1. J. RuppertHot Quarks 2006, May 2006 What does the rho? Lessons from NA60's di-muon measurement. Jörg Ruppert Nuclear Theory, Department of Physics, Duke University, Durham, NC, USA In collaboration with: Thorsten Renk Department of Physics, University of Jyväskylä, Jyväskylä, Finland

2. J. RuppertHot Quarks 2006, May 2006 Outline 1.Introduction: EM Probes of strongly interacting matter 2.Dynamical Evolution 3.NA60’s 158 AGeV In-In di-muon spectra 4.From In-In to Pb-Pb 5.Conclusions

3. J. RuppertHot Quarks 2006, May 2006 EM Probes of strongly interacting matter Focus on dileptons in this talk

4. J. RuppertHot Quarks 2006, May 2006 Dilepton emission from URHIC URHIC produce a hot and dense medium - but it is by all means not static!

5. J. RuppertHot Quarks 2006, May 2006 Dilepton spectra in HICs Focus on low and intermediate mass region in this talk

6. J. RuppertHot Quarks 2006, May 2006 Theory of dilepton emission (modulus factor including lepton masses) In-medium effects and the fireball evolution as input are needed! Averaged in-medium photon spectral function (EM correlator) On top of that non-thermal sources (hadron decays, Drell-Yan, open charm etc.)

7. J. RuppertHot Quarks 2006, May 2006 E. M. correlator in vacuum Continuum V Vector meson dominance Rho-meson dominant! Compilation from Rapp, Wambach, Adv.Nucl.Phys.25:1,2000

8. J. RuppertHot Quarks 2006, May 2006 Chiral symmetry breaking Chiral symmetry spontanously broken in vacuum! Chiral partners in the hadronic spectrum split. Hot and dense matter excites the vacuum: Gradual restoration of chiral symmetry => Chiral partners become degenerate!

9. J. RuppertHot Quarks 2006, May 2006 Chiral symmetry restoration Barate et al, ALEPH, Eur. Phys. J. C4, 409 (1998), Compilation from Rapp, Wambach, Adv.Nucl.Phys.25:1,2000 Vacuum Brown, Rho, Phys. Rev. Lett., (1991) In-Medium rho and a 1 In-medium chiral mixing (leading order, M large) Broadening e. g. from hadronic many-body calculations Compilation from Rapp, Wambach, Adv.Nucl.Phys.25:1,2000 Dey, Eltsky, Ioffe, Phys. Lett. B252 (1990) 620 Krippa Phys. Lett. B427 (1998) 13.

10. J. RuppertHot Quarks 2006, May 2006 SU(3) chiral model at finite densities and temperature

11. J. RuppertHot Quarks 2006, May 2006 Hot meson gas: Pion/Rho system treated in Phi - functional approach Phi-Functional approach [Baym, Luttinger, Ward, Cornwall, Jackiw, Tomboulis] Systematic resummation scheme of certain classes of diagrams: Many-Body calculation that includes non-perturbative broadening effects due to a finite width of the pion. Ruppert, Renk, Phys.Rev.C71:064903,2005 approximation Self-energies Included: finite broadening Not-included: mass shifts (disregard changes in the real part of the self-energy)

12. J. RuppertHot Quarks 2006, May 2006 Dynamical evolution model for URHIC! Reliable dynamical evolution model absolutely necessary!

13. J. RuppertHot Quarks 2006, May 2006 CERES data Compilation of calculations for the dilepton spectrum at CERES for different models of in-medium modifications. One fireball evolution model for all spectral functions Renk,Ruppert, Phys.Rev.C71:064903,2005. Klingl, Kaiser, Weise, Nucl.Phys.A624:527-563,1997, Renk, Schneider, Weise, Phys.Rev. C66:014902,2002, Renk, Mishra, Phys.Rev.C69:054905,2004

14. J. RuppertHot Quarks 2006, May 2006 Rescaling for 158 AGeV In-In collisions Since no freeze-out analysis is available the Pb-Pb collision model is rescaled! The choice of the decoupling temperature T F =130 MeV is not strongly restricted. This translates primarily into an uncertainty in the normalization of the final result.

15. J. RuppertHot Quarks 2006, May 2006 Comparison with NA60 p t >1 GeV p t <0.5 GeV P t integrated

16. J. RuppertHot Quarks 2006, May 2006 From In-In to Pb-Pb! p t <0.5 GeV P t integrated p t >1 GeV

17. J. RuppertHot Quarks 2006, May 2006 What dominates M>1 GeV? QGP vs. low T four pion annihilation? van Hees, Rapp, hep-ph/0603084 Low T contributions would be significant due to fugacity ! Is such a description valid down to T f ? Is chiral mixing effective at low T? Can low T contributions account for NA60’s p t cuts (next slide)? ? ?

18. J. RuppertHot Quarks 2006, May 2006 QGP vs. low T four pion: p t -dependence Significant QGP contribution (high T, insignificant flow) High T => exponential Spectrum in p t Significant low T chiral mixing contribution (significant flow) Flow pushes to higher p t => exponential spectrum with shoulder in p t Different evolution models (different T, different flow) can lead to similar spectra either at low p t or high p t at given M but not at both..

19. J. RuppertHot Quarks 2006, May 2006 Comparison I: Integrated p t van Hees, Rapp Renk, Ruppert, hep-ph/0605130

20. J. RuppertHot Quarks 2006, May 2006 Comparison II: p t <0.5 GeV van Hees, Rapp Renk, Ruppert, hep-ph/0605130

21. J. RuppertHot Quarks 2006, May 2006 Comparison III: p t >1 GeV van Hees, Rapp Renk, Ruppert, hep-ph/0605130

22. J. RuppertHot Quarks 2006, May 2006 Conclusions