Transcript Document

Gojko Vujanovic
Electromagnetic Probes of Strongly
Interacting Matter: Status and Future of LowMass Lepton-Pair Spectroscopy
ECT*: Trento, Italy
May 22nd 2013
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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 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
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Evolution of a nuclear collision
Space-time diagram
Thermal dilepton sources: HG+QGP
a) QGP: q+q-bar-> g* -> e+eb) HG: In-medium vector mesons V=(r,
w, f)
V-> g* -> e+eKinetic 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
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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.
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Thermal Dilepton Rates from HG
 Model based on forward scattering amplitude [Eletsky, et. al., Phys.
Rev. C, 64, 035202 (2001)]
Resonances
contributing
to r’s
scatt. amp.
& similarly
for w, f
 Effective Lagrangian method by R. Rapp [Phys. Rev. C 63, 054907
(2001)]
 The dilepton production rate is :
;
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3+1D Hydrodynamics
 Viscous hydrodynamics equations for heavy ions:
Energy-momentum conservation
h/s=1/4p
 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)
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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).
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Viscous corrections to HG rates?
 Two modifications are plausible:
 Self-Energy
1
2
;
;
 Performing the calculation => these corrections had no effect on
the final yield result!
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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)].
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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 =>
to the yields are expected.
is small, so very small viscous corrections
 Direct computation shows this!
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Dilepton yields Ideal vs Viscous Hydro
0-10%
The presence of df in the rates
doesn’t affect the yield!
M=mr
 Since viscous corrections to HG rates don’t matter, only viscous flow is
responsible for the modification of the pT distribution.
 Also observed viscous photons HG [M. Dion et al., Phys. Rev. C 84, 064901
(2011)]
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Dilepton yields Ideal vs Viscous Hydro
M=mr
 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 pT region.
 Hence, at low M there isn’t 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
M=mr
Notice: y-axis scale!
 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 pT region.
 Hence, at low M there isn’t a significant difference between ideal and viscous
yields. One must go to high invariant masses.
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A measure of elliptic flow (v2)
 Elliptic Flow
- 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
x
 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 yield weighted average.
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v2 from ideal and viscous HG+QGP (1)
 Viscosity lowers elliptic flow.
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v2 from ideal and viscous HG+QGP (1)
 Viscosity lowers elliptic flow.
 Viscosity slightly broadens the v2 spectrum with M.
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v2(pT) from ideal and viscous HG+QGP (2)
M=1.5GeV
M=mr
 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)
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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.
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Charmed Hadrons yield and v2
0-10%
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.
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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.
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Reassessing effects of viscosity on QGP v2 (2)
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.
 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)].
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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.
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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.
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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.
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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.
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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
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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%).
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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).
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Effect of new dR on v2(pT)
M=1.5 GeV
h/s=1/4p
h/s=1/4p
 New dR introduces additional terms E and 1/E terms which helps v2(pT) to peak at
lower pT relative 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.
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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.
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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.
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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
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Hadron Spectra from MUSIC
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Born, HTL, and Lattice QCD
Ding et al., PRD 83 034504
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V2 including charm at Min Bias
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Reassessing effects of viscosity on QGP v2 (2)
h/s=1/4p
h/s=1/4p
M=mrr
M=m
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