A Promising Solution to the Elliptic
Quench Puzzle at RHIC
William A. Horowitz
Columbia University
August 4-5, 2005
Quark Matter 2005
W. A. Horowitz
What is the Puzzle?–Data
• Naïvely combine published
RAA(pT) and v2(pT) data
• Preliminary PHENIX p0 data
• Data centrality classes:
– STAR1,2 charged hadron
• 0-5%, 10-20%, 20-30%, 30-40%,
40-60%
– PHENIX3,4 charged hadron
• 0-20%, 20-40%, 40-60%
– PHENIX5 p0
• 10-20%, 20-30%, …, 50-60%
• Note: error regions are only a rough estimate
Quark Matter 2005
W. A. Horowitz
What is the Puzzle?–Theory
• Can’t fit the RHIC phenomena
• Hydrodynamics
– Not applicable at intermediate and higher pT
• Parton Cascade and Energy Loss
– Don’t work: jet quenching and anisotropy anticorrelated
– Models over-suppress RAA in order to reproduce large
observed v2
Quark Matter 2005
W. A. Horowitz
GLV Energy Loss
• A geometric approximation: the gGLV
• Fractional energy loss:
• Integral through the 1D expanding medium that
captures the L2 dependence of energy loss in a
static medium:
Quark Matter 2005
W. A. Horowitz
The gGLV
• Use Glauber, factorization, and power law
spectrum to yield:
– 10% difference between n=4 and n=5, use n=4
• To calculate RAA and v2, generate this at multiple
values of f and find the Fourier modes
• Use hard sphere nuclear geometry
– Systematically enhances v26
Quark Matter 2005
W. A. Horowitz
Model Failures
• Models can’t match
intended data point for
any value of their free
parameter (opacity of the
medium)
– MPC7: calculated for 2535% centrality
– gGLV: 40-50% centrality
Quark Matter 2005
W. A. Horowitz
Modify gGLV
• Absorption model: add thermal absorption and
stimulated emission8,
– Integral through 1D expanding medium that captures
linear in L dependence of energy gain in static media:
• Punch model: add a momentum boost (DpT) to the
parton in the direction normal to the edge of
emission
Quark Matter 2005
W. A. Horowitz
Fixing the Parameters
• As in Drees, et al.6, gGLV
(k) model fit to PHENIX
most central RAA
• gGLV+abs (k, k) and
gGLV+punch (k, DpT)
parameters uniquely
determined by a single
(RAA,v2) point:
– 20-30% centrality p0
Quark Matter 2005
W. A. Horowitz
Success!
• Having fixed the
parameters for a single
centrality, allow the
impact parameter to
vary
Quark Matter 2005
W. A. Horowitz
But!
• For radiative energy loss and thermal absorption,
asymptotic expansions7 give:
where
Quark Matter 2005
W. A. Horowitz
Failure of Absorption
• Too high a multiplicity required for absorption
part of gGLV+absorption (k = .5 and k = .25):
– For E = 6 GeV, L = 5 fm, l0 = .2 fm, and as = .4:
– For E = 10 GeV, L = 5 fm , l0 = .2 fm, and as = .4:
Quark Matter 2005
W. A. Horowitz
Success of the Punch
• Reasonable multiplicity required for energy loss
part of gGLV+punch (k = .18)
– For E = 10 GeV, L = 5 fm, and as = .3:
• Punch needed (DpT = .5 GeV) is on the order of
the energy boost (~1 GeV) expected from
deflagration, latent heat, or the effect of the bag
constant
Quark Matter 2005
W. A. Horowitz
Cu+Cu Predictions
Use parameters for Au+Au, apply models to Cu+Cu
– Cu+Cu v2 vs. RAA:
– Centrality-binned Results:
Quark Matter 2005
W. A. Horowitz
Conclusions
• Previous theories don’t follow the elliptic quench
pattern at RHIC
• Energy loss modified with either absorption or a
punch agrees with the RAA and v2 data
• Absorption ruled out by the multiplicity results
• Possible punch sources exist, with effects on the
same order of magnitude
– Smallness of punch (.5 GeV) should allow for
necessary scaling when a more realistic nuclear density
geometry is used and v2 enhancement is lost
Quark Matter 2005
W. A. Horowitz
References
Quark Matter 2005
W. A. Horowitz