Initial correlations of the Glasma energy-momentum tensor

Abstract

We present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor ( T µν (x ⊥ )T σρ (y ⊥ ) and T µν (x ⊥ ) , respectively) at proper time τ = 0 + . Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of the energy-momentum tensor of the produced gluon fields via the solution of the classical equations of motion in the presence of external currents. The color sources in the two colliding nuclei are characterized by Gaussian correlations, albeit in more generality than in the McLerran-Venugopalan model, allowing for non-trivial impact parameter and transverse dependence of the two-point correlator. We compare our results to those obtained under the Glasma Graph approximation, finding agreement in the limit of short transverse separations. However, important differences arise at larger transverse separations, where our result displays a slower fall-off than the Glasma Graph result (1/r 2 vs. 1/r 4 powerlaw decay), indicating that the color screening of the correlations in the transverse plane occurs at distances larger than 1/Q s by a logarithmic factor sensitive to the infrared. In the Glasma flux tube picture, this implies that the color domains are larger than originally estimated.

Topological charge fluctuations in the Glasma

“…1, although both results agree exactly in the small transverse separation limit r → 0, in the rest of the spectrum (approximately for r > 1/Q s ) our computation yields a significantly harder curve. As shown in Fig.2, this is also the case for the two-point function of the energy density, computed in the exact analytical approach in [34]. Another major difference observed in said paper -and one of its main results-consists in a comparatively slow vanishing behavior in the infrared limit, where the covariance of the energy density decreases following a ∼ 1/r 2 asymptotic curve, in stark contrast with the much steeper ∼ 1/r 4 decreasing behavior displayed by the Glasma Graph result.…”

“…This object characterizes a source of fluctuations of axial charge density in the Glasma state produced in the initial stage of an ultra-relativistic HIC. With this calculation we expand on the results presented in a previous work [34], where we computed the covariance of the Glasma energy-momentum tensor. We performed both calculations following a classical approach based on the CGC effective theory, which we introduced by summarizing the computation of the gluon fields produced at τ = 0 + .…”

“…Specifically, we take h(b ⊥ ) as a slowly varying function over lengths of the order of an infrared length scale 1/m (or smaller), which can be understood as a cut-off that imposes color neutrality at the nucleon size. In addition, we assume that f (r ⊥ ) behaves in such a way that its Fourier transform f (k ⊥ ) tends to unity in the infrared limit (see [34] for details). When finally substituting our building block Eq.…”

“…The remarkable length of this function is a consequence of an specific step of its derivation process, namely the propagation of a non-trivial color state via a 6×6 matrix that represents the correlator of four Wilson lines in the adjoint representation in color space (see [34] for details). Having defined these functions, we can write our building block compactly as:…”

“…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:…”