The RHIC hadron production data in hadronic collisions at the forward rapidities may hint the evidence of the Color Glass Condensate (CGC). However, in the opposite region, backward rapidities, new effects should be important in order to describe the observables. In this work, the charged hadron and π 0 productions are investigated in the fragmentation region of the nucleus (backward rapidities) considering dAu and pp collisions in the context of the Color Glass Condensate. In the backward rapidity region, only the proton can be treated as a CGC, and the large x nuclear effects need to be considered in order to describe the cross section. The results are shown by means of the nuclear modification ratio comparing the proton-nucleus and proton-proton cross sections and such ratio presents some dependences on the large x nuclear effects

Gay Ducati

Marcos André Betemps

Maria Beatriz

CiteSeerX

522 Brazilian Journal of Physics, vol. 38, no. 3B, September, 2008
Hadron Production in the Nucleus Fragmentation Region
Marcos André Betemps∗
Conjunto Agrotécnico Visconde da Graça,
Universidade Federal de Pelotas
Rua Eng. Ildefonso Simoes Lopes, 2791,
96060-290 Pelotas, Rio Grande do Sul, Brazil
Maria Beatriz Gay Ducati†
Instituto de Fı́sica,
Universidade Federal do Rio Grande do Sul
Caixa Postal 15051, 91501-970 Porto Alegre,
Rio Grande do Sul, Brazil
(Received on 20 June, 2008)
The RHIC hadron production data in hadronic collisions at the forward rapidities may hint the evidence of
the Color Glass Condensate (CGC). However, in the opposite region, backward rapidities, new effects should
be important in order to describe the observables. In this work, the charged hadron and π0 productions are
investigated in the fragmentation region of the nucleus (backward rapidities) considering dAu and pp collisions
in the context of the Color Glass Condensate. In the backward rapidity region, only the proton can be treated as
a CGC, and the large x nuclear effects need to be considered in order to describe the cross section. The results
are shown by means of the nuclear modification ratio comparing the proton-nucleus and proton-proton cross
sections and such ratio presents some dependences on the large x nuclear effects.
Keywords: Color Glass Condensate; Backward Rapidities; Hadron Production
1. INTRODUCTION
The hadron production in the high energy hadronic colli-
sions at RHIC [1] is one of the recent data that should indi-
cate the existence of the Color Glass Condensate (CGC) [2]
in the forward rapidity region. The ratio between deuterium-
proton and proton-proton differential cross sections, consid-
ering the transverse momentum distributions, is employed to
investigate the existence of the Color Glass Condensate. This
ratio presents a Cronin enhancement at moderate transverse
momentum and more central rapidities, and a suppression at
forward ones. The suppression of the ratio with rapidity is re-
lated to the quantum evolution of the gluons in the target, and
is being considered as one of the evidences of the Color Glass
Condensate [3].
Looking to the opposite region in the detector (backward
rapidities), new effects like large x nuclear effects or final
state effects, should be relevant in order to describe the ob-
servables. At this region the nucleus can not be considered
as a Color Glass Condensate, once the large x components
contribute to the cross section, and only the proton should be
treated in this way. Considering the recently measured hadron
nuclear modification at backward rapidities, it shows a pro-
nounced peak as more negative values are reached (∼−2) for
0.5 GeV < pT < 4 GeV [4], which is not well understood.
However, as we will show in this work, it should be due to
final states interactions.
The main goal of this work is to investigate the hadron pro-
duction at backward region considering the Color Glass Con-
∗marcos.betemps@ufpel.edu.br
†beatriz.gay@ufrgs.br
densate approach. The CGC theory is well justified at forward
rapidities, where the nucleus interacts by means of the small
x partons. The use of this approach at the backward kine-
matical region need to be carefully analyzed. In recent works
[5, 6] the CGC approach is considered in order to describe the
proton-proton collision, which implies to describe the proton
as a CGC. If it is so, them we are free to change proton and
nucleus in the CGC approach, and investigate the large x nu-
clear effects in the nucleus, by means of the nuclear parton
distributions, while the proton being described by the CGC
theory.
Considering this goal, the paper is organized as follows. In
the next section, we discuss the hadron production at back-
ward rapidities, presenting all the quantities in order to obtain
the cross section for the hadron production. In section 3 we
present and discuss the main results of this work and in section
4 the conclusions of the work are presented.
2. HADRON PRODUCTION
The hadron production at forward rapidities is investigated
in a considerable number of works (for instance [5, 6]). The
cross section could be expressed as a convolution of the stan-
dard parton distributions for the dilute projectile, the dipole-
hadron scattering amplitude, in which the high-density effects
should be included, and the parton fragmentation functions.
The idea in this work is to consider the same cross section at
forward rapidities, however, changing the target and the pro-
jectile, being now the nucleus interacting at large x the target
and the proton at small x the projectile (similar considerations
were performed for dilepton production at backward rapidi-
ties in the dipole approach [7]). Considering this idea, the
cross section for the hadron production at backward rapidities
Marcos André Betemps and Maria Beatriz Gay Ducati 523
in Deuterium-Nucleus collisions, could be written in the form,
d2σdA→hX (Backward)
dyd2 pT
=
1
2π
∫ 1
xF
dx2
x2
xF
{
fq/A(x2, pT )NF
(
x2
xF
pT ,x1
)
Dh/q(
xF
x2
, pT )
+ fg/A(x2, pT )NA
(
x2
xF
pT ,x1
)
Dh/g(
xF
x2
, pT )
}
, (1)
where pT , y and xF are the transverse momentum, rapidity
and the Feynman-x of the produced hadron, respectively. The
variable x1 denotes the momentum fraction of a projectile par-
ton, f (x1, p2T ) is the projectile parton distribution functions
(nucleus in dA or proton in pp collisions) and D(z, p2T ) rep-
resents the parton fragmentation functions into hadrons (we
use the KKP fragmentation function [8]). In Eq. (1), NF(k̃,x)
and NA(k̃,x) are the fundamental and adjoint representations
of the forward dipole amplitude in momentum space, which
represent the probability for scattering of a quark and a gluon
of the deuterium (or proton), respectively. Moreover, for this
kinematical region xF =
pT√
s e
−y, and the momentum fraction
of the target partons is given by x2 = x1e−2y.
Concerning the nuclear parton distribution function, we use
CTEQ5 [9] as the parton distribution function (PDF) of free
protons and the EKS parametrization for the nuclear parton
distributions (nPDF) [10, 11]. EKS parameterization gives
the nPDF as the free proton PDF multiplied by a factor,
f Aq (x,Q) = R
A
q (x,Q) f
p
q (x,Q), (2)
and is available only at leading order. We perform the investi-
gation considering other nuclear parton distribution proposed
by Sassot and de Florian (nDS) [12] which gives the nPDF as
a convolution of the free proton PDF and a weight function:
f Aq (x,Q) =
∫ A
x
dy
y
Wq(y,A) f pq
(
x
y
,Q
)
. (3)
However, this parametrization is not well behaved at large x,
as can be seen in the Fig. 1, where the ratio between nuclear
and nucleon parton distributions functions RF2 is presented.
For this reason, the results in this work are obtained with the
EKS parametrization. In the Fig. 1 the distinct nuclear effects
should be identified: Fermi motion effects (0.8 < x), EMC
effects (0.3 < x < 0.8), anti-shadowing (0.1 < x < 0.3) and
shadowing effects (x < 0.1).
The dipole scattering amplitude parametrization is consid-
ered from the DHJ parametrization [5]. This parametrization
was proposed in order to describe the forward region of dAu
collisions at RHIC, and present explicit Geometric Scaling
violation. The dipole scattering amplitude proposed in the
DHJ model was based in the parameterization porposed by
Kharzeev, Kovchegov and Tuchin, which incorporates GS vi-
olation [13], however, in the DHJ model, this GS violation is
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
x
0
0.5
1
1.5
2
R
F
2
nDS (Q=1 GeV)
EKS (Q=1 GeV)
EKS (Q=3 GeV)
nDS (Q=3 GeV)
FIG. 1: Comparison between EKS and nDS parametrization at small
Q. At large x the nDS parametrization predicts negative values for
the ratio between nuclear and proton structure functions.
strong. The DHJ model is written in the form,
NA(pT ,x) =
∫
d2rei ~pT ·~r
×
[
1− exp
(
−1
4
(r2Q2s (x))
γ(pT ,x)
)]
. (4)
In this parameterization, the problems that appear in the
Fourier transformation [14] are prevented by the pT depen-
dence of the γ instead of the r dependence. The expression
for NF is obtained by means of the replacement r2Q2s (x) →
(CF/CA)r2Q2s , where CF/CA = 4/9. The anomalous dimen-
sion γ of the DHJ parameterization has the form,
γ(pT ,x) = γs+∆γ(pT ,x)
γ(pT ,x) = γs+(1− γs) log(p
2
T /Q
2
s (x)
λy+d√y+ log(p2T /Q2s (x))
, (5)
where y = log1/x. The saturation scale Qs and the parameter
λ are taken from the GBW model [15]. In this parameteriza-
tion, d = 1.2 is determined by the fit procedure to the RHIC
data on hadron production and γs = 0.628. The GS violation
in the DHJ model is represented by the term ∆γ(pT ,x) in the
equation 5.
Having presented all the components in order to obtain the
cross section for the hadron production at backward rapidities,
in what follows the cross section could be evaluated consid-
ering pp and dAu collision at RHIC energies, analyzing the
charged hadron and π0 productions. In the Fig. 2 the spectra
524 Brazilian Journal of Physics, vol. 38, no. 3B, September, 2008
for π0 production is presented as a function of the transverse
momentum of the produced hadron.
0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV)
10
−10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
d2
N
/d
yd
2 p
T
 (
G
eV
−
1 )
 (
π0
)
pp (y=−2)
pp (y=−3)
pp (y=−4)
dA (y=−2)
dA (y=−3)
dA (y=−4)
FIG. 2: π0 production at RHIC energies in pp and dAu collisions.
Analyzing the Fig. 2 we verify the expected behavior, the
spectra is enlarged to more central rapidities (the behavior is
similiar for charged hadron production). In these calculations
no K factor is under consideration (the K factor should sim-
ulate NLO contributions). It should be interesting to address
that the calculations performed here are justified only at back-
ward rapidities. It should not describe the cross section in the
central rapidity region, since at this kinematical regime, the
proton should not be described as a Color Glass Condensate.
It is an approximation, which is considered reasonable only at
backward or forward rapidities.
Having discussed the hadron production at the backward
rapidities, in the next section the nuclear modification ratio is
investigated at this kinematical region.
3. RESULTS AND DISCUSSIONS
The cross section presented in this work is evaluated in the
LO calculation. In order to describe the data, a K factor should
be employed. It should be verified that in the forward rapidi-
ties the pp and dAu spectra are described considering the same
K factor at same rapidity and energy. This implies that the
production mechanism is the same considering pp and dAu
processes at forward rapidities, and the saturation effects are
being considered in both cases. In the backward rapidities,
new effects are present in the nucleus (large x effects), which
are not present in the proton. This should be the main approx-
imation realized in this work: we consider the same K factor
in pp and dAu collision at backward rapidities, in order to in-
vestigate the nuclear modification factor, which is defined in
the form,
RdA =
d2N(dA)/dyd2 pT
d2N(pp)/dyd2 pT
. (6)
In this definition, we have not included any normalization fac-
tor. The normalization of the ratio RdA is a crucial point of
this investigation, however, we intend to analyse this aspect in
a complete version of this work, which is in progress [16]. At
the moment, we will investigate only the pT dependence of the
ratio RdA considering π0 and charged hadron productions. In
the Fig. 3 and 4 the nuclear modification ratio is investigated
for these observables at RHIC energies
√
s = 200 GeV and
backward rapidities y =−2,−3,−4. We consider the CTEQ5
LO parametrization for the free proton, deuterium without nu-
clear effects and EKS parametrization for the nuclear parton
distributions.
0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
R
dA
u 
(π
0 )
y=−2
y=−2 (without nuclear effects)
y=−3
y=−3 (without nuclear effects)
y=−4
y=−4 (without nuclear effects)
FIG. 3: Nuclear modification ratio for the π0 production at RHIC
energies.
In order to identify the large x effects in the nuclear modi-
fication factor, we perform calculations with and without nu-
clear effects. In the cross section (Eq. 1), the integration over
x2 with the limits xF and 1, implies that all the nuclear effects
for x > xF are contributing to the cross section. Only concern-
ing the fragmentation function the results presented here are
distinct considering charged hadron and π0 productions.
0.5 1 1.5 2 2.5 3 3.5 4
pT (GeV)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
R
dA
u 
(h
+
+
h−
)
y=−2 (EKS)
y=−2 (without nuclear effects)
y=−3 (EKS)
y=−4 (EKS)
FIG. 4: Nuclear modification ratio for the charged hadron production
at RHIC energies.
In the Fig. 3 the nuclear modification factor for the π0 pro-
duction is presented. For the rapidity y = −2 the nuclear ef-
fects provide an increment on the nuclear modification ratio.
Marcos André Betemps and Maria Beatriz Gay Ducati 525
This behavior is due to the large x effects present in this re-
gion. The anti-shadowing, EMC and Fermi motion are con-
tributing to the cross section and the net result is an increment
of the nuclear cross section, since the RF2 is larger than 1 for
anti-shadowing and Fermi motion regions. For y = −3 the
nuclear effects provide a reduction of the nuclear modifica-
tion ration at large pT (EMC effect) and an increment on the
RdA at small pT (anti-shadowing effect). Considering very
backward rapidities, the nuclear effects implies that the RdA is
reduced at small pT (EMC effect) and present a peak at large
pT , which is due to the dominance of the Fermi motion effect.
In the Fig. 4 the nuclear modification factor for the charged
hadron production is presented. The conclusions considering
the charged hadron are the same obtained in the π0 production,
once the calculation are distinct only concerning the fragmen-
tation function.
4. CONCLUSIONS
In this work, the large x nuclear effects (Fermi motion,
EMC and antishadowing) provide a reduction of the nuclear
modification ratio in some RHIC kinematical regions, how-
ever, these effects should implie in an increment in the ratio
RdA for other regions. The behavior of the ratio RdA is simi-
lar considering π0 and charged hadron productions. We verify
that the nuclear effects at backward rapidities at RHIC ener-
gies provide an increment on the ratio RdA for y = −2. For
y = −3, the nuclear effects produce an increment in the ra-
tio RdA at small pT and a reduction of the ratio at large pT .
Considering y = −4, only at large pT the large x nuclear ef-
fects provides a strong increment on the nuclear modification
factor, which is associated to the Fermi motion nuclear effect.
The results obtained in this work should be interesting to
compare with the nuclear modification factor data at RHIC
backward rapidities for the hadron production [4] (the data
present the nuclear modification factor from the central ra-
pidites up to y = −2). This investigation will be present in a
complete version of this work, which includes a comparison
with the RHIC data and an estimation of the magnitude of the
final state effects contributions. The results presented in this
contribution should be contrasted with eletromagnetic observ-
ables at this kinematical region [7], which should be another
way of investigation of the large x nuclear effects, that we in-
tend to address in a near future.
Acknowledgments:
We would like to thanks to all participants of the II Latin
American Workshop on High Energy Phenomenology due to
the excellent discussions. This work was partially financed by
the Brazilian funding agencies CNPq and FAPERGS.
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Hadron Production in the Nucleus Fragmentation Region

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Hadron Production in the Nucleus Fragmentation Region

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