Core-Corona Separation in Ultra-Relativistic Heavy Ion Collisions
Core-Corona Separation in Ultra-Relativistic Heavy Ion Collisions
Klaus Werner∗
SUBATECH, University of Nantes – IN2P3/CNRS– EMN, Nantes, France
Abstract: Simple geometrical considerations show that the collision zone in high energy nuclear
collisions may be divided into a central part (“core”), with high energy densities, and a peripheral
part (“corona”), with smaller energy densities, more like in pp or pA collisions. We present calcula-
tions which allow to separate these two contributions, and which show that the corona contribution
is quite small (but not negligible) for central collisions, but gets increasingly important with de-
creasing centrality. We will discuss consequences concerning results obtained in heavy ion collisions
at the Relativistic Heavy Ion Collider (RHIC) and the Super Proton Synchrotron (SPS).
Nuclear collisions at the Relativistic Heavy Ion Col-
lider (RHIC) are believed to provide sufficiently high en-
ergy densities to create a thermalized quark-gluon fireball
which expands by developing a strong collective radial
flow [1, 2, 3, 4]. However, not all produced hadrons par-
ticipate in this collective expansion: the peripheral nu-
cleons of either nucleus essentially perform independent
pp or pA-like interactions, with a very different particle
production compared to the high density central part.
For certain observables, this “background” contribution
spoils the “signal”, and to get a detailed understanding
of RHIC and SPS data, we need to separate low and high
density parts.
In order to get quantitative results, we need a simula-
tion tool, and here we take EPOS [5], which has proven to
work very well for pp and dAu collisions at RHIC. EPOS
is a parton model, so in case of a AuAu collision there
are many binary interactions, each one represented by a
parton ladder. Such a ladder may be considered as a lon-
gitudinal color field, conveniently treated as a relativistic
string. The strings decay via the production of quark-
antiquark pairs, creating in this way string fragments –
which are usually identified with hadrons. Here, we mod-
ify the procedure: we have a look at the situation at an
early proper time τ0, long before the hadrons are formed:
we distinguish between string segments in dense areas
(more than ρ0 segments per unit area in given transverse
slices), from those in low density areas. We refer to high
density areas as core, and to low density areas as corona.
In figure. 1, we show an example (randomly chosen) of
a semi-peripheral (40-50%) AuAu collisions at 200 GeV
(cms), simulated with EPOS.
There is always a contribution from the low density
area, but much more importantly, as discussed later, the
importance of this contribution depends strongly on par-
ticle type and transverse momentum. For central colli-
sions, the low density contribution is obviously less im-
portant, for more peripheral collisions this contribution
will even dominate.
We adopt the following strategy: the low density part
will be treated using the usual EPOS particle production
which has proven to be very successful in pp and dAu
scattering (the peripheral interactions are essentially pp
-6 -4 -2 0 2 4 6
     40-50%
FIG. 1: A Monte Carlo realization of a semi-peripheral (40-
50%) AuAu collision at 200 GeV (cms). We show string seg-
ments in the core (full gray circles) and the corona (open
circles). The big circles are put in just to guide the eye: they
represent the two nuclei in hard sphere approximation.We
consider a projection of segments within z = ±0.4 fm to the
transverse plane (x,y).
or pA scatterings). For the high density part, we sim-
ply try to parameterize particle production, in the most
simple way possible (it is not at all our aim to provide a
microscopic description of this part).
In practice, we consider transverse slices characterized
by some range in η = 0.5 ln(t+z)/(t−z). String segments
in such a slice move with rapidities very close to η. We
subdivide a given slice into elementary cells, count the
number of string segments per cell, and determine such
for each cell whether it belongs to the core or the corona
(bigger or smaller than the critical density ρ0). Con-
nected cells (closest neighbors) in a given slice are con-
sidered to be clusters, whose energy and flavor content
are completely determined by the corresponding string
segments. Clusters are then considered to be collectively
expanding: Bjorken-like in longitudinal direction with
in addition some transverse expansion. We assume par-
ticles to freeze out at some given energy density εFO,
having acquired at that moment a collective radial flow.
The latter one is characterized by a linear radial rapidity
profile from inside to outside with maximal radial rapid-
ity yrad. In addition, we impose an azimuthal asymme-
try, being proportional to the initial spatial eccentricity
y2 − x2
y2 + x2
, with a proportionality factor
fecc. By imposing radial flow, we have to rescale the
http://arxiv.org/abs/0704.1270v1
cluster mass M as
M → M × 0.5 y2rad/(yrad sinh yrad − cosh yrad + 1),
in order to conserve energy. Hadronization then occurs
according to covariant phase space, which means that the
probability dP of a given final state of n hadrons is given
speciesα
d3pi gi si
(2πh̄)32Ei
δ(M − ΣEi) δ(Σ~pi) δf,Σfi ,
with pi = (Ei, ~pi) being the four-momentum of the i-th
hadron, gi its degeneracy, and fi its quark flavor con-
tent (u− ū,d− d̄...). The number nα counts the number
of hadrons of species α. The term M/εFO is the clus-
ter proper volume. We use a factor si = γs
±1 for each
strange particle (sign plus for a baryon, sign minus for a
meson), with γs being a parameter. We believe that si
mimics final state rescattering, but for the moment we
can only say that this factor being different from unity
improves the fit of the data considerably. The whole
procedure perfectly conserves energy, momentum, and
flavors (microcanonical procedure).
So the core definition and its hadronization are param-
eterized in terms of few global parameters (in brackets
the values): the core formation time τ0 (1 fm), the core
formation density ρ0 (2/fm
2), the freeze out energy den-
sity εFO(0.22GeV/fm
3), the maximum radial flow yrad
(0.75+0.20log(
s/200GeV)), the eccentricity coefficient
fecc (0.45), and the factor γs (1.3). At RHIC energies,
the final results are insensitive to variations of τ0: even
changes as big as a factor of 2 do not affect the results.
This is a nice feature, indicating that the very details of
the initial state do not matter so much. We call these pa-
rameters “global”, since they account for all observables
at all possible different centralities and all energies. In
the following, we are going to discuss results, all obtained
with the above set of parameters.
Our hadronization of the core part is certainly moti-
vated by the remarkable success of statistical hadroniza-
tion models [6] and blast-wave fits [7, 8]. We use co-
variant statistical hadronization, whereas usual the non-
covariant procedure is employed, but the difference is
minor. We also impose a collective flow, with an as-
sumed flow profile, as in the blast wave fit. So the gen-
eral ideas are the same. However, a really new aspect
is the possibility of making a “global fit”, considering
all energies, centralities, and colliding systems with one
set of parameters. In the above-mentioned models one
has a set of fit parameters for each of these possibili-
ties. An important new aspect is also the separation of
a (collectively behaving) core and a corona contribution,
which seems to be very important for understanding the
centrality dependence of hadron yields. Finally, our sta-
tistical hadronization is based on initial energy densities
provided by a parton model (EPOS), which works well
0 0.5 1 1.5 2 2.5 3
 mt-m
EPOS 1.30
 ____ core 0-5% AuAu 200GeV
 _ _ _ pp 200GeV
FIG. 2: Invariant yields 1/2πmt dn/dydmt of pions and lamb-
das, for the core contribution corresponding to a central (0-
5%) AuAu collision (full lines) and proton-proton scattering
(dashed lines). The core spectra are divided by the number
of binary collisions.
EPOS 1.30
..... 0-5%  _ _ _ 40-50%  ____ 70-80%
0 1 2
 mt-m (GeV)
0 1 2 3
 mt-m (GeV)
FIG. 3: The relative contribution of the core
(core/(core+corona)) as a function of the transverse mass for
different hadrons (π, K, p, Λ) at different centralities.
for pp and dAu scattering. This fixes the overall multi-
plicity already within 10%, flow and freeze out condition
have only a minor effect on this quantity.
All the discussion of heavy ion data will be based on
the interplay between core and corona contributions. To
get some feeling, we first compare in fig. 2 the mt spec-
tra of pions and lambdas from the core in central (0-
5%) AuAu collisions with the corresponding spectra in
pp scattering (which is qualitatively very similar to the
corona contribution). The core spectra are divided by
the number of binary collisions. We observe several re-
markable features: the shapes of the pion and lambda
curves in pp are not so different, whereas there is much
more species dependence in the core spectra, since the
heavier particles acquire large transverse momenta due
to the flow effect. One observes furthermore that the
0 50 100 150 200 250 300 350 400
 participant number Np
EPOS 1.30
FIG. 4: Rapidity density dn/dy per participant as a function
of the number of participants (Np) in Au+Au collisions at 200
GeV (RHIC) for π−, K−, p̄, Λ̄, Ξ̄+. We show data (points)
[9, 10] together with the full calculation (full lines) and just
the core part (dotted lines).
yields for the two spectra in pp are much wider spread
than the ones from the core; in particular, pion produc-
tion is suppressed in the core hadronization compared to
pp, whereas lambda production is favored. All this is
quite trivial, but several “mysteries” discussed in the lit-
erature (and to be discussed later in this paper) are just
due to this.
In fig. 3, we plot the relative contribution of the core
(relative to the complete spectrum, core + corona) as a
function of mt−m, for different particle species. For cen-
tral collisions, the core contribution dominates largely,
whereas for semi-central collisions (40-50%) and even
more for peripheral collisions the core contribution de-
creases, giving more and more space for the corona part.
Apart of these general statements, the precise mt depen-
dence of the relative weight of core versus corona depends
on the particle type.
We are now ready to investigate data. In fig. 4, we
plot the centrality dependence of the particle yield per
participant (per unit of rapidity) in Au+Au collisions at
200 GeV (RHIC), for π+, K+, p, Λ̄, Ξ̄+: we show data
[9, 10] together with the full calculation (quite close to
the data), but also indicating the core contribution. In
fig. 5, we show the corresponding results for Pb+Pb colli-
sions at 17.3 GeV (SPS). Concerning the SPS results, we
consider dn/dy/Np in case of Ks, Λ̄, and Ξ̄
+, whereas we
have 4π multiplicities per participant in case of π− and
K−(for simulations and data). Whereas central collisions
are always clearly core dominated, the core contributes
less and less with decreasing centrality. The difference
between solid and dotted curves (in other words: the
importance of the corona contribution) is bigger at the
SPS compared to RHIC, and it is bigger for light parti-
cles compared to heavy ones. For example there is a big
corona contribution for pions and a very small one for Ξ̄
0 50 100 150 200 250 300 350 400
 participant number
EPOS 1.30
FIG. 5: Multiplicity per participant as a function of the num-
ber of participants (Np) in Pb+Pb collisions at 17.3 GeV
(SPS) for π−, K−, Ks, Λ̄, Ξ̄
+. We show data (points)
[11, 12, 13, 14] together with the full calculation (full lines)
and just the core part (dotted lines).
0 50 100 150 200 250 300 350 400
 participant number Np
EPOS 1.30only core
π+  K+  p  Λ
at 200 GeV
π-(4π)  K-(4π)  Ks  Λ
 at 17.3 GeV
FIG. 6: Multiplicity per participant as a function of Np for
only the core part. We show results for π−, K−, p̄, Λ̄, Ξ̄+ in
Au+Au collisions at 200 GeV (dotted lines), and for π−, K−,
Ks, Λ̄, Ξ̄
+ in Pb+Pb collisions at 17.3 GeV (dashed lines).
particles. Also the strength of the centrality dependence
depends on the hadron type: for example Ξ̄+particles
show a stronger centrality dependence than pions. It
seems that the centrality dependence is essentially deter-
mined by relative importance of the corona contribution:
the less the corona contributes, the more the yield varies
with centrality.
To further investigate the connection between relative
corona weight and centrality dependence, we plot in fig.
6 the centrality dependence of multiplicities per partici-
pant for different hadrons, at 200 GeV (RHIC) and 17.3
GeV (SPS), for the core contribution. We observe two
universal curves, one per energy. So for a given energy,
the core contributions for all the different hadrons show
the same centrality dependence. This proves that the
different centrality dependencies for the different hadron
0 0.5 1 1.5 2 2.5 3
EPOS 1.30
  0-5%  AuAu 200GeV
FIG. 7: Nuclear modification factors in central AuAu colli-
sions at 200 GeV. Lines are full calculations, symbols rep-
resent data [9, 10]. We show results for pions (dashed line;
triangles), protons (full line; circles), and lambdas (dashed-
dotted line; squares).
species are simply due to different core-corona weights.
For example the fact that Ξ̄ particles show a stronger cen-
trality dependence than pions is simply due to the fact
that the former ones have less corona admixture than the
latter ones.
Lets us come to pt spectra. We checked all available
pt data (π
+, K+, p, Λ̄, Ξ̄+, for pt ≤ 5GeV), and our
combined approach (core + corona) describes all the data
within 20%. Lacking space, we just discuss a (typical) ex-
ample: the nuclear modification factor (AA/pp/number
of collisions), for π+, p, Λ̄ in central AuAu collisions at
200 GeV, see fig. 7. For understanding these curves, we
simply have a look at fig. 2, where we compare the core
contributions from AuAu (divided by the number of bi-
nary collisions) with pp. Since for very central collisions
the core dominates largely, the ratio of core to pp (the
solid lines divided by the dotted ones in fig. 2) corre-
sponds to the nuclear modification factor. We discussed
already earlier the very different behavior of the core
spectra (flow plus phase space decay) compared to the
pp spectra (string decay): pions are suppressed, whereas
heavier particles like lambdas are favored. Or better to
say it the other way round: the production of baryons
compared to mesons is much more suppressed in string
decays than in statistical hadronization. This is why the
nuclear modification factor for lambdas is different from
the one for pions. So what we observe here is nothing
but the very different behavior of statistical hadroniza-
tion (plus flow) on one hand, and string fragmentation
on the other hand. This completely statistical behavior
indicates that the low pt partons get completely absorbed
in the core matter.
The Rcp modification factors (central over peripheral)
are much less extreme than RAA, since peripheral AuAu
collisions are a mixture of core and corona (the latter one
being pp-like), so a big part of the effect seen in RAA is
simply washed out.
To summarize: we have discussed the importance
of separating core and corona contributions in ultra-
relativistic heavy ion collisions. The core-corona sepa-
ration is realized based on the determination of string
densities at an early time. Particle production from the
corona is done as in proton-proton scattering, whereas
the core hadronization is parameterized in a very sim-
ple way, imposing radial flow. The corona contribution
is quite small (but not negligible) for central collisions,
but gets increasingly important with decreasing central-
ity. The core shows a very simple centrality dependence:
it is the same for all hadron species, at a given bombard-
ing energy. The fact that the centrality dependence of
the total hadron yield is strongly species dependent, is
simply due to the fact that the relative corona contribu-
tion depends on the hadron type.
∗ Electronic address: werner@subatech.in2p3.fr
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