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Physics Letters B 803 (2020) 135322

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Hybrid Color Glass Condensate and hydrodynamic description of the

Relativistic Heavy Ion Collider small system scan

Björn Schenke

a,∗

, Chun Shen

b,c

, Prithwish Tribedy

Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA

Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201, USA

RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA

a r t i c l e i n f o a b s t r a c t

Article history:

Received 3 September 2019

Received in revised form 17 February 2020

Accepted 19 February 2020

Available online 24 February 2020

Editor: J.-P. Blaizot

Multi-particle correlation observables in the Relativistic Heavy Ion Collider small system scan are

computed in a framework that contains both initial state momentum anisotropies from the Color Glass

Condensate effective theory and ﬁnal state hydrodynamic evolution. The initial state is computed using

the IP-Glasma model and coupled to viscous relativistic hydrodynamic simulations, which are followed

by microscopic hadronic transport. All parameters of the calculation were previously constrained using

experimental data on Au+Au collisions at the same center of mass energy. We ﬁnd that the qualitative

features of the experimental data, such as the system and centrality dependence of the charged hadron

momentum anisotropy, can only be reproduced when ﬁnal state interactions are present. On the other

hand, we also demonstrate that the details of the initial state are crucially important for the quantitative

description of observables in the studied small systems, as neglecting the initial transverse ﬂow proﬁle

or the initial shear stress tensor, which contain information on the momentum anisotropy from the Color

Glass Condensate, has dramatic effects on the produced ﬁnal state anisotropy. We further show that the

initial state momentum anisotropy is correlated with the observed elliptic ﬂow in all small systems, with

the effect increasing with decreasing multiplicity. We identify the precise measurement of v

in d+Au

and Au+Au collisions at RHIC energy at the same multiplicity as a means to reveal effects of the initial

state momentum anisotropy.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

The origins of azimuthal anisotropies in the produced hadron

momentum distributions observed in high energy collisions involv-

ing protons or other small nuclei at the Relativistic Heavy Ion

Collider (RHIC) and the Large Hadron Collider (LHC) have been

under strong debate [1,2]. The main question is whether initial

state momentum correlations, which originate from both classi-

cal

and quantum effects in the multi-particle production process

[3–20] and can be computed using Color Glass Condensate (CGC)

effective theory [21–23], contribute signiﬁcantly to the observed

anisotropy coeﬃcients, or whether ﬁnal state interactions in the

produced medium [24–37]are absolutely dominant.

Both contributions have been studied in a combined framework

of the IP-Glasma initial state [38,39] and a microscopic description

of the gluonic ﬁnal state interactions via solutions of the Boltz-

mann

equation in [40]. It was found that initial state correlations

survive for transverse momenta p

 1.5 GeV even in high multi-

plicity

p+Pb events, with their effect and affected p

range increas-

Corresponding author.

E-mail address: bschenke@bnl.gov (B. Schenke).

ing with decreasing multiplicity. We go beyond this study in two

essential ways. First, we allow for the comparison to experimental

data by computing hadronic ﬁnal states instead of studying parton

spectra, and second, we quantify how strongly the CGC initial state

momentum anisotropy can affect experimental observables if ﬁnal

state interactions are described by realistic hydrodynamic simula-

tions

that were constrained by heavy ion data.

Previous calculations involving the IP-Glasma initial state cou-

pled

to a hydrodynamic description of the ﬁnal state evolution

[41–43]in principle also contain information on both CGC initial

state and geometry driven ﬁnal state sources of correlations. How-

ever,

only the work on p+Pb collisions at LHC in [37]included the

full initial energy momentum tensor from the IP-Glasma calcula-

tion

to initialize hydrodynamics, which is necessary in order to

keep the full initial state information, and to conserve energy and

momentum when switching descriptions.

The striking results from the recent small system scan at RHIC

[44]provide a strong motivation to extend our work to lower en-

ergies

and to analyze in more detail the features of initial and

ﬁnal state effects on the observed momentum anisotropies. We

https://doi.org/10.1016/j.physletb.2020.135322

SCOAP

2 B. Schenke et al. / Physics Letters B 803 (2020) 135322

study different collision systems (p+p, p+Au, d+Au, and

He+Au)

at the top RHIC energy, using the hybrid framework of IP-Glasma

+ Music hydrodynamics + UrQMD [45,46]with parameters con-

strained

by heavy ion collisions [47]. Apart from presenting results

for two- and four- particle correlations and comparison to experi-

mental

data, we show the multiplicity and system dependence of

the initial elliptic momentum anisotropy, and its correlation with

the observable elliptic ﬂow.

The energy momentum tensor from the IP-Glasma framework,

used to initialize the hydrodynamic simulation, includes the sin-

gle

particle CGC momentum anisotropy. We study individually the

effects of the initial transverse ﬂow proﬁle and the viscous compo-

nents

of the energy momentum tensor. This allows us to determine

the importance of different features of the initial state description,

many of which are neglected in recently explored approximations

to the IP-Glasma model [48–50](see also [51]).

1. Framework

We employ the hybrid framework described in [37] and [47],

consisting of the boost-invariant IP-Glasma initial state, which pro-

vides

the spatial (x

⊥

) distribution of (locally anisotropic) energy-

momentum

tensors as input for the hydrodynamic simulation Mu-

sic,

which in turn is coupled to the hadronic transport simulation

UrQMD, which describes the low energy density regime. The use of

hydrodynamics even in small systems is motivated by recent work

on the applicability of hydrodynamics and the fast emergence of

quasi-universal, attractor behavior in the QGP (see the review [52]

and

references therein).

The IP-Glasma model samples nucleon positions from nuclear

density distributions, including a three-hotspot substructure for

each nucleon to generate the nuclear geometry of a single con-

ﬁguration.

For the deuteron, we sample a Hulthen wave function

[53,54], for

He we use the same conﬁgurations as in [55], ob-

tained

using Green’s function Monte Carlo calculations [56]. For

gold nuclei we use Woods-Saxon distributions as described in

[47]. Given that geometry, the IPSat model [57], constrained by

HERA data [58] provides the distribution of the color charge den-

sity,

which determines the variance of the Gaussian distributed

color charges, which are then sampled. These color charges are

the sources for the gluon ﬁelds, which are found by solving the

SU(3) Yang-Mills equations numerically [59]. From the two incom-

ing

sheets of gluon ﬁelds one determines the gluon ﬁelds after

the collision [38,39,59], which are then evolved in time. At time

init

we switch from the Yang-Mills to the hydrodynamic descrip-

tion

by using the gluon ﬁelds’ energy momentum tensor T

μν

CYM

⊥

)

as initial condition for the hydrodynamic simulations. We use

init

= 0.4fm/c and will comment on the effect of varying τ

init

between 0.2 and 0.6fm/c.

As in [37] and [47], we include the full energy momentum ten-

sor,

which has the shear stress contribution

μν

= T

μν

CYM

−

εu

μν

. (1)

The initial energy density ε and ﬂow velocity u

can be extracted

by solving u

μν

CYM

=εu

On the Yang-Mills side, the pressure is given by P

CYM

= ε/3,

while in the hydrodynamic simulation we employ a lattice QCD

equation of state [60,61]with pressure P

lat

. There are various ways

of dealing with this mismatch. One way is to absorb the difference

in an effective initial bulk viscous term  = ε/3 − P

lat

, which van-

ishes

on a time scale approximately given by the bulk relaxation

time. The initial  constructed this way leads to an additional

outward push [47]. Alternatively, one can accept a jump in the

pressure at the time of matching, by setting the initial  = 0. The

former option is our preferred one, as it was used in [47]. We will

also study the latter option, which will determine one contribution

to our systematic uncertainties.

Once initialized at time τ

init

, the energy momentum tensor fol-

lows

∂

μν

=0, where

μν

=εu

−(P +)

μν

+π

μν

, (2)

with 

μν

= g

μν

− u

. We use the same second order consti-

tutive

relations for the shear and bulk viscous parts as derived

in [62,63] and used in [47], and solve them within the simula-

tion Music [41–43].

We use the same shear and bulk viscosities

as in [47]. Because the second order transport coeﬃcients are not

well known, we will vary all (except the relaxation times) between

what was used in [47](values determined from a Boltzmann gas

in the small mass limit [62,63]) and zero, which constitutes the

other contribution to our systematic errors.

We note here that another uncertainty, which is diﬃcult to

quantify, arises from the presence of bulk viscosity. It can lead

to regions of negative effective pressure, which has the potential

to cause cavitation [64–68]. The detailed mechanism of how this

would occur in a QGP is not well understood, and the observ-

able

consequences are unclear [67]. For this work, we continue

to evolve regions of negative pressure within the hydrodynamic

framework. We checked that when setting any negative pressures

to zero during the evolution, the v

) are reduced, with the re-

sults

lying within the systematic error bands shown in Fig. 3.

When the medium temperature drops to the switching temper-

ature

= 145 MeV, the ﬂuid is converted to particles by ﬁrst

computing the particle spectra according to the Cooper-Frye for-

mula

[69], using equilibrium distributions f

with viscous correc-

tions

δ f

given in [70–72]for shear and bulk viscous terms. From

these non-equilibrium distribution functions f = f

+δ f

we sam-

ple

particles on the switching surface

that then undergo the mi-

croscopic

transport processes of UrQMD [45,46]. To ensure enough

statistics, each individual hydrodynamic hypersurface is oversam-

pled

until we reach at least 100,000 particles per unit of rapidity.

2. Multiplicity distributions

Multi-particle correlations in small systems are very sensitive

to event-by-event ﬂuctuations. Consequently, basic observables like

the charged particle multiplicity distributions must be described

correctly. We present both the gluon multiplicity distributions

(folded with a Poisson distribution to estimate the effect of (grand

canonical) sampling on the switching surface), which is used to

determine our centrality classes, and for d+Au collisions also the

ﬁnal state charged hadron distribution. The gluon multiplicity N

is obtained directly from the gluon ﬁelds in the IP-Glasma model

as described in detail in [39].

Results for multiplicity distributions scaled by the mean mul-

tiplicity

in p+p, p+Au, and d+Au systems at

√

s = 200 GeV are

shown in Fig. 1, comparing to experimental data (of the uncor-

rected

charged particle multiplicity on the Au going side) in d+Au

collisions from the STAR Collaboration [73] and (to the corrected

charged particle multiplicity data within |η| < 0.5) in p+p colli-

sions

from the UA5 Collaboration [74]. While the statistics for the

computed charged hadron multiplicity distribution is limited, one

can see that the (scaled) gluon distribution is a good proxy for the

ﬁnal state charged hadron distribution. Furthermore, the shape of

the experimental distributions in p+p and d+Au collisions is well

reproduced in our framework.

We employ the publicly available numerical code iSS: https://github .com /

chunshen1987

/iSS.

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