(3+1)D dilute Glasma initial conditions in simulations of heavy-ion collisions

Abstract

In this thesis, an approximation for the full (3+1)D dynamics of the Glasma is presented, which breaks boost-invariance on the level of the nuclear fields and leads to rapidity dependence in the final results. For this treatment, the Yang-Mills equations are linearized in covariant gauge, where lower-order, nonlinear contributions are neglected and the dynamics are captured by the (3+1)D dilute Glasma. The analytic solutions of the (3+1)D dilute Glasma are derived in both position and momentum space formulations, providing a comprehensive understanding of the involved (3+1)D dynamics. In position space, the field strength tensor results from the integration of free-streaming gluons that are produced in $2\rightarrow1$ scattering processes where the initial nuclear fields overlap. In momentum space, the event-averaged gluon number distribution for the (3+1)D dilute Glasma is derived in Coulomb gauge. A generalized, three-dimensional McLerran-Venugopalan nuclear model is developed for nuclei with realistic envelopes and intrinsic longitudinal correlations. Numerical results are presented for the rapidity structure of the energy-momentum tensor, the gluon number distribution, and the transverse energy of the (3+1)D dilute Glasma. In position space, the extended longitudinal collision geometry and finite longitudinal correlation length break boost-invariance. In momentum space, the results each follow universal parametrizations and are fixed by the values of two scaling parameters. Furthermore, the numerical results exhibit limiting fragmentation where the rapidity profiles approach a limiting distribution at large rapidities. This feature is also derived locally in position space for the analytic expressions of the field strength tensor and, in momentum space, for the transverse energy of the (3+1)D dilute Glasma.

Figures (43)

• Figure 1: The cylindrical geometry of HICs is described by a coordinate system where the $z$-axis is aligned with the beam axis. The $x$ and $y$-axes span the plane transverse to the beam with the azimuthal angle $\varphi \in [0, 2\pi)$. The polar angle $\theta \in [0,\pi]$ is measured from the $z$-axis and is closely related to the pseudo-rapidity $\eta=\mathop{\mathrm{artanh}}\nolimits(p^z/|\vec{p}|) \in (-\infty, \infty)$. The nucleus with label $\mathrm{A}$ moves in the negative $z$ direction, while the nucleus with label $\mathrm{B}$ moves in the positive $z$ direction.
• Figure 2: The $t$-$z$ plane is additionally parametrized by light cone coordinates $x^\pm=(t\pm z)/\sqrt{2}$ (blue) and the curvilinear Milne coordinates (orange) with proper time $\tau^2=t^2-z^2$ and spacetime rapidity $\eta_s=\mathop{\mathrm{artanh}}\nolimits(z/t)$. Grey curves are lines of constant $\tau$.
• Figure 3: The collision of two nuclei, as described by the CGC, can be divided into two distinct regions along the thick black lines. In Region I, the covariant gauge, single-nucleus solutions are localized to the support given by the $x^\pm$-dependence of the charge distributions. All interactions occur in Region II, where one set of nonlinear YM equations has to be solved for both nuclei. Figure adapted from Ipp:2024ykh.
• Figure 4: The gauge field $A_\mathrm{(II)}$ in Region II develops as a result of the collision of two boost-invariant currents $\mathcal{J}_\mathrm{A}$ and $\mathcal{J}_\mathrm{B}$. Region I from \ref{['fig:two-ncl-collision-regions']} is split up into Regions 0, 1, and 2 with distinct solutions for $A_\mathrm{(I)}$ in light cone gauge. Each current fills the spacetime in its wake with the pure gauge fields $\alpha^\mathbf i_{\mathrm{A}/\mathrm{B}}$ in the transverse direction. Figure adapted from Leuthner:2025vsd.
• Figure 5: Illustration of the field configuration shortly after the collision of nucleus $\mathrm{A}$ and $\mathrm{B}$. Chromo-electric and chromo-magnetic fields point in orthogonal directions in the transverse plane and are distributed according to the color charge density of each nucleus. Between the infinitesimally thin sheets of CGC for each nucleus, longitudinal "flux-tubes" are formed, with a typical transverse size given by the inverse saturation scale $1/Q_s$.