchanged above T c ? Even P-wave can survive? (Umeda et al.) quench Full

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / 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) Decrease of string tension (Hashimoto et al., ’86) Debye screening (Matsui-Satz ’86) Debye screening (Matsui-Satz ’86) Ambiguity in the choice of lattice-based potential for Schrödinger Eq. F or U or... F or U or... G ( t ) agrees with lattice, but melting just above T c (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

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / 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 (PRL100,PRC77, ) For pure gluonic matter Gluon condensates suddenly decrease across T c Mass and/or width suddenly decreases/increases Larger mass shift for P-wave Applicability : up to T ~1.05 T c

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / QCD Sum Rules at Finite Temperature Start with current-current correlation function Take spacelike momentum : q 2 = -Q 2 < 0 OPE and truncation valid for ： 4m 2 + Q 2 > L 2 QCD, T 2 Both heat bath and meson at rest: q = ( w, 0) Dispersion relation ( w 2 < 0) OPE side : in terms of QCD Temperature through condensates Phenomenological side : Hadron spectral density Matching → Hadron properties (Hatsuda-Koike-Lee ’93)

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Borel transformation Definition (Q 2 =- w 2 ) 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) Dispersion relation

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / OPE side (Bertlmann, ’82) Borel-transformed correlation function Bare loop radiative correction gluon condensates Bare loop radiative correction gluon condensates T - dep

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / 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

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Borel Window : validating QCDSR Borel Window : M 2 range such that... Criterion 1 – OPE convergence in the Window Power correction is small enough Criterion 2 – Pole should dominate Criterion 3 – Mass should not depend on M 2, or must have local mininum/maximum SP M 2 min M 2 max

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Pole only case No stability?

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Incorporating continuum & width No stable curve at 1.2 T c without continuum and width Possible to obtain stable mass!

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / How to choose the best solution? Evaluation of flatness Find s 0 and G giving the minimum Find s 0 and G giving the minimumCaveats 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)

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Result : J / y for linearly decreasing s 0 1/2

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Result : h c for linearly decreasing s 0 1/2

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Result : c c0 for linearly decreasing s 0 1/2

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Result : c c1 for linearly decreasing s 0 1/2

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Summary and Discussion Extension to higher temperature using Borel sum sule Incorporating both continuum and width can remedy the breakdown in previous calculation T dis : Tc for S-wave, Tc for P-wave Not conclusive Not the best solution, but stability holds even at higher temperatures S-wave : 1.6Tc, G > 300MeV P-wave : Borel window closes – Melting into continuum? Difference between J / y and h c as well as c c0 and c c1 ? Difference between J / y and h c as well as c c0 and c c1 ? How to specify the s 0 ( T )? How to specify the s 0 ( T )?

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Backup

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Behavior of mass as a function of M 2 Ideally, m should not depend on M 2 ex ： J/ y w / o continuum Power correction dominates Continuum dominates Best approximated

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Effect of Continuum Reducing high energy part Become flat at some s 0

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Effect of Width (see Lee, Morita, Nielsen, ) Change of RHS with varying G Rise at small M 2

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Borel curve at 1.5T c

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Mass-width relation J / y

Kenji Morita, Yonsei University ATHIC2008, Tsukuba 10 / 13 / Mass-width relation h c May survive at high T if s 0 increases?