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									 Heavy quark system near Tc


                       Su Houng Lee
                   In collaboration with Kenji Morita


Also, thanks to group members:
 Present: T. Song, K.I. Kim, W.S. Park, H. Park, K. Jeong
 Former: K. Ohnishi, S. Yasui, Y. Song




                                                            1
     Early work on J/y                      (Hashimoto, Miyamura, Hirose, Kanki)




                                            small

                                        r



                       4  s (r )                                             (GeV 2 )
          V (r )                  r
                       3 r




                                   (T )   (0)  Tdec  T  / Tdec  b



                                                                                          T / Tdec
S H Lee                                                                                              2
          J/y in Quark-gluon plasma

    •     Matsui and Satz: J/y will dissolve at Tc due to color screening


    •     Lattice MEM :     Asakawa, Hatsuda, Karsch, Petreczky ….
                           J/y will survive Tc and dissolve at 2 Tc


    •     Potential models (Wong …) :
                           Consistent with MEM Wong.


    •     Refined Potential models with lattice (Mocsy, Petreczky…)
                          : J/y will dissolve slightly above Tc


    •     Lattice after zero mode subtraction (WHOT-QCD)
                          : J/y wave function hardly changes at 2.3 Tc


    •     AdS/QCD (Kim, Lee, Fukushima ..)
                          : J/y mass change
    •     And so on ……….
S H Lee                                                                     3
                      Comparison with experimental data of RHIC (√s=200 GeV at
                                                                   midrapidity)

                                                               T. Song (preliminary)


                 1
                0.9                           With g=1.82
                0.8
                0.7
                0.6
                0.5

          RAA   0.4
                0.3
                          Nuclear absorption &
                          Thermal decay in QGP & HG                         Total
                0.2
                0.1
                                  Recombination
                 0
                      0            100           200           300          400
                                         No. of participants
S H Lee                                                                                4
          Some perspectives on sQGP and
             relation to deconfinement




S H Lee                                   5
          Some perspectives from Lattice data on (e , p) near Tc

          Lattice data (Karsch et al) vs. Resummed perturbation (Blaizot et al.)



                                sQGP
                                 J/y                    Karsch hep-lat/0106019




          Operator representation: Gluon condensates



            M2          STG  G         e  p
                                           T


                                                                      sQGP
                   11              2 
            M 0    G2             G   e 3p
                   8      T          0




S H Lee                                                                             6
           M0 and Bag pressure


                       e 
                           3     1
                             M2  M0                 B
                                                           1
                                                             M 0 (Tc )  M 0 (0)
                           4     4                         4
                           1     1
                       p    M2  M0                   1 9      
                                                          G 2   189 MeV
                                                                               4
                           4     4                       8 
                                                       4         
                                                                  



                                        2            2            8
           M0 and Gluon condensate      G            G             M0
                                            T            0       11


                                                               Dominated by non perturbative change
            2                                                 at Tc          
           
             G                                                             0.3        G2
                   T                                                               
          GeV 
                                                                                            0
              4


                                                                      SHLee PRD40,2484(89)




S H Lee                                                                                               7
           Relation to Electric and Magnetic condensate
                            Kaczmarek et al (prd04)



                       2             2      3  s T 
                       E             M0             M2                   </ B2 >T =0
                           T         9      4 
                       2          2     3  s T 
                       B         M0             M2                       </ E2 >T
                           T      9     4 




           Relation to deconfinement
                        Time


                                                  exp(- V(T))
                                   W(S-T)
                                                                                E   2
                                                                                          
                                                                                               d 3k      2k   2
                                                                                                                 3m 2    
                                                OPE  1- </ E2> (ST)2 +…
                                                                                             2 3 Ek     e Ek / T  1
                                       L
                                                        Space                   B   2
                                                                                          
                                                                                               d 3k         
                                                                                                          2k 2
                                      L                                                      2 3 Ek e Ek / T  1
                            W(S-S)         OPE 1- </ B2> (SS)2 +…

          Space
S H Lee                                                                                                                       8
          Heavy quark system in sQGP


             OPE,   QCD Stark Effect, and
                    QCD sum rules




S H Lee                                     9
     Heavy quark system near Tc

                                                             Large increase in E2
                             2
                                       0.35 GeV 
                                                     4
               QCD vacuum     G
                                 0


                       B
                                             sQGP at Tc
          MIT Bag
                                  Vacuum with negative pressure
                                       2                   2
                                        G         0.7      G
                                           Tc                  0




S H Lee                                                                         10
          Heavy quark correlation function (q2)

         Definition                                                       c

           (q)   dxeiqx c c( x), c c(0)
                                                               q
                                                                           c

                                                                               Gn
         Operator product expansion (OPE)

                          1                 F ( q 2 , x)
            (q)  ...  dx                                          G n  ..
                          0
                               4m   2
                                          q  (2 x  1) q
                                            2              2
                                                                
                                                               2 n




           •    OPE makes sense when               4m2  q 2  G          vacuum
                                                                                   2
                                                                                     QCD

           •    Even at finite temperature or as long as

                                 4m2  q 2  G            medium
                                                                   QCD  aT  2

S H Lee                                                                                    11
         q2=0 : photo production of open charm
                                                       c
              4m2  2QCD                    q2  0

                                Cn                     c
              (q 2  0)              Gn
                               4m 
                                  2 n
                                                           Gn

         q2=m2J/y : OPE for bound state (Peskin 79)

              4m2  q 2  2m e  2
                                   QCD




         -q2 >0 : QCD sum rules for heavy quarks


              4m2  Q2  2
                           QCD




S H Lee                                                         12
                                                       c
                                              q2  0
                                                       c

                                                           Gn

         q2=m2J/y : OPE for bound state (Peskin 79)

              4m2  q 2  2m e  2
                                   QCD




S H Lee                                                         13
    QCD 2nd order Stark Effect : e >                        qcd


         OPE for bound state: m infinity
                                                               
                e 0  mNc g / 16   O(mg ),
                                        2
                                   2              4
                                                              |k |    O(mg 2 )
                           c
                    c                       c
               q                                      g 2  mg 4 (mg 2 ) 3
                                                                                O (1)
                                                            4      4       2 2
                           c                             (mg )( mg )( mg )
                    c                       c


         Attractive for ground state


                                  2
                             128 a0     x3/ 2      1       2
                mJ /y      2
                             9 e 0  (1  x)6 x  a02em  E
                                     dx                 
                                                                               T

                    T/Tc                    1.0         1.05              e0
                   mJ/y               -44 MeV        -105 MeV         311 MeV
                    mU                -4.3 MeV       -10 MeV          580 MeV
S H Lee                                                                                  14
      2nd order Stark effect from pNRQCD

         LO Singlet potential from pNRQCD : Brambilla et al.   1/r > Binding >  QCD,




                                                          S     O
         Derivation

          • Take expectation value

          • Large Nc limit

          • Static condensate

          • Energy


          •
S H Lee                                                                                  15
                                                       c
                                              q2  0
                                                       c

                                                           Gn




         -q2 >0 : QCD sum rules for heavy quarks


              4m2  Q2  2
                           QCD




S H Lee                                                         16
    Q2=-q2>0, QCD sum rules for Heavy quark system

         sum rule at T=0 : can take any Q2 >=0,                                    4m2  Q2  G            vacuum
                                                                                                                     2
                                                                                                                       QCD


                                                                n
                                            d                             ( s)
                                     M n   2   J (Q), J (0)   ds
                                            dQ 
                                                                      (s  Q 2 )n


               Phenomenological side                                                          OPE

           
                   J/y                                                                            (n  4)! G
                                                                                                              2
                                                                                                                  
                                                                                 M n  an 1                 ..
                           Y’
                                                                                          
                                                                                                            
                                                                                                      n! 4mc2 2 
                                                                                                                  

                                                                    s
                                                                        M n 1
                                                                        Mn                                            with G 2
                                                 n
                                                        
                              f  c mJ /y   
                                       2

                                                      ..
                    1                        
          Mn 
                 m 
                    2
                    J /y
                           n  J /y
                             
                                     m2
                                     y'
                                              
                                              
                                                        
                                                        
                                                                                                                        G2  0
          M n1
                 mJ /y 
                   2
                           2
                             
                          my '  mJ /y2
                                           m
                                           
                                              2
                                              J /y
                                                        
                                                        
                                                            n


          Mn                   f J /y      m  2        
                                              y'       

S H Lee                                                                                                                          17
         sum rule near Tc                  4m2  Q2  G 0   G       T



          Phenomenological side                                                          OPE

      
            J/y
                                                                          (n  4)! <G2>+c<G2>
                                                                                    G2                     
                                                         M n  an 1                         .......... 
                                                                                        ..........      ...
                    Y’                                            
                                                                                    
                                                                              n! 4mc2 2                   
                                                                                                           
                                             s

                                                                                          <G2>
                          f sG
           (s) 
                    s  m 
                          2
                          J /y
                               2
                                    sG 2                                     <G2>


                            ( s)
          M n   ds
                         (s  Q 2 )n
                                                               M n 1
                                                               Mn
  Matching Mn-1/Mn from Phen to OPE
   Obtain constraint for mJ/y and G



S H Lee                                                                                                        18
   QCD sum rule constraint     (Morita, Lee 08)


                         n
                1 d                           (s)
                            
                    dQ 2   Q 
                               2
                                     ds
                n!       
                                          s  Q 
                                                  2 n 1




                                     G MeV]
                                     G MeV]
                                                       m   MeV]   m   MeV]




S H Lee                                                                          19
                          Summary
   Mass and width of J/y near Tc (Morita, Lee 08)


                                                m from QCD Stark Effect
  MJ /y
                          G
  GeV                                          QCD sum rule limit with G =0



                                                     NLO QCD Song (07)




   GJ /y
   GeV                                     G (MeV)
                                                G =constraint-m (Stark effect)




                                                               T/Tc

S H Lee                                                                           20
                      Prediction from the bottom-up AdS/QCD model




                             Deconfinement + temperature effects.
          Effect of gluon condensate is missing. So, above Tc detailed study about the
             competition between the temperature and gluon condensate should be
                                             done .
                            YK, J.-P. Lee, and S. H. Lee, PRD (2007)
S H Lee                                                                                  21
          S-wave vs. P-waves Summary
                 OPE breaks down




S H Lee                                22
          bb system   Summary




S H Lee                         23
     Experimental observation from RHIC is difficult at present
     1. Expected mass shift for J/y is order 50 MeV at Tc

     2. Larger effect for excited states
     3. Small effect for U but larger cb




S H Lee                                                           24
   Gluon condensate in nuclear matter
          •   Linear density approximation

                                          N                                 
                Op   n.m .
                              Op   0
                                               N | Op | N ,   M0      N | T (Chiral) | N  mN  750 MeV
                                                                                               0

                                          2mN
                                                               M 2  mN  dxxG( x, 2 )             0.45 mN


                                                                       2             2                  
          •   Gluon condensate at finite density                        G             G      1 - 0.061
                                                                                                               
                                                                                         0            n.m. 
                                                                                                                



                                                                                          RHIC energy scan
                                                                                          FAIR




                             5  0

S H Lee                                                                                                             25
   Other approaches for mass shift in nuclear matter

                    Quantum   QCD 2nd          Potential          QCD sum         Effects of
                    numbers   Stark eff.        model               rules          DD loop


            hc        0-+      –8 MeV                             –5 MeV
                                                                    (Klingl,
                                                                                  No effect
                                                                  SHL ,Weise,
                                                                    Morita)


            J/y       1--      –8 MeV
                              (Peskin, Luke)
                                                -10 MeV
                                               (Brodsky et al).
                                                                  –7 MeV
                                                                    (Klingl,
                                                                                  <2 MeV
                                                                                   (SHL, Ko)
                                                                  SHL ,Weise,
                                                                    Morita)


            cc      0,1,2++   -40 MeV                             -15 MeV
                                                                  (Morita, Lee)
                                                                                  No effect
                                                                                  on chi_1


          y(3686)     1--     -100 MeV                                            < 30 MeV



          y(3770)     1--     -140 MeV                                            < 30 MeV




S H Lee                                                                                        26
      Observation of m through p-A reaction


                                                                                   e
                             k  4 to 6 GeV/c


                                                                y
                   Anti                                                             e
                  proton
                                                                    Heavy nuclei
                                                  1
                                                                 1.2 fm
                                          0.17 fm 3  5 fm 2

          Can be done at J-PARC




    Expected luminosity at GSI 2x 1032cm-2s-1


S H Lee                                                                                  27
                                    Summary

    1.    Properties of QQ system in sQGP is still controversial



    2.    The mass and width will suddenly change at Tc  different for s p wave
          and bottonium  can probe confinement physics


    3.    Partial observation at nuclear matter through p A reaction might be possible.
          FAIR, J-PARC



    4.    A new constraint for heavy quark system near Tc




S H Lee                                                                                   28

								
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