Thermal dileptons at RHIC

1. Thermal dileptons at RHIC GojkoVujanovic Thermal Radiation Workshop Brookhaven National Laboratory December 7th 2012

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 & v2 Intermediate Mass Dileptons • Charmed Hadrons: Yield & v2 • Conclusion and outlook

3. Evolution of a nuclear collision Space-time diagram Thermal dilepton sources: HG+QGP • QGP: q+q-bar-> g* -> e+e- • HG: In-medium vector mesons V=(r, w, f) V-> g* -> e+e- Kinetic freeze-out: c) Cocktail Dalitz Decays (p0, h, h’, etc.) Other dilepton sources: Formation phase d) Charmed hadrons: e.g. D+/--> K0 + e+/- ne e) Beauty hadrons: e.g. B+/-->D0 + e+ /-ne 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.

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)]

6. Vector meson self-energies (1) • Vacuum part is described by the following Lagrangians • For r:

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

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

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)] Resonances [R] contributing to r’s scatt. amp. & similarly for w, f

10. Imaginary part of the retarded propagator r w Eletsky et al., PRC 64 035202 Martell et al., PRC 69 065206 T=150MeV n0=0.17/fm3 f Vujanovic et al., PRC 80 044907

11. 3+1D Hydrodynamics Energy-momentum conservation • 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)] (Tf=136 MeV) h/s=1/4p

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). ;

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

14. Low Mass Dilepton Yields: HG+QGP • 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)].

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

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

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

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

19. A measure of elliptic flow (v2) • 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. z • Elliptic Flow • To describe the evolution of the shape use a Fourier decomposition, i.e. flow coefficients vn • Important note: when computing vn’s from several sources, one must perform a yieldweighted average. x

20. v2 from ideal and viscous HG+QGP (1) • Similar elliptic flow when comparing w/ R. Rapp’s rates.

21. v2 from ideal and viscous HG+QGP (1) • Similar elliptic flow when comparing w/ R. Rapp’s rates. • Viscosity lowers elliptic flow.

22. v2 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 v2 spectrum with M.

23. v2(pT) from ideal and viscous HG+QGP (2) • 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 v2(pT). • Viscosity stops the growth of v2 at large pT for the HG (dot-dashed curves) • Viscosity shifts the peak of v2 from to higher momenta (right, solid curves). Comes from the viscous corrections to the rate: ~ p2 (or pT2) M=1.5GeV M=mr

24. Charmed Hadron contribution • Since Mq>>T (or LQCD), 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.

25. Charmed Hadrons yield and v2 0-10% • 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 v2 through energy loss (Langevin dynamics) so there is a non-zero v2 in the intermediate mass region. 0-10%

26. Conclusion & Future work • Conclusions • First calculation of dilepton yield and v2 via viscous 3+1D hydrodynamical simulation. • v2(pT) for different invariant masses has good potential of separating QGP and HG contributions. • Modest modification to dilepton yields owing to viscosity. • v2(M) is reduced by viscosity and the shape is slightly broadened. • Studying yield and v2 of leptons coming from charmed hadrons allows to investigate heavy quark energy loss. • Future work • Include cocktail’s yield and v2 with viscous hydro evolution. • Include the contribution from 4p scattering. • Include Fluctuating Initial Conditions (IP-Glasma) and PCE. • Results for LHC are on the way.

27. A specials thanks to:Charles GaleClint YoungBjörnSchenkeSangyongJeon Jean-François PaquetIgor Kozlov Ralf Rapp

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

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

30. Dispersion relation • The dispersion relation • The f dispersion graphs Vujanovic et al., PRC 80 044907

31. V2 including charm at Min Bias