Heavy quark system in medium Su Houng Lee  Introduction on phase transition  Perturbative methods  QCD sum rule methods  Experiments 1S H Lee

2 T Color superconductivity Early universe FAIR RHIC, LHC Λ C /D ρ, ω J/ψ, χ C Quark-gluon plasma Nuclear matter S H Lee B B  QCD Phase Diagram

3 Confinement: L=e -F Chiral sym: EOS: e, p Heavy quark V(r) Susceptibility  mq  L Quark number  q S H Lee Lattice results for QCD phase transition (from Karsch’s review)

4 Order Parameter  Order parameter in QCD? S H Lee Order parameter in Superconductivity

5 T/Tc  String Tension: QCD order parameter S H Lee Early work on J/  at finite T (Hashimoto, Miyamura, Hirose, Kanki)

6 J/  suppression in RHIC Matsui and Satz: J/  will dissolve at Tc due to color screening S H Lee Lattice MEM : Asakawa, Hatsuda, Karsch, Petreczky …. J/  will survive Tc and dissolve at 2 Tc Potential models (Wong …) :. Refined Potential models with lattice (Mocsy, Petreczky…) : J/  will dissolve slightly above Tc Lattice after zero mode subtraction (WHOT-QCD) : J/  wave function hardly changes at 2.3 Tc AdS/QCD (Kim, Lee, Fukushima, Hohler, Stephanov…...) : J/  mass change by Y. Kim, J. Lee, SHLee (PRD 07) Wiki page … Perturbative approaches: Blaizot et al… Imaginary potential pNRQCD: N. Brambial et al. Recent works on J/  in QGP

7 Lattice result on singlet potential F(T,r) =V(T,r) -TS(T,r) J/  from potential models Kaczmarek, Zantow hep-lat/ V(T,r) at 1.3 Tc F(T,r) at 1.3 Tc V(r) at T=0 S H Lee Quarkonium dissociation temperature for different potentials Using F(T,r) Using V(T,r) Wong 04 Another model independent approach ? r [fm]

States from ISR S H Lee

9 Tc region is important in HIC Statistical production may occur at or slightly below Tc Large non-perturbative change at Tc Resumed perturbation fails near Tc Karsch hep-lat/ T (GeV) Au+Au 200 Agev, b=0 (fm/c) (e-3p)/T 4 T/T c S H Lee Few things to note about Tc region

10 Approaches to Heavy quark system in medium Mass: Real part Width: Imaginary part 1. Introduction 2.Perturbation for bound states 3.QCD sum rule approach S H Lee

11 Perturbative treatment are possible because Basics in Heavy quark system Heavy quark propagator

S H Lee 12 Perturbative treatment are possible when System with two heavy quarks

S H Lee 13 q2 q2 process expansion parameter example 0 Photo-production of open charm m 2 J/  > 0Bound state properties Formalism by Peskin (79) J/  dissociation: NLO J/  mass shift: LO -Q 2 < 0 QCD sum rules for heavy quarks Predicted m  c <m J/  before experiment Perturbative treatment are possible when

S H Lee 14 Subtlety for bound states Applequist, Dine, Muzinich (78), Peskin (79 ), pNRQCD  Separation scale

15 Approaches to Heavy quark system in medium Mass: Real part Width: Imaginary part 1. Introduction 2.Perturbation for bound states 3.QCD sum rule approach S H Lee

16 1.Peskin (79), Bhanot and Peskin (79) 2.Kharzeev and Satz (94,96), Arleo et.al.(02,04) 3.Y.Oh, SHL (02) Rederived using Bethe-Salpeter amplitude Quarkonium Hadron interaction in QCD  Imaginary part LO calculation

S H Lee 17 LO Amplitude

S H Lee 18 Not so large, however, LO QCD result is known to underestimate nucleon absorption cross section s 1/2 (GeV) Exp data from pA Oh, Kim,SHL 02

S H Lee 19 NLO Amplitude (Song, SHL, PRD 05) Quasi-free approximation: R. Rapp et al. (02)

S H Lee 20 11 Collinear divergence when  1 =0. Cured by mass factroization NLO Amplitude :  + q  c + c + q

S H Lee 21 11 Gluons whose kcos  1 < Q scale, should be included in parton distribution function Integration of transverse momentum from zero to scale Q 11 Mass factorization

S H Lee 22 NLO Amplitude :  + g  c + c + g

S H Lee 23 Large higher order corrections Even larger correction for charmonium NLO/LO T. Song and SHL, PRD 72, (2006) Total cross section for Upsilon by nucleon: NLO vs LO

S H Lee Large NLO correction near threshold, due to log terms 2. But at finite temperature, thermal masses will regulate the large correction Thermal quark and gluon masses of 300 MeV will Reduce the large correction Lessons from NLO calculation 3. But should be used for T< 

S H Lee 25 Thermal dissociation cross section Separation scale For large T  modify Wilson Coefficient For small T  modify matrix element Ways to asses convergence 1.T<   (Matrix) < (Matrix element in Vacuum)

26 Summary LO NLO Thermal width:  J/ x thermal gluon (Park, Song, Lee, Wong 08,09) S H Lee No further regularization (mass factorization) needed if thermal mass is introduced. Need lattice EOM. Thermal width with model EOS near Tc

27 E,B Condensate Confinement model: Schneider, Weise S H Lee

28 Summary Thermal width of J/  near Tc (Morita, Lee 08, Park, etal.07, M, L & Song 09) S H Lee

29  OPE for bound state: m  infinity Mass shift: QCD 2 nd order Stark Effect : Peskin 79  >  qcd  Attractive for ground state S H Lee Separation scale For small T  modify matrix element

30  LO Singlet potential from pNRQCD : Brambilla et al.  Derivation 1/r > Binding >  QCD, Take expectation value Large Nc limit Static condensate Energy  S H Lee Derivation of 2 nd order Stark effect from pNRQCD

31 Lattice result for purge gauge (Boyd et al 96) p/T 4 /T 4 Rescaled pressure (Karsch 01) Karsch hep-lat/ Sudden increase in  Slow increase in p S H Lee Lattice data on ( e,p) near Tc

32 At finite temperature: from Gluon Operators near Tc Two independent operators Twist-2 Gluon Gluon condensate or T G0G0 G2G2 S H Lee

33 W(ST)= exp(-  ST) Time Space S W(S-T) = 1- (ST) 2 +… W(S-S) = 1- (SS) 2 +… OPE for Wilson lines: Shifman NPB73 (80), vs confinement potential Local vs non local behavior W(SS)= exp(-  SS) T Behavior at T>Tc W(SS)= exp(-  SS) W(ST)= exp(-  g(1/S) S) T S H Lee

34 Linear density approximation Condensate at finite density At  = 5 x  n.m. S H Lee Operators in at finite density and hadronic phase

35 Result using Stark effect S H Lee  J/ mass shift near Tc (Morita, Lee 08)  J/ mass shift in nuclear matter : Luke, Manohar, Savage (92) similar to other approaches, potential model (glue ball exchange) (Brodsky (97), Teramond.. (98)  m from QCD Stark Effect

36 Approaches to Heavy quark system in medium Mass: Real part Width: Imaginary part 1. Introduction 2.Perturbation for bound states 3.QCD sum rule approach S H Lee

37 Including Temperature effects For High T > 2 Tc For small and T close to Tc Separation scale

38 Constraints from QCD sum rules for Heavy quark system OPE Phenomenological side s  J/  ’’  sum rule at T=0 : can take any Q 2 >=0, S H Lee

39 QCD sum rule constraint (Morita, Lee PRL08)   MeV]  m   MeV] Can also use Borel sum rule S H Lee OPE breaks down

40 Summary GeV /  J M   m from QCD Stark Effect Mass and width of J/  near Tc (Morita, Lee 08, M, L & Song 09)  QCD sum rule limit with  =0  =constraint-m (Stark effect) S H Lee Constraints from Borel sum rule NLO QCD + confine-model

41 Summary Summary of analysis Due to the sudden change of condensate near Tc S H Lee T G0G0 G2G2 Abrupt changes for mass and width near Tc

S H Lee 42 Karsch et al. 0.75T c 0.9 T c K.Morita, Y. Song, SHL 1.1T c 400 MeV 1.1T c 1 GeV 0.9T c T c 1.5T c 400 MeV 1.5T c 400 MeV Karsch et al. K.Morita, Y. Song, SHL Comparison to other approach T=0 1.1T c Mocsy, Petreczky  c state from lattice  b state from lattice

43 At higher temperature Within our approach, need additional information 1.For mass, need lattice information for temperature dependence of higher dimensional operators 2.For width, Need information of higher twist contribution S H Lee Other possible approach 1.NLO or resumed perturbation, ………………. ? 2.AdS/QCD Y. Kim, J.P.Lee, SHLee (07) sudden drop followed by steady increase. J ’’ deconfinement Thermal effect?

44 Can such effect be observed ? R AA from RHIC and Charmonium production ratio in RHIC and Mass shift at Nuclear matter S H Lee

45 Melting of  ’  c Slope:  J/  Melting T of J/  Height: mass of J/  S H Lee RAA from RHIC (√s=200 GeV y=0, 2-comp model (Rapp) Song, Park, Lee 10)

46 Effects of width and mass At LHC Mass shift by -100 MeV Assumed recombination effect to be the same S H Lee

47 S H Lee Charmonium production ratio in HIC (K. Morita, SHL in preparation) Chemical freeze-out at near phase boundary (Andronic et al NPA772) CERN-SPS BNL-RHIC QCD sum rules

48 Matrix element Hadron gas model with excluded volume S H Lee Calculation in hadron gas

49 S H Lee Results using QCD sum rules Only 17 GeV Pb+Pb data is available with large error bars

50 Quantum numbers QCD 2 nd Stark eff. Potential model QCD sum rules Effects of DD loop  c 0 -+ –8 MeV–5 MeV (Klingl, SHL,Weise, Morita) No effect J/  1 -- –8 MeV (Peskin, Luke) -10 MeV (Brodsky et al). –7 MeV (Klingl, SHL,Weise, Morita) <2 MeV (SHL, Ko) c c 0,1, MeV-15 MeV (Morita, Lee) No effect on  c1  (3686) MeV< 30 MeV  (3770) MeV< 30 MeV S H Lee Application to nuclear matter

51 Anti proton Heavy nuclei Observation of  m through p-A reaction Expected luminosity at GSI 2x cm -2 s -1 Can be done at J-PARC S H Lee

52 1.Deconfinement  Disappearance of mass gap  Quarkonium masses 2.Abrupt changes for quarkonium masses and widths 3.Looking forward to charmonium production ratio and finer mass resolution from RHIC and LHC 4.production inside a nuclear at FAIR and hopefully Jparc Summary S H Lee

53 1.Perturbative approach at Finite temperature: T. Song, Y. Park, SHLee, C.Y. Wong, PLB 659 (2008) 621; PRC 76, (2007). SHLee, K. Morita, PRD79, (2009). 2.Sum rule method at finite: K.Morita, SHLee, PRL 100, (2008). K. Morita, SHLee, PRC 77, (2008). T: Y. Song, SHLee, K. Morita, PRC 79, (2009) AdS/QCD: Y. Kim, JP Lee, SHLee, PRD 75, (2007). 4.J/Psi Phenomenology: T.Song, W. Park, SHLee, PRC 81, (2010) 5.LO,NLO: Y Oh, S. Kim, SHLee, PRC 65, (2002). T. Song, SHLee, PRD 72, (2005) 6.Nuclear medium: S. Kim, SHLee, NPA 679 (2001) 517. SHLee, C.M.Ko, PRC 67, (2003). My reference S H Lee