Viscosity & Dilepton Production

Viscosity & Dilepton Production GojkoVujanovic Electromagnetic Probes of Strongly Interacting Matter: Status and Future of Low-Mass Lepton-Pair Spectroscopy ECT*: Trento, Italy May 22nd 2013

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 • Importance of viscous corrections to the QGP v2 • Conclusion and outlook

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

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.

Thermal Dilepton Rates from HG • Model based on forward scattering amplitude [Eletsky, et. al., Phys. Rev. C, 64, 035202 (2001)] • Effective Lagrangian method by R. Rapp [Phys. Rev. C 63, 054907 (2001)] • The dilepton production rate is : Resonances contributing to r’s scatt. amp. & similarly for w, f ;

3+1D Hydrodynamics Energy-momentum conservation • 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, 024901 (2012)] (Tf=136 MeV) h/s=1/4p

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). ;

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! ; ;

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)].

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%; h/s=1/4p • 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!

Dilepton yields Ideal vs Viscous Hydro The presence of df in the rates doesn’t affect the yield! 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

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

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!

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

v2 from ideal and viscous HG+QGP (1) • Viscosity lowers elliptic flow.

v2 from ideal and viscous HG+QGP (1) • Viscosity lowers elliptic flow. • Viscosity slightly broadens the v2 spectrum with M.

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

Open Charm contribution • Since Mq>>T, heavy quarks come from early times after the collision; Mq>> LQCD 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, 064904 (2005)] • Charmed Hadron production [C. Young et al. , PRC 86, 034905, 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.

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%

Reassessing effects of viscosity on QGP v2 (1) M=1.5 GeV h/s=1/4p • When we previously compared the differential v2(pT) going from ideal to viscous hydrodynamics (with viscous dR corrections), it seemed as though it behaved similarly to hadrons.

Reassessing effects of viscosity on QGP v2 (2) M=1.5 GeV • When we previously compared the differential v2(pT) going from ideal to viscous hydrodynamics (with viscous dR corrections), it seemed as though it behaved similarly to hadrons. h/s=1/4p • However, looking at v2(pT) with viscous hydro evolution alone, v2(pT) rises owing to the growth of the anisotropy (pmn) at early times; unlike hadrons! • Also observed in viscous photons [M. Dion et al., Phys. Rev. C 84, 064901 (2011)].

Reassessing effects of viscosity on QGP v2 (3) M=1.5 GeV h/s=1/4p h/s=1/4p • v2(M) exhibits an even more pronounced effect coming from dR. • Hence, the magnitude of the viscous correction must be further studied by improving dR, beyond its Israel-Stewart from. • Note that v2(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.

How important are viscous corrections to QGP v2? • Reminder of viscous QGP rate: • We will define viscous corrections to be large when |dR/Ro|>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 tDtDxDyDh) having |dR/Ro|>1 for a particular qm , are not considerer in the calculation.

Removing cells with |dR/Ro|>1 • v2(M) is not particularly sensitive to the cut in dR at low M region, however the situation worsens at higher M where large dRs increase v2(M) by as much as a factor of ~3 at M=2.5GeV.

Removing cells with |dR/Ro|>1 M=1.5 GeV h/s=1/4p • Our v2(pT) results are robust at pT<1.5GeV: most of the fluid elements have |dR/Ro|<1. • v2(pT) for pT above ~1.5GeV, is strongly dependent on the dR (or rather dn of the quarks) being used. • Hence, it is instructive to go beyond I-S form of dn, by revisiting the fundamental physics it contains, and derive a new dn.

Viscous correction QGP rate: revisited • To improve dR, 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. • The new from of dn includes higher order corrections in k0/T, and we made sure that the series converges before truncating it. Let x=k0/T: • The low and the high energy G(x) were matched via a tanh function at x=11.2

Beyond Israel-Stewart: removing cells with |dR/Ro|>1 • v2(M) w/ and w/o the cut in |dR/Ro|>1, is not significantly different at all M (at most ~20%).

Beyond Israel-Stewart: removing cells with |dR/Ro|>1 M=1.5 GeV h/s=1/4p • v2(M) w/ and w/o the cut in |dR/Ro|>1, is not significantly different at all M (at most ~20%). • v2(pT) is also better described and starts to breaking down for pT above ~2GeV. • Key message: v2(M) is a better quantity to measure as it is less sensitive to the form of dR (or dn).

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

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. • In the HG phase, v2(M) is reduced ~20%, (h/s=1/4p) by viscosity and the shape is slightly broadened. • In the QGP phase, v2(M) is greatly affected by viscosity, more studies are on the way. • Studying yield and v2 of leptons coming from charmed hadrons allows to investigate heavy quark energy loss.

Future work • Further investigate the effects of viscous corrections and temperature dependent h/s on elliptic flow of the QGP. • Include cocktail’s yield and v2 with viscous hydro evolution. • Include the contribution from 4p scattering. • Include Fluctuating Initial Conditions (IP-Glasma). • Results for LHC are on the way.

A specials thanks to:Charles GaleClint YoungGabriel S. DenicolBjörnSchenkeSangyongJeon Jean-François PaquetIgor Kozlov Ralf Rapp

Hadron Spectra from MUSIC

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

V2 including charm at Min Bias

Reassessing effects of viscosity on QGP v2 (2) h/s=1/4p h/s=1/4p M=mr M=mr

Viscosity & Dilepton Production