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Heavy quark system in medium

Heavy quark system in medium. Su Houng Lee Introduction on phase transition Perturbative methods QCD sum rule methods Experiments . QCD Phase Diagram . Early universe. T. g . J/ ψ , χ C. Quark-gluon plasma. RHIC, LHC. Λ C /D. ρ , ω. FAIR. Color superconductivity.

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Heavy quark system in medium

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  1. Heavy quark system in medium Su Houng Lee Introduction on phase transition Perturbative methods QCD sum rule methods Experiments

  2. QCD Phase Diagram Early universe T g J/ψ, χC Quark-gluon plasma RHIC,LHC ΛC /D ρ, ω FAIR Color superconductivity Nuclear matter mB

  3. EOS: e , p Quark number cq Lattice results for QCD phase transition (from Karsch’s review) Heavy quark V(r) Confinement: L=e-F Chiral sym: <qq> Susceptibility cmqcL

  4. Order parameter in Superconductivity Order Parameter r Order parameter in QCD?

  5. Early work on J/y at finite T (Hashimoto, Miyamura, Hirose, Kanki) s String Tension: QCD order parameter T/Tc

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

  7. J/y from potential models • Lattice result on singlet potential F(T,r) =V(T,r) -TS(T,r) V(r) at T=0 Kaczmarek, Zantow hep-lat/0510094 V(T,r) at 1.3 Tc F(T,r) at 1.3 Tc r [fm] • Quarkonium dissociation temperature for different potentials Using F(T,r) Wong 04 Using V(T,r) Another model independent approach ?

  8. 1-- States from ISR

  9. Few things to note about Tc region • Tc region is important in HIC • Statistical production may occur at or slightly below Tc Au+Au 200 Agev, b=0 T (GeV) t (fm/c) • Large non-perturbative change at Tc (e-3p)/T4 T/Tc • Resumed perturbation fails near Tc Karsch hep-lat/0106019

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

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

  12. System with two heavy quarks Perturbative treatment are possible when

  13. Perturbative treatment are possible when

  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 Perturbation for bound states QCD sum rule approach

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

  17. LO Amplitude

  18. Exp data from pA Not so large, however, LO QCD result is known to underestimate nucleon absorption cross section Oh, Kim ,SHL 02 s1/2 (GeV)

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

  20. q1 NLO Amplitude : y+ q  c + c + q Collinear divergence when q1=0. Cured by mass factroization

  21. q1 q1 Integration of transverse momentum from zero to scale Q Mass factorization Gluons whose kcos q1 < Q scale, should be included in parton distribution function

  22. NLO Amplitude : y+ g  c + c + g

  23. Total cross section for Upsilon by nucleon: NLO vs LO NLO/LO Large higher order corrections Even larger correction for charmonium T. Song and SHL, PRD 72, 034002 (2006)

  24. Thermal quark and gluon masses of 300 MeV will Reduce the large correction Lessons from NLO calculation 1. Large NLO correction near threshold, due to log terms 2. But at finite temperature, thermal masses will regulate the large correction 3. But should be used for T< e

  25. Thermal dissociation cross section For large T  modify Wilson Coefficient Separation scale For small T  modify matrix element Ways to asses convergence T< e D (Matrix) < (Matrix element in Vacuum)

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

  27. Confinement model: Schneider, Weise • E,B Condensate

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

  29. Mass shift: QCD 2nd order Stark Effect : Peskin 79 e > Lqcd • OPE for bound state: m infinity Separation scale For small T  modify matrix element • Attractive for ground state

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

  31. Lattice data on ( e ,p) near Tc e/T4 Sudden increase in e Slow increase in p p/T4 Lattice result for purge gauge (Boyd et al 96) Karsch hep-lat/0106019 Rescaled pressure (Karsch 01)

  32. G0 <a/p B2>T <a/p E2>T G2 Gluon Operators near Tc • Two independent operators Gluon condensate or Twist-2 Gluon • At finite temperature: from

  33. <E2>, <B2> vs confinement potential • Local vs non local behavior Time W(ST)= exp(-s ST) OPE for Wilson lines: Shifman NPB73 (80) T S W(S-T) = 1- <a/p E2> (ST)2 +… W(S-S) = 1- <a/p B2> (SS)2+… Space W(SS)= exp(-s SS) Space • Behavior at T>Tc W(SS)= exp(-s SS) <a/p B2>T W(ST)= exp(-g(1/S) S) <a/p E2>T

  34. Operators in at finite density and hadronic phase • Linear density approximation • Condensate at finite density • At r = 5 xrn.m.

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

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

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

  38. Constraints from QCD sum rules for Heavy quark system • sum rule at T=0 : can take any Q2 >=0, Phenomenological side OPE r J/y Y’ s

  39. QCD sum rule constraint (Morita, Lee PRL08) G [MeV] OPE breaks down G [MeV] Dm [MeV] Dm [MeV] Can also use Borel sum rule

  40. D M y / J GeV G Mass and width of J/y near Tc (Morita, Lee 08, M, L & Song 09) Summary Dm from QCD Stark Effect QCD sum rule limit with DG =0 NLO QCD + confine-model G =constraint-Dm (Stark effect) Constraints from Borel sum rule

  41. G0 <a/p B2>T <a/p E2>T G2 Summary of analysis Summary • Due to the sudden change of condensate near Tc • Abrupt changes for mass and width near Tc

  42. 400 MeV 0.75Tc 1.1Tc 1.1Tc 1 GeV 400 MeV 1.5Tc 1.5Tc 400 MeV Comparison to other approach cc state from lattice K.Morita, Y. Song, SHL 0.9 Tc Mocsy, Petreczky Karsch et al. T=0 1.1Tc cb state from lattice K.Morita, Y. Song, SHL 0.9 Tc Karsch et al. 0.9Tc

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

  44. Can such effect be observed ? RAA from RHIC and Charmonium production ratio in RHIC and Mass shift at Nuclear matter

  45. RAA from RHIC (√s=200 GeV y=0 , 2-comp model (Rapp) Song, Park, Lee 10) Melting of y’ cc Slope: GJ/y Melting T of J/y Height: mass of J/y

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

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

  48. Calculation in hadron gas • Hadron gas model with excluded volume • Matrix element

  49. Results using QCD sum rules • Only 17 GeVPb+Pb data is available with large error bars

  50. Application to nuclear matter

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