Eur. Phys. J. C (2019) 79:600
https://doi.org/10.1140/epjc/s10052-019-7097-5
Regular Article - Theoretical Physics
Non-eikonal corrections to multi-particle production in the color
glass condensate
Pedro Agostini
1
, Tolga Altinoluk
2
, Néstor Armesto
1,a
1
Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain
2
National Centre for Nuclear Research, 00-681 Warsaw, Poland
Received: 19 February 2019 / Accepted: 1 July 2019 / Published online: 16 July 2019
© The Author(s) 2019
Abstract We consider the non-eikonal corrections to parti-
cle production in the color glass condensate stemming from
the relaxation of the shockwave approximation for the tar-
get that acquires a finite longitudinal dimension. We derive
a modified expression of the Lipatov vertex which takes into
account this finite target width. This expression is employed
to compute single, double and triple gluon production in
the Glasma graph limit valid for the scattering of two dilute
objects, at all orders in the expansion in the number of col-
ors. We justify and generalize previous results, and discuss
the possible implications on two particle correlations of these
non-eikonal corrections that induce differences between the
away- and near-side peaks.
1 Introduction
Particle production at high energies in the soft and semi-
hard regimes is usually computed resourcing to high energy
approximations [1], namely the eikonal approximation. This
is the case in the color glass condensate (CGC) [2–4]. In this
framework, the process of propagation of an energetic parton
from the projectile through the target, considered as a back-
ground field, is computed in the light cone gauge neglecting
its transverse components and considering it as infinitely time
dilated and Lorentz contracted (thus treated as a shockwave),
see for example the discussion in [5]. Also terms subleading
in energy (among them, spin flip ones) are neglected. On the
other hand, in the calculation of elastic and radiative energy
loss of energetic partons traversing a medium composed of
coloured scattering centers – jet quenching – the shockwave
approximation is relaxed and the target is considered to have
a
e-mail: nestor.armesto@usc.es
a finite length, see e.g. the reviews [6,7].
1
In this context, a
systematic expansion of the gluon propagator in non-eikonal
terms was done in [5,11] and applied to particle production
in the CGC in [12]. Non-eikonal corrections at high energies
have also been treated recently in the context of Transverse
Momentum Distributions and spin physics [13–19], and soft
gluon exponentiation [20–22].
In the CGC, particle production and correlations have been
computed within several approximation schemes, providing
an alternative explanation to final state interactions for the
ridge phenomenon observed in small systems, proton–proton
and proton–nucleus, at the Large Hadron Collider (LHC)
at CERN [23–36] and the Relativistic Heavy Ion Collider
(RHIC) at BNL [37–41]. The “Glasma graph” approximation
[42,43], suitable for collisions between two dilute objects
like proton–proton and containing both Bose enhancement
and Hanbury–Brown–Twiss effects [44–47], has been used
to describe experimental data [48–51], and to compute three
and four gluon correlations [52,53]. Quark correlations have
also been calculated in this framework [54,55]. It was later
extended to dilute–dense (proton–nucleus) collisions both
numerically [56] and analytically [57–59], and used to cal-
culate three gluon correlations [58]. A description of data has
been obtained [60,61]. Density gradients [62] have also been
considered to explain the observed azimuthal structure.
Beyond the analytical extension to dense–dense colli-
sions, the remaining key theoretical problem for the descrip-
tion of azimuthal structure in small systems in the CGC lies
in odd harmonics that are absent in usual calculations. For
this, density corrections in the projectile [63–65], quark cor-
relations [60,66,67] and a more involved description of the
target [68,69] than the one provided by the commonly used
McLerran–Venugopalan (MV) model [
70,71], have been
1
The relation between jet quenching and CGC calculations, using the
formalism in [8,9], was established in [10] where the validity of the
eikonal approximation for this type of computations was also addressed.
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