5 Nov '07 Seminar at Univ. of Tokyo 1 Mass and width of charmonia in medium from QCD sum rules Kenji Morita and Su Houng Lee Institute of Physics and Applied Physics, Yonsei University Contact : Reference ) arXiv: [nucl-th] 1.Introduction 2.QCD Sum Rules and Gluon Condensates 3.Charmonium in Hot Gluonic Medium 4.Charmonium in Nuclear Matter and implication for GSI-FAIR

5 Nov '07 Seminar at Univ. of Tokyo 2 Introduction  Charmonium : sensitive to the confinement nature of strong int.  Success of potential models in spectroscopy  “ Melting ” in QGP due to Debye screening (Matsui-Satz)  Recent Lattice QCD (Umeda et al, Asakawa-Hatsuda, Datta et al,…)  Computation of the spectral functions based on MEM  Bound states survive in deconfined medium up to ～ 1.5-2T c ???  Non-perturbative nature  QCD Sum Rules : well-established method with non- perturbative effects based on QCD  Gluon condensates play an essential role  This study - changes around T c ?

5 Nov '07 Seminar at Univ. of Tokyo 3 QCD Sum Rules  Current-current Correlation  Dispersion Relation “Phenomenologica l Side” Hadronic spectral function “OPE (Operator Product Expansion) side” QCD perturbation ＋ condensates Pole(s) + continuum Calculation at large -q 2 : perturbation OK Condensates : Non-trivial QCD vacuum = Mass, width, threshold, etc…

5 Nov '07 Seminar at Univ. of Tokyo 4 Hot Gluonic Medium

5 Nov '07 Seminar at Univ. of Tokyo 5 Spectral Func. QCD Sum Rules at Finite T  Current-current Correlation  Medium and resonance at rest  Dispersion Relation Gluonic matter, T << 2m c Spectral func. = pole + cc continuum + scattering by fermions (Bochkarev and Shaposhnikov, 1986) (Landau damping)

5 Nov '07 Seminar at Univ. of Tokyo 6 QCD Sum Rules at Finite T Spectral func. = pole + cc continuum + scattering by fermions Gluonic matter, T << 2m c (Bochkarev and Shaposhnikov, 1986) (Landau damping)

5 Nov '07 Seminar at Univ. of Tokyo 7 QCD Sum Rules : Charmonium in Medium  Operator Product Expansion  Gluon Operators : No quark op. in OPE  Lowest order correction Up to dim.4 gluon operator C n : Hard Scale ( ～ Q 2 ) O n : Soft Scale ( ～  QCD ), T Twist-2 contribution +

5 Nov '07 Seminar at Univ. of Tokyo 8  Relations btw gluon condensates and thermodynamic quantities Gluon Condensates Energy-Momentum Tensor Extract from LGT (pure SU(3)) Rapid Change around T c

5 Nov '07 Seminar at Univ. of Tokyo 9 Moment Method  Definition  Phenomenological side  OPE side  Power q n in  (q)  large n – long distance Contribution : –p 2 /n, -k 2 /n (p, k : mometum of q,g in loop)  Weight 1/(s+Q) n+1 →Suppress continuum contribution Same with T=0 case except for G 0 and G 2 Twist-2 term

5 Nov '07 Seminar at Univ. of Tokyo 10 Parameters  Physical :  s (  =1) = 0.21, m c (  =1)=1.24 GeV, G 0 vac = (0.35 GeV) 4  External : ,n  M n-1 /M n takes its minimum value at the best n (asymptotic free) (Reinders et al., 1981) Find hadron-side quantities satisfying Choose , n so that the pole dominates the integral Asymptotic freedom ： large , small n Sum Rules – spectral func. is integrated w.r.t. 

5 Nov '07 Seminar at Univ. of Tokyo 11 Moment ratio of the OPE Side n becomes large as T increases No minumum at T>1.04T c →breakdown of OPE Improvement at large  / smaller  s Min. ratio value decreases with T : reflecting reduction of G 0 and G 2 Analyse phen.side corresponding to the minima

5 Nov '07 Seminar at Univ. of Tokyo 12 Moment ratio of the Phenomenological Side  M n-1 /M n as a function of  Numerical int. with Adaptive MC  Weak  dependence → need large broadening for 2GeV 2 reduction Steep at large n (= large T).  large  : dependence becomes weaker but n also larger →  independence  =0 : minimum mass (maximum mass shift) Pole : Breit-Wigner

5 Nov '07 Seminar at Univ. of Tokyo 13 Relation btw Mass shift and Width slight above T c  We cannot determine both quantities simultaneously Similar behavior in J/  and  c Width proportional to Mass shift

5 Nov '07 Seminar at Univ. of Tokyo 14 Critical Behavior around T c  Fix either mass or width  Rapid Change around T c Reflecting gluon condensates   m for  =0 Decrease with T : almost proportional  m~-( )MeV   for  m=0 Increase with T : almost proportional  ~ MeV.

5 Nov '07 Seminar at Univ. of Tokyo 15 Implications for exp. / Other studies  Heavy Ion LHC  Statistical Hadronization – T=170MeV,  m=-100 MeV leads to factor 2 enhancement of J/   (  ) -1 ～ Life time of QGP→decay of mass-shifted charmonium in QGP  QGP : 4-5 fm/c →  m J/  ～ 150 MeV for  ～ 50 MeV (  ～ 4fm/c) Mass resolution : 35 MeV for dielectron and 75 (ALICE) and 150 (PHENIX) MeV for dimuon  Thermal Width by pQCD (Park et al.,) : small width near T c  Other Studies  AdS/QCD (Kim et al.) : Sudden Change of mass at T c  Spectral function from lattice-motivated potential (M ó csy et al.) ： Shift of peak at 1.1T c  full lattice QCD (Aarts et al.) : Shift of peak above T c Consistent with these studies

5 Nov '07 Seminar at Univ. of Tokyo 16 Implications for exp. / Other studies  Heavy Ion LHC  Statistical Hadronization – T=170MeV,  m=-100 MeV leads to factor 2 enhancement of J/   (  ) -1 ～ Life time of QGP→decay of mass-shifted charmonium in QGP  QGP : 4-5 fm/c →  m J/  ～ 150 MeV for  ～ 50 MeV (  ～ 4fm/c) Mass resolution : 35 MeV for dielectron and 75 (ALICE) and 150 (PHENIX) MeV for dimuon  Other Studies  AdS/QCD (Kim et al.) : Sudden Change of mass at T c  Spectral function from lattice-motivated potential (M ó csy et al.) ： Shift of peak at 1.1T c  full lattice QCD (Aarts et al.) : Shift of peak above T c Consistent with these studies

5 Nov '07 Seminar at Univ. of Tokyo 17 Summary  What We Have Done and Found  Analysis of mass and width of J/  and  c using non- perturbative / model-independent method Extracting gluon condensates at finite T from Lattice QCD  Relation btw mass shift and width If mass shift is small →  ～ 100 MeVIf mass shift is small →  ～ 100 MeV If width change is small → : MeV mass reductionIf width change is small → : MeV mass reduction If fixing one, the other is proportional to TIf fixing one, the other is proportional to T  Behavior around phase transition Rapid change of mass and width →reflecting gluon condensates Better probe at LHC than suppression? – many pairs will be produced

5 Nov '07 Seminar at Univ. of Tokyo 18 Summary  What We Should Do Next  Going to Higher T : How to cure the breakdown of OPE? Higher order / dimensional ？ Temperature correction to Wilson coefficient  P-wave (  c ) : important for comparison with exp. (Sequential melting) Need to compute Twist-2 Wilson coefficient  Full QCD : Scattering/Continuum contribution (quarks at finite T) Pole dominance? quenched results (hopefully) seem to survive in full  Dynamics indispensable for comparison with experiments Combining with QGP fluid Consistent description from production to melt/decay/re-production

5 Nov '07 Seminar at Univ. of Tokyo 19 Nuclear Matter

5 Nov '07 Seminar at Univ. of Tokyo 20 Motivation  J/  suppression in Relativistic Heavy Ion Collisions Absorption (or dissociation) of into two D mesons by nucleus or co-movers (the latter most important in AA collisions where co-movers more copious) Cold Nuclear Matter (CNM) Suppression  abs ～ 1-3 mb? Wanted : J/  -nucleon interaction

5 Nov '07 Seminar at Univ. of Tokyo 21 Motivation  Panda experiment at GSI-FAIR (  Charmonium production via p-pbar annihilation  Spectroscopy  Nuclear medium effect  J-PARC? The Kernphysik III division investigates annihilations of antiprotons at an internal target with the Panda Experiment in the high-energy storage ring (HESR) which will be part of FAIR the Facility for Antiproton and Ion Research and heavy ion reactions at SIS18 energies in experiments with the ALADIN Spectrometer. Annihilation reactions of antiprotons with protons and with nuclear targets can be used for precise spectroscopy of all states in the charmonium spectrum, for glueball and hybrid meson searches in the mass region above 3 GeV/c 2, and for the study of nuclear medium effects of mesons with hidden and open charm. Precise gamma-ray spectroscopy of abundantly produced hypernuclei will be part of the program. The design and construction of a new versatile detector Panda is currently in the R&D phase.

5 Nov '07 Seminar at Univ. of Tokyo 22  No scattering term  Medium effect imposed on gluon condensates  Linear Density Approx.  Gluon condensates QSR m N 0 = 750 MeV(chiral limit)  N = 0.17fm - 3

5 Nov '07 Seminar at Univ. of Tokyo 23 Results  Width & Mass shift  Collisional Broadening p f ～ 250 MeV,  ～ 2 mb  col ～ 1.8 MeV  m ～ 5-6 MeV

5 Nov '07 Seminar at Univ. of Tokyo 24 Can the mass shift be observable?  Estimation for Panda experiment  Breit-Wigner + mass shift  m – J/  : -7 MeV,  c : -4 MeV,  c : -60 MeV (scalar only)  med -free parameter : 1-20 MeV  Annihilation with proton in nucleus Fermi Motion –Average over momentum of target proton

5 Nov '07 Seminar at Univ. of Tokyo 25 Cross sections  J/  and  c Broadening due to Fermi motion Difficult to observe  med affects magnitude only

5 Nov '07 Seminar at Univ. of Tokyo 26 Cross sections cc More promising

5 Nov '07 Seminar at Univ. of Tokyo 27 # of Events  For  med = 20 MeV  Luminosity – 2x10 32 cm -2 s -1 J/ cc  c0  c1  c2 Max.  BW 0.435pb10.7pb18.0pb4.5pb19.8pb Events/day (e + +e - ) (J/  +  )  c0 and  c2 will be the best

5 Nov '07 Seminar at Univ. of Tokyo 28 Backup Slides

5 Nov '07 Seminar at Univ. of Tokyo 29  Coupling Constant from (quenched) LQCD  Definition of the  s (T) is NOT unique  At short distance (< 0.1fm), independent of T  Determined from Free-energy  At short distance (rT ≪ 1) and high temperature (rT ≫ 1), C.C. should connect to perturbative one Running Coupling

5 Nov '07 Seminar at Univ. of Tokyo 30 Running Coupling  Color Singlet Free Energy from LQCD   distance   distance low T!!! (confinement) Use maximum value (at r=r screen ) Too large, not consistent with  V at low T T

5 Nov '07 Seminar at Univ. of Tokyo 31 Running Coupling  2-loop fit for large distant part