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					  Intermediate-mass lepton pairs
in relativistic heavy-ion collisions
              Charles Gale
                McGill




                                Charles Gale
                                  McGill
       Introduction and Outline
• The physics of (very) hot and dense matter
  is best explored in the laboratory with
  relativistic nuclear collisions
• Photons and dileptons are penetrating
  probes         s  0.2
                 em  0.007
 • New physics: collective, many-body effects
      • Quark-gluon plasma
      • In-medium modifications
         –   Modified spectral densities
         –   Chiral symmetry restoration
         –   Mixing effects
         –   Pion dispersion relation      Charles Gale
                                             McGill
                Outline, cont’nd
• Experiments (IM): DLS, Helios, NA-38, -50, -60
  CERES,WA98, HADES, PHENIX
• Electromagnetic radiation as a tool for hadronic
  tomography:
   –   Low mass dileptons
   –   Intermediate mass dileptons    SPS
   –   Low pT photons
   –   High pT photons               Sangyong Jeon’s talk
   –   High pT intermediate mass      RHIC
       dileptons                      LHC




                                                  Charles Gale
                                                    McGill
Why? Investigation of the QCD phase
             diagram




F. Karsch, E. Laermann, hep-lat/0305025



                                                         Charles Gale
            S. B. Ruster et al., PRD 72, 034004 (2005)     McGill
     How? The information carried by EM
                   probes
 Emission rates:
               d 3R   g                   1
               3          Im   (k ) 
                                  R
                                              [photons]
               d k   (2 ) 3
                                         e 1
      McLerran, Toimela (85), Weldon (90), Gale, Kapusta (91)

        d 6R    2e2 1                  1
E E 3                 L Im   (k ) 
                                R
                                            [dileptons]
     d p d p (2 ) k
            3       6  4
                                       e 1
•The electromagnetic spectra will be direct probes of the in-medium
 photon self-energy
•They are hard probes:  EM
                               s 3%
       •EM signals as probes for hadronic tomography
                                                                Charles Gale
                                                                  McGill
                 The current-current correlator
  A model for the hadronic electromagnetic current: VMD
       e 2          e 2      e 2
J      m       m   m                    The current-field identity
       g          g        g                              (J. J. Sakurai)

                 VMD
Im  J  J T    Im     T  Im D  Spectral density
                                        T




      The photon/dilepton signal can tell us about the in-medium
     spectral densities of vector mesons. Rates need to be integrated
        over the space-time history, with some dynamical model
                          dR
                E E 3            C  ( p , p ) Im D (k , T )
                                                          R

                      d p d 3 p
                                                        k  k
                                    L             T
                                  P           P
                  D (k , T )   2         2         2 2
                                  k  m  F k  m  G m k
                                       2          2
                                                                          Charles Gale
                                                                            McGill
What is expected (dileptons)
                      • Low masses receive
                        significant contribution
                        from radiative decays
                      • High masses dominated
                        by DY
                      • Intermediate mass
                        region interesting from
                        QGP perspective, DD
                        (Shuryak (78), Shor
                        (89))


                      • Photons: similar story,
                        but featureless spectra

                      • Experiments: DLS,
                        Helios, TAPS, NA38, -
                        50, WA98, CERES,
                        PHENIX, HADES,
                        NA60
                                     Charles Gale
                                       McGill
Vector Meson Spectral Densities: A
       Sample Calculation I




    Ralf Rapp and Charles Gale, Phys. Rev. C 60, 024003 (1999)
                                                         Charles Gale
                                                           McGill
  The interaction is constrained by basic
        hadronic phenomenology
Chiral, Massive Yang-Mills:
O. Kaymakcalan, S. Rajeev, J. Schechter, PRD 30, 594 (1984)


L  F Tr DUD U  F Tr M  U + U† 
   1 2             †   1 2
   8                    8
     Tr  F F L  F F R   m0 Tr  A AL  A AR 
      1      L           R            2       L        R

      2
     non-minimal terms
   Parameters and form factors are constrained by
   hadronic phenomenology:
   •Masses & strong decay widths
   •Electromagnetic decay widths
   •Other hadronic observables:
       • e.g. a1   D / S                                   Charles Gale
                                                                McGill
Low Masses:Vector Meson Spectral
    Densities:Hot Meson Gas

                     The spectral density is flattened
                     and broadened. Even more with
                     baryons.




                  Rapp, Gale (PRC, 99)
                                             Charles Gale
                                               McGill
       NA60 Comparison of data to RW, BR and
                    Vacuum 
                                  Sanja Damjanovic
                                  Quark Matter 05 (and
pT dependence
                                  this meeting)




                                             Charles Gale
                                               McGill
    Two approaches:
                                        H. Van Hess, R. Rapp, nucl-th/0603084




T. Renk, J. Ruppert, hep-ph/0603110
    See J. Ruppert’s talk this aft.
                                                                 Charles Gale
           Many-body (in-medium) effects are observed!             McGill
            The intermediate mass sector: some
                       background
                                                                            NA50
                                                                   Pb-Pb 158 GeV




A. Shor, PLB 233, 231 (1989)
                                                        charm         DY
                                                             _
                                                            DD             DY



                                              central collisions

• Direct connection to Hard Probes
• Off-shell effects are potentially important for effective
  hadronic interactions Gao & Gale, PRC 57, 254
  (1998)

                                                                    Charles Gale
                                                                      McGill
On the dangers of extrapolations…
                                       • (a) B. A. Li, Phys.
                                         Rev D 52, 5165
                                         (1995).
                                       • (b) Gomm,
                                         Kaymakcalan,
                                         Schechter, Phys. Rev.
                                         D 30, 2345 (1984).
                                       • (c) Janssen, Holinde,
                                         Speth, Phys. Rev. C
                                         49, 2763 (1994).
                                       • (d) Ko, Rudaz, Phys.
                                         Rev. D 50, 6867
                                         (1994).
                                       • (e) Xiong, Shuryak,
                                         Brown, Phys. Rev. D
                                         46, 3798 (1992).

  Gao & Gale, PRC 57, 254 (1998)
                                                    Charles Gale
       But, a lot of data exists!...                  McGill
e+ e- Data: A Wealth of Information




             •   OLYA
             •   CMD
             •   DM-1(2)
             •   ARGUS
             •   M3N
             •   gg2




                                  Charles Gale
                                    McGill
                 4 2                   em            2  V                   
                      M T K1 ( M / T )   ( M )        ( M )   ( M )  
            dR                                                          
               
           dM 2 2                                    2                       
I. Kvasnikova, C. Gale, and D. K. Srivastava, PRC 65, 064903 (2002)
Z. Huang, PL B361, 131 (1995)

                                                                      Charles Gale
                                                                        McGill
A larger comparison
        • Agreement across theoretical
            models
        • Those channels are mostly
          absent from the spectral
          densities used in comparisons
          with CERES and the new
          NA60 data.




                                Charles Gale
                                  McGill
Intermediate mass data
                 A. L. S. Angelis et al.
                    (Helios 3), Eur. Phys. J.
                    (1998)



                  Li and Gale, PRC (1998)




         R. Rapp & E. Shuryak, PLB (2000)



                                     Charles Gale
                                       McGill
NA50 Data (cont’nd)




 I. Kvasnikova, C. Gale, and
  D. K. Srivastava, PRC 2002

               •In agreement with multiplicity dependence
               •Includes detector acceptance & efficiency   Charles Gale
                   (O. Drapier, NA50)                         McGill
NA60 IMR analysis: weighted offset fits (A. David’s talk)

Extract prompts by fixing
Open Charm contribution


 Fix Charm contribution to
   “world average” value


            or               1




 Fix Charm contribution to
 NA50 p-A expected value



            

  Fit always requires
~2 times more Prompts

                                                     Charles Gale
                                                       McGill
      Low and Intermediate masses: partial
                   summary
• Thermal sources shine in the LMR and IMR. No great
  sensitivity to the QGP. Intermediate-mass excess is not charm
  enhancement!
• The new data is precise enough to consider a differentiation of
  space-time models
• DY? At low M, medium-enhanced multiple parton scatterings
  might be large (Qiu, Zhang (02), Fries, Schaefer, Stein, Mueller
  (00). pA measurement.)




 d AB      d NN
                2 
     2
        AB        1  RAB (Q) 
 dQ          dQ

                                                             Charles Gale
                                                               McGill
A recent analysis: (van Hees & Rapp, hep-ph/0603084)




•Sensitive to the space-time modeling:R  e (4  )
•Still sensitive to the low-mass spectral densities
          Analyses should be redone with those         Charles Gale
                                                         McGill
                 Homework
• Unite (standardize?) space-time modeling [nD
  hydro, fireballs, transport approaches…].
• The power of the data is fully realized if a
  general-purpose acceptance filter exists. (On
  the way!...)
• Chiral symmetry? Still not obvious… An
  independent access to a1 spectral density is
  missing. More work on the theory side too.
  (Urban, Buballa, Hochsch. & Wambach, PRL,
  88, 042002 (2002))

                                         Charles Gale
                                           McGill
Charles Gale
  McGill
                                  Jet-quenching
                                       leading                                      leading
                                       particle
                                                                                    particle
                                                                                    suppressed


          hadrons                                      hadrons


               q                                            q



                              q                                            q



     hadrons                                      hadrons


                    leading particle                             leading particle
                                                                 suppressed




Source of energy loss: medium-induced gluon                                                Charles Gale
Bremsstrahlung (+ elastic scattering?)                                                       McGill
Quenching = Jet-Plasma interaction.
 Does this have an EM signature?



                          qg  qg

                         The plasma mediates
                         a jet-photon
                         conversion

        Fries, Mueller & Srivastava, PRL 90, 132301 (2003)
                                                  Charles Gale
                                                    McGill
             Photon sources
• Hard direct photons


• Fragmentation


• Thermal photons from hot medium


• Jet-photon conversion


• Jet in-medium bremsstrahlung

                                    Charles Gale
                                      McGill
               Dilepton sources
• Drell-Yan dileptons



• Thermal dileptons



• Jet-virtual photon conversion




                                  Charles Gale
                                    McGill
Energy loss in the jet-photon conversion? Jet
              bremsstrahlung?
Use the approach of Arnold, Moore, and Yaffe
   JHEP 12, 009 (2001); JHEP 11, 057 (2001)
• Incorporates LPM
• Complete leading order in S
• Inclusive treatment of collinear enhancement, photon and gluon
   emission




                                                   Can be expressed in
                                                   terms of the solution to
                                                   a linear integral
                                                   equation
                                                                   Charles Gale
                                                                     McGill
                  E loss/gain: some systematics
                                                             •Includes E gain
                    (k  p, k )
                       q
                       qg                                    •Evolves the whole
                                                              distribution function

 dPq ( p)                        d  qg ( p  k , k )
                                     q
                                                                     d qg ( p, k )
                                                                        q

              Pq ( p  k )                             Pq ( p)
    dt            k                     dk dt                           dk dt
                                      d  qq ( p  k , k )
                                          g

                    2 Pg ( p  k )
                                            dk dt
dPg ( p)                      d  qg ( p  k , p)
                                  q
                                                                     d  gg ( p  k , k )
                                                                         g

             Pq ( p  k )                          Pg ( p  k )
  dt          k                     dk dt                                  dk dt
                         d  qq ( p, k ) d  gg
                              g               g
                                                           
               Pg ( p)                        (2k  p) 
                         dk dt            dk dt           
                                                          

           S. Jeon’s talk                                                             Charles Gale
                                                                                        McGill
Jet characteristics:




                       Charles Gale
                         McGill
Time-evolution of quark distribution




                                   The entire
                                   distribution is
                                   evolved by the
                                   collision Kernel(s)
                                   of the FP equation




                  Turbide, Gale, Jeon, and Moore (2004)
                                             Charles Gale
                                               McGill
                       Jet-plasma dileptons?
 • Same basic idea as photons, details are slightly
   different:
      – High pT cut helps with background subtraction
 • Go beyond LO, do a HTL analysis
                                                

                                      d R 4
                                                                Im   
                                                                        R

                                                     
                                      d4 p             12 4 M 2 1  e  E
                                      2
                                  ef      d 3q
                 ( p)  3e 2    T         Tr g  S D (q)g  S (q  p) 
                                           (2 )3                            
                 
                               f  e   n



            g 0 g q g 0 g q
S D (q)                                     D (q)  iq0  q  A  B
            2 D (q)       2 D (q)

                                                                             Charles Gale
                                                                               McGill
Im




     The thermal “baseline” calculation agrees with that of   Charles Gale
     M. Thoma, C. T. Traxler, Phys. Rev. D 56, 198 (1997)       McGill
      Dileptons from jet-thermal interactions
•Jet-thermal as large as
DY/heavy quark decay
(RHIC)
•Jet-thermal still as large
as DY. S/B could improve
with harder pT cut.
•At RHIC, there is a
contribution to the IM
region
•In-medium jet
bremsstrahlung will also
add to the signal
•No heavy quark energy
loss
•Signal as large as it is for
photons
          Turbide, Gale, Srivastava, Fries, PRC (2006)   Charles Gale
                                                           McGill
  But: other signature of jet-photon
             conversion?



                   dN        dN                           
                                     1   2vn cos  n 
                pT dpT d 2 pT dpT       n               


• Jet-plasma photons will come out of the
  hadron-blind region. “Optical” v2 < 0
     Turbide, Gale, Fries (PRL 06)
                                                       Charles Gale
                                                         McGill
Photons from primordial interactions and fragmenting jets
All photons (NN, frag, jet-photon conv., bremss., Th.)
              0 +            -              -      +

                                                            Charles Gale
                                                              McGill
• v2 from “Isolated photon cut” is negative
• Photons associated with a “crowded photon cut” show v2 with
  changing sign
• Same game can be played with dileptons (in progress)
• See talk by U. Heinz
                                                                Charles Gale
         Similar story for the LHC                                McGill
               Conclusions, part I
 Intermediate-mass dileptons
•New data will put further stringent tests on models, both rates
& space-time modeling
Jet-plasma interactions: measurable EM signatures! These are
fairly robust with respect to changing temperature &
dynamics

  • RHIC & LHC:
      – Jet-plasma interactions: dilepton channel: signal
        competes with Drell-Yan (NLO)
      Towards a consistent treatment of jets & EM radiation

                                                              Charles Gale
                                                                McGill
              Conclusions, part II

• Low and mass dileptons: NA60 data can
  distinguish between models. In-medium effects!
• RHIC/LHC: There are measurable electromagnetic
  signatures of jet-plasma interaction: those
  constitute complementary observables to signal the
  existence of conditions suitable for jet-quenching
• Photon v2: a revealing probe
• EM radiation and hard probes: the start of a
  beautiful friendship…
• EM radiation: change of paradigm


                                                Charles Gale
                                                  McGill
• Interested in the
  techniques discussed
  here?
• Want to know more?




  Found where fine books are sold
           (July 2006)




                             Charles Gale
                               McGill
Charles Gale
  McGill
• Chatterjee, Frodermann, Heinz, Srivastava, nucl-th/0511079


                                                           Charles Gale
                                                             McGill
        Jet-plasma photons:




• S. Jeon’s talk              Charles Gale
                                McGill
New (preliminary) PHENIX Data




                                Charles Gale
                                  McGill
Charles Gale
  McGill
Vector Meson Spectral Densities, II
          (adding baryons)

                    R. Rapp & J.Wambach, 1999




                                           Charles Gale
                                             McGill
           Soft photons @ RHIC:



• There is a window




                      Turbide, Rapp & Gale PRC (2004)

                                               Charles Gale
                                                 McGill
    Same spectral densities:Low
   mass dileptons and real photons




S. Turbide, R. Rapp, and C. Gale, PRC (2004)



                                               Charles Gale
                                                 McGill
                                                      Turbide, Rapp & Gale
                                                      PRC 2004



•   Same spectral densities as low mass dileptons
•   Same dynamical model; same boundary conditions
•   Cronin contribution estimated from pA data (E629, NA3)
•   QGP: small
                                                                  Charles Gale
                                                                    McGill

				
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