Trieste Miller by tQ7Cr31i

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									    Quantum Opacity, RHIC HBT
    Puzzle, and the Chiral Phase
             Transition
Gerald Miller and John Cramer, UW
• RHIC Physics, HBT and RHIC HBT Puzzle
• Formalism
• Quantum mech. treatment of optical
  potential, U (Chiral symmetry)
• Reproducing data, wave function
• Summary
         The RHIC HBT Puzzle
Data from the first five years of RHIC
Some evidence supports the presence of QGP formed in early
  stages of Au+Au collisions:
    Relativistic hydrodynamics describes the low and medium
     energy dynamic collision products

   Elliptic flow data implies very high initial pressure and
     collectivity

     Most energetic pions, produced early, strongly
     suppressed
       Strong suppression of back-to-back jets.
       D Au vs     Au Au, central vs peripheral
       Hydrodynamics works
       BUT NOT FOR HBT
                 HBT- 2 particle interferometry

                       p1                                                  p2
                                               q=p1-p2               p2
                                    q
                            qside

                                               +
Rside




                                        qout
                      p2                                                  p1
        Rout           qlong



               Quantum mechanical interference-space time
               separation of source   K=(p +p )/2            1   2
                  Hydrodynamics predicts big RO/RS,
                  Data RO ,p /(s(p 1 HBT puzzle
               C(q,K) =s(p /RS )about)s(p ))-1 ~
                               1    2              1     2
               λ(1-q2L R2L-q2S R2S –q2O R2O )
Time extent of source R2o >>R2s
 j=w1 t1 +w2 t2




   Expect R2o >>R2s
         Rs =Ro
A highlight from this week




                      Burt Holzman, PHOBOS
        Old Formalism
  source current density =J

Chaotic sources, Shuryak ‘74 S0~<J J*>




     σ(p1)
         Source Properties
hydrodynamics inspired source function of Wiedemann
Heinz et al

Bjorken tube model-boost invariant
   S0(x,K) ~freeze out surface
      but π emission allowed
      everywhere
      ρ(b) medium density
      radial flow
        Overview of Our Model
 Allow pions to be emitted anywhere in
  medium, not only at freeze-out surface
 Pions interact with the matter on their way
  out.
 Pion absorption implemented via
  imaginary part of optical potential.
 Real part of optical must exist, acts as mass
  and velocity change of pions due to chiral-
  symmetry breaking as they pass from the hot,
  dense collision medium to the outside
  vacuum
                Formalism


• Pions interact U with dense medium


  Gyulassy et al ‘79
      is distorted (not plane) wave
DWEF- distorted wave emission function
        Wave Equation Solutions
Matter is infinitely long Bjorken tube and azimuthal
 symmetry, wave functions factorize: 3D 
 2D(distorted)1D(plane)



 We solve the reduced Klein-Gordon wave equation for yp:



Partial wave expansion ! ordinary diff eq
     Son & Stephanov 2002

v2, v2 m2 (T) approach 0 near T = Tc

                                =ω2-m2π




Both terms of U are negative (attractive)
             Fit STAR Data

6 source, 3 optical potential parameters
Fit central STAR data at sNN=200 GeV

reproduce Ro, Rs, Rl
reproduce dN/dy (both magnitude and shape)
8 momentum values (i.e., 32 data points)
         Fit to 200 GeV Au+Au Radii


U=0


Re U=0
Potential Effects
  200 GeV Au+Au Spectrum



                 U=0
noBE




                   no flow
  Meaning of the Parameters

• Temperature: 193 MeV fixed at phase transition temperature
  S. Katz, QM05
• Transverse flow rapidity: 1.5  vmax=0.85 c, vav=0.6 c
• Pion emission between 6.2 fm/c and 11 fm/c  soft EOS .
• WS radius: 11.8 fm = R (Au) + 4.4 fm > R @ SPS
• Re(U): 0.14 + 0.85 p2  deep well  strong attraction.
• Im(U): 0.12 p2  mfp  8 fm @ KT=1 fm-1  strong
  absorption  high density
• Pion chemical potential: m= mass()

Consistent with CHIRAL PHASE TRANSITION!
Wave Functions |y(q,                 b)|2 r(b)
            DWEF        DWEF           Eikonal
            (Full)   (Im Pot only)     Approx.



KT=
100 MeV/c




KT=
250 MeV/c




KT=
600 MeV/c
Centrality & Nuclear Dependence
 Au+Au                         Cu+Cu
                  Au+Au                         Cu+Cu
                                               Centrality:
         Rout    Centrality:           Rout
                   0-5%                          0-10%

                   5-10%                        10-20%

                  10-20%                        20-30%

                  20-30%                        30-40%
         Rside                         Rside
                  30-50%                        40-50%

                  50-80%                        50-60%




         Rlong                         Rlong
                       Summary
 Quantum mechanics solves technical problems of applying
  opacity to HBT.
 Excellent fits sNN=200 GeV data: three radii, pT spectrum.
 Fit parameters: indicate strong collective flow, significant
  opacity, and huge attraction. Describe pion emission in hot,
  highly dense matter (a soft pion equation of state) .
 Replace the RHIC HBT Puzzle with evidence for a chiral
  phase transition. In most scenarios, the QGP phase transition
  is accompanied by chiral phase transition at about same
  critical temperature.
• Phys.Rev.Lett.94:102302,2005, nucl-th/0507004

            The End
SPARES FOLLOW
For details see:
Phys.Rev.Lett.94:102302,20
05
  and a newer preprint:
          nucl-th/0507004 ,
submitted PRC

       The End
        Source Properties
 S0 ( x, k ) = S0 ( , ) B (b, KT ) /(2 )3
                 cosh             (   0 )2     
                                                     2
 S 0 ( , ) =                exp                   2
                 2 ( )          2           2  
                            2                 2

  (“hydrodynamics inspired” source function of Heinz & collaborators)

                               1
 B (b, KT ) = M T                             r (b)
                         K  u  m  (medium density)
                   exp 
                               T        1
                                        
 =t z
  2    2    2
                    (Bose-Einstein thermal function)

         tz          K = particle momentum 4-vector
 = 2 ln 
    1
              
          tz         u = trasverse flow 4-vector
 S0(x,K) ~freeze out surface
Correlation/Gaussian Fit
Eikonal Magnitude of wave function
                                l
                            b




                            q
       b/R            RO = R/4.48 HV
Correlation Functions
9 Fits: 200 GeV/A Au+Au
c2 vs. Temp for 9 Fits

								
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