arXiv:0902.4028v1 [hep-ph] 24 Feb 2009
Soft Open Charm Production in Heavy-Ion Collisions.
V. Topor Pop,1
J. Barrette,1and M. Gyulassy2
1McGill, University, Montreal, Canada, H3A 2T8
2Physics Department, Columbia University, New York, N.Y. 10027
(Dated: February 23, 2009)
Effects of strong longitudinal color electric fields (SCF) on the open charm production in nucleus-
nucleus (A + A) collisions at 200A GeV are investigated within the framework of the HIJING/B¯B
v2.0 model. A three fold increase of the effective string tension due to in medium effects in A + A
collisions, results in a sizeable (≈ 60-70 %) enhancement of the total charm production cross sections
c ¯ c). The nuclear modification factors show a suppression at moderate transverse momentum (pT)
consistent with RHIC data. At Large Hadron Collider energies the model predicts an increase of
c ¯ c by approximately an order of magnitude.
PACS numbers: 25.75.Dw, -25.75.Cj, 25.75.+r, 24.85.+p
The phase transition from hadronic degrees of free-
dom to partonic degrees of freedom in ultra-relativistic
nuclear collisions is a central focus of experiments at the
Relativistic Heavy Ion Collider (RHIC). Heavy-flavor
quarks are an ideal probe to study early dynamics in
these nuclear collisions. Several theoretical studies pre-
dict [1, 2, 3] a substantial enhancement of open charm
production associated to plasma formation of the de-
confined parton matter relative to the case of a purely
hadronic scenario without plasma formation. A recent
analysis shows that the dynamics of heavy-quarks at
RHIC are dominated by partonic or “pre-hadronic” in-
teractions in the strongly coupled plasma (sQGP) stage
and can neither be modeled by “hadronic interactions”
nor described appropriately by color screening alone .
Therefore, these quarks are key observables in the study
of thermalization of the initially created hot nuclear
A review of heavy-flavor production in heavy-ion col-
lisions has been recently published . Direct recon-
structed D0mesons via hadronic channel (D0→ Kπ)
in d + Au , Cu + Cu  and Au + Au  colli-
sions have been measured. Due to the difficulty to re-
construct D-mesons hadronic decay vertex, both STAR
and PHENIX have studied open charm indirectly via
semileptonic decay to non-photonic electrons (NPE) or
muons [7, 9, 10, 11, 12, 13, 14, 15]. Theory predict
that charm quarks are produced by initial gluon fu-
sion  and their production rates are expected to
be well described by perturbative Quantum Cromody-
namics (pQCD) at Fixed Order plus Next to-leading
Logarithms (FONLL) . Total charm cross sections
reported by both experiments are however only com-
patible with the upper limit of the FONLL predictions.
In addition, the data indicate a suppression as large as
that of light quarks , while, due to their large
mass and to the dead cone effect charm quarks are pre-
dicted to loose less energy than light quarks by gluon
radiation in the medium .
Recent model calculations based on in-medium charm
resonances/diffusion or collisional dissociation [19, 20,
21], radiative energy loss via few hard scatterings 
or radiative energy loss via multiple soft collisions ,
have been applied to describe the non-photonic elec-
trons (NPE) spectra. They all predict less suppression
than that observed in experiments. On the other hand,
a good description of the nuclear modification factor
AA(pT), was obtained in non-perturbative
time-dependent heavy-quark diffusion in the Quark-
Gluon Plasma (QGP) .
In previous papers [25, 26] we have shown that the dy-
namics of strangeness production deviates considerably
from calculations based on Schwinger-like estimates for
homogeneous and constant color fields  and point
to the contribution of fluctuations of transient strong
color fields (SCF). These fields are similar with those
which could appear in a “glasma”  at initial stage
of the collisions. In a scenario with QGP phase transi-
tions the typical field strength of SCF at RHIC energies
was predicted to be about 5-12 GeV/fm . Recently
Schwinger mechanism has been revisited  and pair
production in time-dependent electric fields has been
studied . It is concluded that particles with large
momentum are likely to have been created earlier than
particle with small momentum and for very short tem-
poral widths (∆τ ≈ 10tc, where the Compton time
tc = 1/mc) the Schwinger formula strongly underes-
timates the reachable particle number density.
In this paper we extend our study in the framework of
HIJING/B¯B v2.0 model  to open charm productions.
We explore dynamical effects associated with long range
coherent fields (i.e strong color fields, SCF), including
baryon junctions and loops , with emphasis on the
novel open charm observables measured at RHIC in p+p
and heavy-ion collisions. Using this model we analyze
the enhancement of total charm production at 200A
For a uniform chromoelectric flux tube with field (E)
the pair production rate [30, 32, 33] per unit volume for
a heavy quark is given by:
where for Q = c or b , mQ = 1.27, or 4.16 GeV
(with ±1% uncertainty ) Note that κ = |eE|eff =
?C2(A)/C2(F)κ0 is the effective string tension in
C2(A), C2(F) are the second order Casimir operators
(see Ref. ). In a nuclear collisions, the local lon-
gitudinal field strength increases with the square root
of the number of color exchanges proportional to the
number of binary collisions per unit area (κ(x⊥,b) ∝
?TAA(x⊥,b)), where for a given impact parameter
Glauber A+A binary collision distribution. Therefore,
the effective string tension κ ∝ A1/3.
A measurable rate for spontaneous pair produc-
tion requires “strong chromo electric fields”, such that
> 1 at least some of the time. On the aver-
age, longitudinal electric field “string” models predict
for heavier flavor a very suppressed production rate per
unit volume γQvia the well known Schwinger formula
terms of the vacuum string tension κ0≈ 1 GeV/fm and
b and transverse coordinate x⊥, TAA ∝ A2/3is the
γQ¯ Q=ΓQ¯ Q
for Q = c and q = u,d. For a color rope on the other
hand, if the average string tension value (< κ >) in-
creases from 1.0 GeV/fm to 3.0 GeV/fm, the rate Γ for
charm pairs to tunnel through the longitudinal field in-
creases from ≈ 1.4 ·10−12to ≈ 3.5 ·10−4fm−4, and this
can lead to a net “soft” tunneling production compara-
ble to the initial “hard” FONLL pQCD production.
The conventional hard pQCD mechanism, mainly
gluon fusion , is calculated via the PYTHIA subrou-
tines in HIJING/B¯B v2.0. The advantage of HIJING over
PYTHIA is the ability to include novel SCF color rope
effects that arise from longitudinal fields amplified by
the random walk in color space of the high x valence par-
tons in A+A collisions. This random walk could induce
a very broad fluctuation spectrum of the effective string
tension. Thus, if the average or mean < κ >= nκ0,
then the typical fluctuation is of order 1/√n which is
large because n ≈ 6 for Au nuclei. A Poisson fluctua-
tion of effective κ about the mean, gives a strong bias
toward less probable but larger than the average value
< κ >. This is amplified for heavy quarks. Here we
do not investigate in details such fluctuations, but we
will estimate the effects of a larger effective value κ >
3 GeV/fm on the enhancement of σNN
Both STAR and PHENIX experiments have mea-
sured charm production cross sections in several colli-
sion systems. Figure 1 shows the measured total charm
production cross sections at mid-rapidity, dσNN
c ¯ c.
c ¯ c/dy
(left panel) and in all phase space, σNN
The data from both experiments seems to indicate a
scaling with number of binary collisions (Nbin), as ex-
pected because of the high mass of charm pairs pro-
duced in initial nucleon-nucleon collisions . How-
ever, there is still an unresolved discrepancy of the order
of a factor of two between STAR and PHENIX data.
c ¯ c(right panel).
FIG. 1: (Color online) Comparison of HIJING/B¯B v2.0 pre-
dictions for mid-rapidity (left panel) and all phase space
(right panel) charm cross sections per nucleon-nucleon col-
lisions as a function of Nbinin (d)A+A collisions. The sym-
bols are the results with (filled squares) and without (open
crosses) SCF effects. Both include quenching and shadow-
ing (ys) effects. The open triangles are the results with SCF
effects but no shadowing (ns). The values of FONLL predic-
tions are shown as a dotted line. The band at the left mark
the FONLL uncertainties . The data are from STAR
(stars) ,,, and PHENIX (solid circles) ,.
Statistical and systematical error bars are shown.
The predictions of HIJING/B¯B v2.0 model without
SCF (open crosses) and including SCF effects (filled
squares) are shown in the figure.
the results with SCF but no gluon shadowing effects
(open triangles) are also included. However, in this sce-
nario multiplicities at mid-rapidity are strongly over-
estimated . The main parameters used in the cal-
culations are given in Table II of reference , and
corresponds to strengths of strong color (electric) field
dependent on collision system (κ = 1.5; 2.0; 3.0 GeV/fm
for p + p, d + Au, and A + A collisions respectively). In
our calculations we estimate the total open charm pro-
duction (c + ¯ c) cross section considering the 12 lightest
D-mesons (D0,¯D0, D0∗,¯D0∗, D+,¯D+, D+∗,¯D+∗, Ds,
bution of higher mass charm hyperons is negligible. For
calculations which take into consideration SCF effects
(filled squares) we obtain an increase of 60 − 70% in
comparison with a scenario without SCF effects (open
crosses). These results describe well the PHENIX data
within statistical and systematical errors and are close
to the upper limit of uncertainty band of the pQCD
FNOLL predictions . Our calculations also show
that the scaling with Nbin is only approximately sat-
isfied, the reason being an interplay between the mass
s), and the hyperons Λcand¯ Λc. The contri-
dependent SCF and shadowing effects, which act in op-
posite directions. In fact, we calculate that only 60% of
total open charm production (c + ¯ c) comes from par-
tons embedded within the target and projectile.
The study of open charm production in d + Au col-
lisions allow to separate “cold nuclear matter” effects.
The initial production of c ¯ c pairs by gluon fusion might
be suppressed due to gluon shadowing. We recall that
shadowing is a depletion of the low-momentum parton
distribution in a nucleon embedded in a nucleus com-
pared to a free nucleon; this leads to a lowering in the
(scaled) c + ¯ c production relative to p + p collisions.
The shadowing in the regular HIJING parameteriza-
tion  implemented also in our model seems to be
too strong . There is a considerable uncertainty (up
to a factor of 3) in the amount of shadowing predicted
at RHIC energies by the different models with HIJING
predicting the strongest effect . This could explain
why the results for scaled cross sections in d + Au colli-
sions are smaller than those obtained for p + p collisions
(see Fig. 1 left panel).
We study if we can find scenarios that would give
larger enhancement of total cross sections for open
charm production, than those reported in Fig. 1 (filled
squares), and that would be consistent with the STAR
data. The random walk in color space of heavy quark
could induce a broad spectrum of the effective string
tension. Therefore, we study the effects of a further
increase of mean value of the string tension from 3.0
GeV/fm to 5.0 GeV/fm on c ¯ c pair production. This
results in only a modest increase of scaled cross sec-
c ¯ c
central collisions. For values between 5 - 10 GeV/fm a
saturation sets in, as an effect of energy and momen-
tum conservation constraints. In our model the mul-
tiplicative factor that accounts for next to leading or-
der corrections  in calculations of hard or semihard
parton scattering processes via pQCD is set to K = 2.
Increasing this factor to K = 3.5, as suggested in refer-
ence  results in an increase of σsNN
70% in central Au + Au collisions, but also overpredicts
by 40% the total charged particle production at mid-
rapidity (Nch(y=0)). Therefore, we conclude that the
large charm cross sections obtained by the STAR collab-
oration cannot be explained within our phenomenology.
The D0-mesons spectra are sensitive to the dynamics
of produced charm particles. In Fig. 2 we present the
calculated D0-mesons spectra for systems where data
are available ,,. In all cases, the calculated yield
is much smaller than the STAR data, consistent with
the results shown in Fig. 1. The calculated spectra show
little shoulder at low pTindicating small radial flow of
D0-mesons consistent with the results of STAR .
Figure 3 shows our predictions for the Nuclear Modi-
fication factor (NMF), RAA(pT) for D0and π0mesons.
Data (filled symbols) are NMF for non photonic elec-
c ¯ c/Nbin, by approximately 20% for
c ¯ c
AA(pT) ,. The data for π0meson (open
FIG. 2: (Color online) Comparison of HIJING/B¯B v2.0 pre-
dictions for pT distribution of invariant yields for recon-
structed D0in minimum-bias (d)A+A collisions. For clarity
the results for Cu + Cu (preliminary) and Au + Au are mul-
tiplied by 10 and 103respectively. The data are from STAR
[7, 8, 9]. Only statistical error bars are shown.
symbols) are from reference . Note, that non pho-
tonic electrons include also electrons from bottom (b)
production (B → lX) and the yields of D0mesons could
be affected by the decay (B → D). For central (0-10 %)
Au + Au collisions we calculate a scaled total cross sec-
tion for bottom production with (without) SCF of σsNN
= 17.8 µb (σsNN
= 0.86 µb). These values are few orders
of magnitude lower than σsNN
c ¯ c
estimated to be negligible for pT < 6.0 GeV/c.
and this contribution is
FIG. 3: (Color online) Comparison of HIJING/B¯B v2.0 pre-
dictions of nuclear modification factor RAA(pT) for D0and
π0mesons in central (0-12 %) Au + Au collisions. Data
from STAR (stars)  and PHENIX (circles)  are NMF
for non photonic electrons, Rnpe
son are from PHENIX . Error bars show the statistical
and systematic uncertainties.
AA(pT). The data for π0me-
In our calculations for low pT(0 < pT < 2.5 GeV/c),
non-perturbative production mechanism via SCF re-
sults in a split between D0and π0mesons. The charged
and π0mesons are suppressed due to conservation of
energy . The yields of the D0-mesons are enhanced
due to an increase of c¯ c pair production rate (see Eq.
1). In central (0 −10%) Au + Au collisions a suppres-
sion at moderate pT (4 < pT < 6 GeV/c) as large
as that of light quarks is observed in contrast to previ-
ous theoretical studies , [19, 22, 23, 41]. Our model
predicts a suppression consistent with the data. We
can interpret this results as experimental evidence for
“in-medium mass modification” of charm quark, due to
possible induced chiral symmetry restoration . An
in-medium mass modification has also been predicted
near the phase boundary (i.e. at lower energy) in .
In contrast statistical hadronization model  predicts
no medium effects at top RHIC energy.
We performed calculations at the much higher Large
Hadrons Collider (LHC) energy using parameters from
reference , i.e κ = 2.0; 5.0 GeV/fm for p + p and cen-
tral (0-10 %) Pb + Pb collisions respectively. The pre-
dicted charm production cross section is approximately
an order of magnitude larger than at RHIC energy. We
c ¯ c= 6.4 mb in p+p collisions and a (scaled)
cross section σsNN
c ¯ c
= 2.8 mb for central Pb + Pb colli-
sions (Nbin= 960 and Nch(y=0) = 2500). This indi-
cates a clear violation of scaling with Nbinat the LHC.
These values increase by a factor of 2 to 3 if the effects
of shadowing are not included ( Nch(y=0) ≈ 5000 and
c ¯ c
≈ 8.4 mb).
In summary, we studied the influence of possible
strong homogenous constant color fields in open charm
production in heavy-ion collisions by varying the ef-
fective string tension that control Q¯Q pair creation
rates. This is equivalent with assuming an in medium
mass modification of charm quark. We show that this
approach is an important dynamical mechanism that
can explain the observed D-mesons enhancement pro-
duction observed by the PHENIX experiments. Our
model is based on the time-independent color field
while in reality the production of Q¯Q pairs is a far-
from-equilibrium, time-dependent phenomenon. Thus
to achieve more quantitative conclusions, such mecha-
nisms  should be considered in future generation of
Monte Carlo codes.
The large cross sections reported by the STAR collab-
oration remain unexplained within our study. Solving
the discrepancy between the measurements is impor-
tant, since confirmation of the STAR results may in-
dicate the importance of other dynamical mechanisms
such as pre-equilibrium production from secondary par-
ton cascades , or hot-glue scenario .
Acknowledgments: We thank C. Gale and S. Jeon
for useful discussions. This work was supported by the
Natural Sciences and Engineering Research Council of
Canada. This work was supported also by the Divi-
sion of Nuclear Science, of the U. S. Department of
Energy under Contract No. DE-AC03-76SF00098 and
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