Simulations of the Glasma in 3+1D
Apr 8, 2019175 pages
Supervisor:
Thesis: PhD - Andreas Ipp
- Vienna, Tech. U.
- Published: 2019
e-Print:
- 1904.04267 [hep-ph]
URN/HDL:
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Abstract: (Vienna, Tech. U.)
The Glasma is a gluonic state of matter which can be created in collisions of relativistic heavy ions. It only exists for a short period of time before it evolves into the quark-gluon plasma. The existence of the Glasma is a prediction of a first-principles classical effective theory of high energy quantum chromodynamics called the color glass condensate (CGC). In many analytical and numerical calculations within the CGC framework, the boost invariant approximation is employed. It assumes that the Lorentz-contracted longitudinal extent of the nuclei can be approximated as infinitesimally thin. Consequently, the Glasma produced from such a collision is boost invariant and can be effectively described in 2+1 dimensions. Observables of interest such as energy density, pressure or gluon occupation number of the boost invariant Glasma are by construction independent of rapidity. The main topic of this thesis is to study how the assumption of infinitesimally thin nuclei can be relaxed. First, we discuss the properties of the CGC and Glasma by starting with the boost invariant case. The McLerran-Venugopalan (MV) model is used as a simple model for large heavy nuclei. The Yang-Mills equations, which govern the dynamics of the Glasma, generally cannot be solved analytically. Numerical solutions to these equations are therefore often the only reliable approach to studying the Glasma. We discuss the methods of real time lattice gauge theory, which are the usual approach to numerically solving the Yang-Mills equations in a gauge-covariant manner. Having established the standard tools used to describe the boost invariant Glasma, we focus on developing a numerical method for the non-boost-invariant setting where nuclei are assumed to be thin, but of finite longitudinal extent. This small change is in conflict with a number of simplifications and assumptions that are used in the boost invariant case. In particular, one has to describe the collisions in 3+1 dimensions in the laboratory or center-of-mass frame, compared to the co-moving frame of the traditional method. The change of frame forces the explicit inclusion of the color charges of nuclei. In numerical simulations this is achieved using the colored particle-in-cell method. The new method is tested using a version of the MV model which includes a parameter for longitudinal thickness. It reproduces the boost invariant setting as a limiting case. Studying the pressure components of the Glasma, one finds that the Glasma in 3+1 dimensions does not differ much from the boost invariant case and that the pressure anisotropy remains large. On the other hand, one finds that the energy density of the Glasma depends on rapidity due to the explicit breaking of boost invariance. The width of the observed rapidity profiles is controlled by the thickness of the colliding nuclei. Using only a very simple model for nuclei, the profiles can be shown to agree with experimental data. If simulation parameters are not carefully chosen, the numerical scheme employed in the 3+1D method suffers from a numerical instability. To eliminate this instability, a completely new numerical scheme for real-time lattice gauge theory is developed. This new scheme is shown to be gauge-covariant and conserves the Gauss constraint even for large time steps.Note:
- PhD thesis based on PRD 94 (2016) no.1, 014020 (arXiv:1605.07184), PLB 771 (2017) 74-79 (arXiv:1703.00017), PoS EPS-HEP2017 (2017) 176 (arXiv:1710.01732) and EPJC 78 (2018) no.11, 884 (arXiv:1804.01995); v2: fixed typos v3: added references, v4: fixed typos
- Glasma
- Schwerionenkollisionen
- Farbglaskondensat
- Particle-in-cell Simulation
- heavy ion collisions
- color glass condensate
- particle-in-cell simulation
- nucleus: charge
- pressure: anisotropy
- quark gluon: plasma
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