Physics Letters B 771 (2017) 374–378
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Elliptic flow in small systems due to elliptic gluon distributions?
Yoshikazu Hagiwara
a
, Yoshitaka Hatta
b,∗
, Bo-Wen Xiao
c
, Feng Yuan
d
a
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
b
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
c
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
d
Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 January 2017
Received
in revised form 1 April 2017
Accepted
29 May 2017
Available
online 31 May 2017
Editor: J.-P.
Blaizot
We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity
and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the
double parton scattering mechanism. We compute the ‘elliptic flow’ parameter v
2
as a function of the
transverse momentum and rapidity, and find qualitative agreement with experimental observations. This
shall encourage further developments with more rigorous studies of the elliptic gluon distributions and
their applications in hard scattering processes in pp and pA collisions.
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
One of the interesting experimental observations from the
proton–proton and proton–nucleus collisions at the Large Hadron
Collider (LHC) and Relativistic Heavy Ion Collider (RHIC) is the
long range rapidity and azimuthal angle correlations between
hadrons [1–9], see, e.g., a recent review in Ref. [10]. These intrigu-
ing
observations have generated great theoretical investigations,
and many models have been proposed to explain the experimen-
tal
results, including (but not limited to) hydrodynamics [11–14],
QCD motivated models [15–18], and in particular, the multi-gluon
correlations calculated in the Color Glass Condensate (CGC) frame-
work [19,20,22–33].
In
this paper, we investigate the contribution from the double
parton scattering (DPS) [34,35] coupled with the so-called elliptic
gluon Wigner distribution [36–38]. In high energy collisions, we
expect the DPS, or in general, the multi-parton scattering, is the
dominant source for multi-particle productions. A unique feature
of DPS is that its contribution is not strongly suppressed for near-
side
particle productions with large rapidity separation as com-
pared
to the single parton scattering (SPS) contribution. Therefore,
DPS may well be the dominant source for long range correlations
among produced hadrons.
It
was first pointed out in Ref. [39] that the DPS plays an im-
portant
role in two particle production in forward pA and dA
collisions
at RHIC. This idea was followed up in the saturation
formalism in Ref. [40] to estimate the so-called pedestal contri-
*
Corresponding author.
E-mail
address: hatta@yukawa.kyoto-u.ac.jp (Y. Hatta).
bution in the correlation measurements. Further study in Ref. [41]
also
confirmed the importance of these contributions in the two
particle production in pA collisions. However, all these studies as-
sumed
that the two hard scatterings are essentially uncorrelated.
In the following, we will extend the DPS mechanism to include the
impact parameter dependence which naturally encodes the corre-
lation
between the two scatterings. If we average over the impact
parameter space, this will reduce to the previous applications of
the DPS mechanism in the CGC framework. However, the uninte-
grated
gluon distribution involved in these scatterings depends on
the impact parameter. In particular, there is a nonzero cos(2φ) az-
imuthal
correlation between the transverse momentum k
⊥
and the
impact parameter b
⊥
, which was referred to as the elliptic gluon
Wigner distribution in Ref. [36]. Since the impact parameters for
the two hard scatterings are correlated due to the DPS mechanism,
we expect the transverse momenta from the two hard scatterings
are correlated as well. This will naturally give rise to the cos(2φ)
two-particle correlation in the final state.
In
Ref. [36], the elliptic gluon Wigner distribution has been
shown to be measurable in diffractive dijet production in lepton-
nucleon
collisions at the future electron-ion collider (EIC). The
present study suggests that the same distribution can affect var-
ious
observables in different types of collisions.
The
rest of this paper is organized as follows. In Sec. 2, we
study the DPS contributions to the two particle production in the
dilute-dense collisions and derive a formula for the ‘elliptic flow’
parameter v
2
. The result is relevant to pp and pA experiments
at RHIC and the LHC. In Sec. 3, we numerically evaluate v
2
in a
model which incorporates the saturation effect in the target. We
point out some generic features of the DPS contributions which
http://dx.doi.org/10.1016/j.physletb.2017.05.083
0370-2693/
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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