1. Gojko Vujanovic Thermal Radiation Workshop Brookhaven National Laboratory December 7 th 2012 1

2. Outline Overview of Dilepton sources Low Mass Dileptons Thermal Sources of Dileptons 1) QGP Rate (w/ viscous corrections) 2) In-medium vector meson’s Rate (w/ viscous corrections) 3+1D Viscous Hydrodynamics Thermal Dilepton Yields & v 2 Intermediate Mass Dileptons Charmed Hadrons: Yield & v 2 Conclusion and outlook 2

3. Evolution of a nuclear collision Thermal dilepton sources: HG+QGP a)QGP: q+q-bar->  * -> e + e - b)HG: In-medium vector mesons V=(   ) V->  * -> e + e - Kinetic freeze-out: c) Cocktail Dalitz Decays (    ’, etc.) 3 Space-time diagram Other dilepton sources: Formation phase d) Charmed hadrons: e.g. D +/- -> K 0 + e +/- e e) Beauty hadrons: e.g. B +/- ->D 0 + e + /- e f) Other vector mesons: Charmonium, Bottomonium g) Drell-Yan Processes Sub-dominant the intermediate mass region

4. Dilepton rates from the QGP An important source of dileptons in the QGP The rate in kinetic theory (Born Approx) More complete approaches: HTL, Lattice QCD. 4

5. Thermal Dilepton Rates from HG The dilepton production rate is : Where, Model based on forward scattering amplitude [Eletsky, et al., Phys. Rev. C, 64, 035202 (2001)] 5 ;

6. Vacuum part is described by the following Lagrangians For  6 Vector meson self-energies (1)

7. Vacuum part is described by the following Lagrangians For  Since  has a small width and 3 body state in the self-energy, we model it as 7 Vector meson self-energies (2)

8. Vacuum part is described by the following Lagrangians For  Since  has a small width and 3 body state in the self-energy, we model it as 8 Vector meson self-energies (3)

9. Vector meson self-energies The Forward Scattering Amplitude Low energies: High energies: Effective Lagrangian method by R. Rapp [Phys. Rev. C 63, 054907 (2001)] 9 Resonances [R] contributing to  ’s scatt. amp. & similarly for , 

10. 10 Imaginary part of the retarded propagator T=150MeV n 0 =0.17/fm 3 Vujanovic et al., PRC 80 044907 Martell et al., PRC 69 065206 Eletsky et al., PRC 64 035202   

11. 3+1D Hydrodynamics Viscous hydrodynamics equations for heavy ions: Initial conditions are set by the Glauber model. Solving the hydro equations numerically done via the Kurganov- Tadmor method using a Lattice QCD EoS [P. Huovinen and P. Petreczky, Nucl. Phys. A 837, 26 (2010).] (s95p-v1) The hydro evolution is run until the kinetic freeze-out. [For details: B. Schenke, et al., Phys. Rev. C 85, 024901 (2012)] (T f =136 MeV) 11 Energy-momentum conservation  /s=1/4 

12. Viscous Corrections: QGP rates Viscous correction to the rate in kinetic theory rate Using the quadratic ansatz to modify F.-D. distribution Dusling & Lin, Nucl. Phys. A 809, 246 (2008). 12 ;

13. Viscous corrections to HG rates? Two modifications are plausible: Self-Energy Performing the calculation => these corrections had no effect on the final yield result! 13 ; ; 1 2

14. For low M: ideal and viscous yields are almost identical and dominated by HG. These hadronic rates are consistent with NA60 data [Ruppert et al., Phys. Rev. Lett. 100, 162301 (2008)]. Low Mass Dilepton Yields: HG+QGP 14

15. Fluid rest frame, viscous corrections to HG rates: HG gas exists from  ~4 fm/c => is small, so very small viscous corrections to the yields are expected. Direct computation shows this! 15 Rest frame of the fluid cell at x=y=2.66 fm, z=0 fm 0-10% How important are viscous corrections to HG rate?

16. Since viscous corrections to HG rates don’t matter, only viscous flow is responsible for the modification of the p T distribution. Also observed viscous photons HG [M. Dion et al., Phys. Rev. C 84, 064901 (2011)] Dilepton yields Ideal vs Viscous Hydro 16 M=m  The presence of  f in the rates is not important per centrality class! This is not a Min Bias effect. 0-10%

17. Dilepton yields Ideal vs Viscous Hydro 17 M=m  For QGP yields, both corrections matter since the shear-stress tensor is larger. Integrating over p T, notice that most of the yield comes from the low p T region. Hence, at low M there isn’t a significant difference between ideal and viscous yields. One must go to high invariant masses.

18. Dilepton yields Ideal vs Viscous Hydro 18 M=m  Notice: y-axis scale! For QGP yields, both corrections matter since the shear-stress tensor is large. Integrating over p T, notice that most of the yield comes from the low p T region. Hence, at low M there isn’t a significant difference between ideal and viscous yields. One must go to high invariant masses.

19. A measure of elliptic flow (v 2 ) Elliptic Flow To describe the evolution of the shape use a Fourier decomposition, i.e. flow coefficients v n Important note: when computing v n ’s from several sources, one must perform a yield weighted average. 19 - A nucleus-nucleus collision is typically not head on; an almond-shape region of matter is created. - This shape and its pressure profile gives rise to elliptic flow. x z

20. v 2 from ideal and viscous HG+QGP (1) Similar elliptic flow when comparing w/ R. Rapp’s rates. 20

21. v 2 from ideal and viscous HG+QGP (1) Similar elliptic flow when comparing w/ R. Rapp’s rates. Viscosity lowers elliptic flow. 21

22. v 2 from ideal and viscous HG+QGP (1) Similar elliptic flow when comparing w/ R. Rapp’s rates. Viscosity lowers elliptic flow. Viscosity slightly broadens the v 2 spectrum with M. 22

23. M is extremely useful to isolate HG from QGP. At low M HG dominates and vice-versa for high M. R. Chatterjee et al. Phys. Rev. C 75 054909 (2007). We can clearly see two effects of viscosity in the v 2 (p T ). Viscosity stops the growth of v 2 at large p T for the HG (dot-dashed curves) Viscosity shifts the peak of v 2 from to higher momenta (right, solid curves). Comes from the viscous corrections to the rate:  p 2 (or p T 2 ) 23 M=1.5GeV M=m  v 2 (p T ) from ideal and viscous HG+QGP (2)

24. Charmed Hadron contribution Since M q >>T (or  QCD ), heavy quarks must be produced perturbatively; come from early times after the nucleus-nucleus collision. For heavy quarks, many scatterings are needed for momentum to change appreciably. In this limit, Langevin dynamics applies [Moore & Teaney, Phys. Rev. C 71, 064904 (2005)] Charmed Hadron production: PYTHIA -> Generate a c-cbar event using nuclear parton distribution functions. (EKS98) Embed the PYTHIA c-cbar event in Hydro -> Langevin dynamics to modify its momentum distribution. At the end of hydro-> Hadronize the c-cbar using Peterson fragmentation. PYTHIA decays the charmed hadrons -> Dileptons. 24

25. Charmed Hadrons yield and v 2 Heavy-quark energy loss (via Langevin) affects the invariant mass yield of Charmed Hadrons (vs rescaled p+p), by increasing it in the low M region and decreasing it at high M. Charmed Hadrons develop a v 2 through energy loss (Langevin dynamics) so there is a non-zero v 2 in the intermediate mass region. 25 0-10%

26. Conclusion & Future work 26 Conclusions  First calculation of dilepton yield and v 2 via viscous 3+1D hydrodynamical simulation.  v 2 (p T ) for different invariant masses has good potential of separating QGP and HG contributions.  Modest modification to dilepton yields owing to viscosity.  v 2 (M) is reduced by viscosity and the shape is slightly broadened.  Studying yield and v 2 of leptons coming from charmed hadrons allows to investigate heavy quark energy loss. Future work  Include cocktail’s yield and v 2 with viscous hydro evolution.  Include the contribution from 4  scattering.  Include Fluctuating Initial Conditions (IP-Glasma) and PCE.  Results for LHC are on the way.

27. A specials thanks to: Charles Gale Clint Young Björn Schenke Sangyong Jeon Jean-François Paquet Igor Kozlov Ralf Rapp 27

28. Born, HTL, and Lattice QCD 28 Ding et al., PRD 83 034504

29. 29 Forward scattering amplitude results Vujanovic et al., PRC 80 044907

30. Dispersion relation 30 The  dispersion graphs The dispersion relation Vujanovic et al., PRC 80 044907

31. V 2 including charm at Min Bias 31