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Gojko Vujanovic Electromagnetic Probes of Strongly Interacting Matter: Status and Future of Low- Mass Lepton-Pair Spectroscopy ECT*: Trento, Italy May 22 nd

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

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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

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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

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Thermal Dilepton Rates from HG Model based on forward scattering amplitude [Eletsky, et. al., Phys. Rev. C, 64, (2001)] Effective Lagrangian method by R. Rapp [Phys. Rev. C 63, (2001)] The dilepton production rate is : 5 Resonances contributing to s scatt. amp. & similarly for, ;

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3+1D Hydrodynamics Viscous hydrodynamics equations for heavy ions: Initial conditions are set by an optical 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) 6 Energy-momentum conservation /s=1/4

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Viscous Corrections: QGP rates Viscous correction to the rate in kinetic theory rate Using the quadratic Israel-Stewart ansatz to modify F.-D. distribution Dusling & Lin, Nucl. Phys. A 809, 246 (2008). 7 ;

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Viscous corrections to HG rates? Two modifications are plausible: Self-Energy Performing the calculation => these corrections had no effect on the final yield result! 8 ; ; 1 2

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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 9

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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! 10 Rest frame of the fluid cell at x=y=2.66 fm, z=0 fm 0-10%; /s=1/4 How important are viscous corrections to HG rate?

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Since viscous corrections to HG rates dont 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 11 M=m The presence of f in the rates doesnt affect the yield! 0-10%

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Dilepton yields Ideal vs Viscous Hydro 12 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 isnt a significant difference between ideal and viscous yields. One must go to high invariant masses.

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Dilepton yields Ideal vs Viscous Hydro 13 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 isnt a significant difference between ideal and viscous yields. One must go to high invariant masses.

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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

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v 2 from ideal and viscous HG+QGP (1) Viscosity lowers elliptic flow. 15

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v 2 from ideal and viscous HG+QGP (1) Viscosity lowers elliptic flow. Viscosity slightly broadens the v 2 spectrum with M. 16

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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 ) 17 M=1.5GeV M=m v 2 (p T ) from ideal and viscous HG+QGP (2)

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Open Charm contribution Since M q >>T, heavy quarks come from early times after the collision; M q >> QCD heavy quarks must be produced perturbatively. 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 [C. Young et al., PRC 86, , 2012]: 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. 18

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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 %

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20 Reassessing effects of viscosity on QGP v 2 (1) When we previously compared the differential v 2 (p T ) going from ideal to viscous hydrodynamics (with viscous R corrections), it seemed as though it behaved similarly to hadrons. M=1.5 GeV /s=1/4

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21 Reassessing effects of viscosity on QGP v 2 (2) However, looking at v 2 (p T ) with viscous hydro evolution alone, v 2 (p T ) rises owing to the growth of the anisotropy ( ) at early times; unlike hadrons! Also observed in viscous photons [M. Dion et al., Phys. Rev. C 84, (2011)]. M=1.5 GeV /s=1/4 When we previously compared the differential v 2 (p T ) going from ideal to viscous hydrodynamics (with viscous R corrections), it seemed as though it behaved similarly to hadrons.

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22 v 2 (M) exhibits an even more pronounced effect coming from R. Hence, the magnitude of the viscous correction must be further studied by improving R, beyond its Israel-Stewart from. Note that v 2 (M) is very small (<1% for all centralities computed) : We start our hydro simulation by initializing our shear-stress tensor to zero In the QGP phase not enough time has passed for flow to build up Neglecting the effects of fluctuations in the initial conditions. /s=1/4 Reassessing effects of viscosity on QGP v 2 (3) M=1.5 GeV /s=1/4

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How important are viscous corrections to QGP v 2 ? Reminder of viscous QGP rate: We will define viscous corrections to be large when | R/R o |>1. Frequent large corrections will yield unphysical results: calculations should not be trusted in the region of phase space where that occurs. So to assess the validity of our calculation, we will perform a test: All fluid elements (an element is 4-volume of size x y having | R/R o |>1 for a particular q, are not considerer in the calculation. 23

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24 Removing cells with | R/R o |>1 v 2 (M) is not particularly sensitive to the cut in R at low M region, however the situation worsens at higher M where large Rs increase v 2 (M) by as much as a factor of ~3 at M=2.5GeV.

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25 Removing cells with | R/R o |>1 Our v 2 (p T ) results are robust at p T <1.5GeV: most of the fluid elements have | R/R o |<1. v 2 (p T ) for p T above ~1.5GeV, is strongly dependent on the R (or rather n of the quarks) being used. Hence, it is instructive to go beyond I-S form of n, by revisiting the fundamental physics it contains, and derive a new n. M=1.5 GeV /s=1/4

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To improve R, a generalized distribution function is used: G is computed using Boltzmann equation for a gas of massless particles with constant cross-section. The viscous correction in I-S form is recovered when G=1. 26 Viscous correction QGP rate: revisited The low and the high energy G(x) were matched via a tanh function at x=11.2 The new from of n includes higher order corrections in k 0 /T, and we made sure that the series converges before truncating it. Let x=k 0 /T:

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27 Beyond Israel-Stewart: removing cells with | R/R o |>1 v 2 (M) w/ and w/o the cut in | R/R o |>1, is not significantly different at all M (at most ~20%).

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28 Beyond Israel-Stewart: removing cells with | R/R o |>1 v 2 (M) w/ and w/o the cut in | R/R o |>1, is not significantly different at all M (at most ~20%). v 2 (p T ) is also better described and starts to breaking down for p T above ~2GeV. Key message: v 2 (M) is a better quantity to measure as it is less sensitive to the form of R (or n). M=1.5 GeV /s=1/4

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29 Effect of new R on v 2 (p T ) New R introduces additional terms E and 1/E terms which helps v 2 (p T ) to peak at lower p T relative to the Israel-Stewart R, thus increasing v2(p T ) for most M. Bottom line: dileptons, unlike hadron, are significantly more sensitive to the form of R (viscous v 2 (M) decreases by ~2 compared to ideal case), so including the most accurate physics possible in R is crucial. /s=1/4 M=1.5 GeV /s=1/4

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Conclusions 30 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. In the HG phase, v 2 (M) is reduced ~20%, ( /s=1/4 ) by viscosity and the shape is slightly broadened. In the QGP phase, v 2 (M) is greatly affected by viscosity, more studies are on the way. Studying yield and v 2 of leptons coming from charmed hadrons allows to investigate heavy quark energy loss.

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Further investigate the effects of viscous corrections and temperature dependent /s on elliptic flow of the QGP. Include cocktails yield and v 2 with viscous hydro evolution. Include the contribution from 4 scattering. Include Fluctuating Initial Conditions (IP-Glasma). Results for LHC are on the way. 31 Future work

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A specials thanks to: Charles Gale Clint Young Gabriel S. Denicol Björn Schenke Sangyong Jeon Jean-François Paquet Igor Kozlov Ralf Rapp 32

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33 Hadron Spectra from MUSIC

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Born, HTL, and Lattice QCD 34 Ding et al., PRD

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V 2 including charm at Min Bias 35

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37 Reassessing effects of viscosity on QGP v 2 (2) M=m /s=1/4

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