Gojko Vujanovic Thermal Radiation Workshop Brookhaven National Laboratory December 7 th

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

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

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

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

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

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)

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)

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

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

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, (2012)] (T f =136 MeV) 11 Energy-momentum conservation  /s=1/4 

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 ;

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

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, (2008)]. Low Mass Dilepton Yields: HG+QGP 14

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?

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, (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%

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.

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.

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 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

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

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

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

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 (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)

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, (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

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 %

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.

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

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

29 Forward scattering amplitude results Vujanovic et al., PRC

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

V 2 including charm at Min Bias 31