Physics Letters B 739 (2014) 209–213
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Long-range azimuthal correlations in proton–proton and
proton–nucleus collisions from the incoherent scattering of partons
Guo-Liang Ma
a,∗
, Adam Bzdak
b,∗
a
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
b
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
11 May 2014
Received
in revised form 27 August 2014
Accepted
30 October 2014
Available
online 4 November 2014
Editor:
J.-P. Blaizot
We show that the incoherent elastic scattering of partons, as present in a multi-phase transport model
(AMPT), with a modest parton–parton cross-section of σ = 1.5–3 mb, naturally explains the long-range
two-particle azimuthal correlation as observed in proton–proton and proton–nucleus collisions at the
Large Hadron Collider.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
Recent experimental observations of the long-range azimuthal
correlations in high-multiplicity proton–proton (p + p) [1] and
proton–nucleus (p + A) collisions [2–5] shed some new light on
our understanding of fireballs created in such interactions.
The
measured two-particle correlation function as a function
of the pseudorapidity separation, η = η
1
− η
2
, and the relative
azimuthal angle, φ = φ
1
− φ
2
, of two particles demonstrates a
great deal of similarity to that measured in peripheral heavy-ion
collisions [6]. In particular, two particles separated by many units
of pseudorapidity prefer to have similar azimuthal angles thus the
two-particle correlation function is peaked at φ = 0. Exactly the
same phenomenon was observed in heavy-ion collisions where it
is believed to originate from hydrodynamical evolution present in
such interactions [7]. In this picture the initial anisotropic distribu-
tion
of matter, characterized e.g. by ellipticity, is translated to the
final momentum anisotropy with cos(2φ) term (and higher har-
monics)
in the correlation function. However, the applicability of
hydrodynamics to small systems, as the ones created in p + pand
p +A interactions, is questionable and so far there is no consensus
in this matter. Nevertheless, hydrodynamics
1
applied to p + pand
p + A collisions results in qualitative and partly quantitative un-
derstanding
of various sets of data [8–14]. On the other hand, the
Color Glass Condensate [15], the effective description of low-x glu-
*
Corresponding authors.
E-mail
addresses: glma@sinap.ac.cn (G.-L. Ma), abzdak@quark.phy.bnl.gov
(A. Bzdak).
1
It should be noted that the long-range rapidity structure is put by hand into
hydrodynamic calculations.
ons in the hadronic/nuclear wave function, results in equally good
description of the two-particle correlation functions [16] (see also
[17,18] for a more qualitative discussion). The advantage of the
CGC approach over hydrodynamics is its microscopic character and
internal consistency. On the other hand, hydrodynamics naturally
describes various sets of data for which the CGC predictions are
often not clear. Moreover, hydrodynamics provides a solid intuitive
understanding of the observed signal which is not the case for the
CGC. To summarize, at present we have two competing languages
2
to understand small systems and it is crucial to establish the true
origin of the long-range azimuthal correlation. Several observables
and arguments [20–33] were recently put forward which hopefully
can help to resolve this interesting issue.
In
this paper, we calculate the two-particle density function,
N
pair
(η, φ), in p +p and p +Pb collisions assuming the incoher-
ent
elastic scattering of partons, as present in a multi-phase trans-
port
model (AMPT) [34]. This approach is simple and intuitive, and
more importantly is closely related to quantum chromodynam-
ics
(QCD). The cascade model with the reasonable parton–parton
cross-section, σ = 1–10 mb, was proved to be very successful in
understanding many features of heavy-ion collision data, see e.g.
[35–38]. This approach has one crucial advantage over hydrody-
namics,
namely, there is no need to assume local thermalization.
So far such a calculation was not published and it is important to
establish whether a simple incoherent scattering of partons with
a reasonable partonic cross-section can generate the long-range
structure in p + p and p + A two-particle correlation functions.
3
2
In Ref. [19] both physical pictures are argued to be rather connected.
3
We note that the negative result was reported by the CMS Collaboration in
Ref. [2]. Our results contradict their conclusion.
http://dx.doi.org/10.1016/j.physletb.2014.10.066
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.
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