by the chiral anomaly [22–24] since event-by-event fluctuations are expected to contribute
a significant fraction of the initial axial charge densities. Therefore, a better theoretical
control of the early stages of the collision is essential to properly characterize the origin
and description of anomalous transport phenomena.
The Color Glass Condensate (CGC) effective theory (see e.g. [25, 26] for a review) is
arguably the most promising framework for the description of the early phase of HICs. CGC
describes the high density of small-x gluons carried by nuclei as strong color fields whose
dynamics obey the classical Yang-Mills equations. The classical approximation is founded
in the fact that for very large occupation numbers the quantum fluctuations represent
a negligible correction to the strong background field. This condition is at the base of
the McLerran-Venugopalan model (MV model from now on) [27–29], where nuclei are
represented by an ensemble of SU(N
c
) color charges that act as sources of the classical fields.
The MV model thus assumes a separation of degrees of freedom that is performed at an
arbitrary light-cone momentum Λ
+
: particles with p
+
>Λ
+
are taken as hard color charges
(which represent the valence quarks), and these generate the small-x dynamical modes
(the strong color fields), which satisfy p
+
< Λ
+
. CGC incorporates the means to compute
the quantum corrections to the MV model via the B-JIMWLK equations, which describe
the evolution of the theory with Λ
+
. This framework has been extensively applied in the
description of the early, non-equilibrium stage of HICs known as Glasma phase [30–33].
In a previous work [34] we provided a first-principles calculation quantifying the size
and extent of the transverse correlations of the energy-momentum tensor of Glasma at early
times (and in a subsequent paper [35] the results of said work were applied in the description
of anisotropic flow harmonic coefficients to excellent agreement with data measured at both
RHIC and LHC). In this follow-up paper we extend the classical treatment to the divergence
of the Chern-Simons current:
˙ν(τ = 0
+
, x
⊥
) ≡ ˙ν
0
(x
⊥
) = Tr{E(τ = 0
+
, x
⊥
)B(τ = 0
+
, x
⊥
)}, (1.3)
where E
i
= −F
0i
and B
k
=
1
2
ijk
F
ij
are, respectively, the Glasma chromo-electric and
-magnetic fields, evaluated at an infinitesimal positive proper time τ = 0
+
at a point x
⊥
of the plane transverse to the collision axis. This object is proportional to the strong CP-
violating term of the QCD Lagrangian, which is the source for local axial charge production
(eq. (1.2)). In the present work we evaluate the correlation function h˙ν
0
(x
⊥
) ˙ν
0
(y
⊥
)i, which
characterizes the early event-by-event fluctuations of the ˙ν distribution. In evaluating this
object we find relatively long-range correlations that contrast with both naive expectations
one could have from the MV model — where we assume local correlations at the level
of color source distributions — and previously obtained results from the Glasma Graph
approximation [36] — which assumes a linear mapping of the statistics followed by the
color sources onto the Glasma fields. Although such a discrepancy mirrors the results found
in [34], it is worth remarking that the calculations presented in this work yield an even
larger difference with respect to those obtained under the Glasma Graph approximation.
This paper is organized as follows. In section 2 we introduce a generalization of the
MV model with explicit impact parameter dependence and relaxed transversal locality. In
this framework we outline the solution to the Yang-Mills equations with two sources at an
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