Müller, Marcel: Meson correlations and spectral functions in the deconfined phase : a systematic analysis in quenched lattice QCD. 2013
Inhalt
- Introduction and Motivation
- Lattice QCD
- Path integrals and observables in QCD
- Lattice gauge action
- Lattice Fermion actions
- The fermion doubler problem
- Dealing with fermion doublers
- The Wilson action and clover improvement
- The staggered action
- The partition function and the quenched approximation
- Meson correlators
- Spectral functions
- Summary
- Parallel Lattice Code
- Starting point and general decisions
- C++ as programming language and git for versioning
- Modular and layered design
- Fundamental data types on single sites and links
- Lattice-wide containers
- Memory layout management through the lattice class
- Positions on and iterations over the lattice
- Communication abstraction and parallelism
- High level functions
- Automated unit tests
- Current state
- Outlook, planned features
- Scale setting
- Determining lattice spacing
- Critical temperature and temperature scale
- Setting the quark mass
- Non-perturbative renormalization for the vector current
- Meson screening masses
- Extracting meson masses on finite size lattices
- Effective meson masses
- Masses extracted through a fit
- Extracting the ground state mass by fitting multiple states
- A study at 1.5 Tc and 3.0 Tc
- The thermodynamic limit
- Ground state extracted from multiple state fits on finite lattices
- The continuum limit
- Interchanging thermodynamic and continuum limit
- Results at 3.0 Tc
- Final results and conclusion
- Thermal dilepton rates
- Heavy ion collisions and thermal dileptons
- Dilepton rates and the vector spectral function
- Ansatz for the vector spectral function
- Setup of a temperature dependence study
- Continuum correlators from the lattice
- Ratios to free continuum and lattice correlators
- A summary of the extrapolation procedure
- Error estimate of the continuum extrapolation
- Spectral function fit procedure
- Fit of the spectral function ansatz
- Systematic error estimation
- Results
- Fit without thermal moments
- Modified ansatz for the spectral function
- Continuum extrapolated correlators at finite momenta
- A momentum-dependent spectral function
- Finite momentum correlators
- Continuum extrapolation at non-vanishing momentum
- Conclusion
- Conclusion
- Bibliography
- Acknowledgements
- Declaration of Originality / Eigenständigkeitserklärung