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Investigations of chiral symmetry breaking and topological aspects of lattice QCD
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gutachter, Stefan Hecht Ph. D. Jansen, D. |
| Copyright Year | 2014 |
| Abstract | The spontaneous breaking of chiral symmetry is a fascinating phenomenon of QCD whose mechanism is still not well understood. It has fundamental phenomenological implications. It is, for instance, responsible for the low mass of the pions which are effectively Goldstone bosons of the spontaneously broken symmetry.In addition, the topological fluctuations of the underlying gauge fields are directly related to the U(1)A chiral anomaly and therefore linked to the unexpected large mass of the η ′ meson. Since these phenomena belong to the low energy regime of QCD, non-perturbative techniques have to be applied in order to study them. Lattice regularization, through the path integral quantization of the theory, is such a non-perturbative method and it enables us to apply both analytical and numerical techniques from statistical mechanics to the study of QCD. In this work we use the twisted mass lattice QCD regularization to compute the chiral condensate, the order parameter of spontaneous chiral symmetry breaking. To this end we apply the recently introduced method of spectral projectors which allows us to perform calculations in large volumes due to its inherently low computational cost. This approach, moreover, enables a direct calculation of the chiral condensate based on a theoretically clean definition of the observable via density chains. We present a continuum limit determination of the chirally extrapolated condensate for Nf = 2 and Nf = 2 + 1 + 1 flavours of twisted mass fermions at maximal twist. We comprehensively investigate the systematic uncertainties arising in this calculation which allows us to present a reliable result for the chiral condensate. A good agreement with other lattice determinations is found. In addition to computing the condensate, we study the chiral behavior of the topological susceptibility, a measure of the topological fluctuations of the gauge fields. We again apply the spectral projector method for this calculation, which is based on a definition of the topological susceptibility free of short distance singularities. In this case one of the biggest advantages is that it avoids the necessity for computationally expensive lattice chiral fermion formulations, and therefore allows us to perform large volume simulations. We comment on the difficulties which appear in the calculation of this observable due to the large autocorrelations involved. When dynamical fermions are present, chiral perturbation theory establishes a relation between the chiral behavior of the topological susceptibility and the chiral condensate. Through this indirect method we extract an alternative determination of the chiral condensate which is in agreement with the previous one. Finally we present the continuum limit result of the topological susceptibility in the pure gluonic theory which allows us to perform a test of the Witten-Veneziano relation. We found that this relation is well satisfied. Our results support the validity of the Witten-Veneziano formula which relates the topological fluctuations of the gauge fields with the unexpectedly large value of the η mass. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://edoc.hu-berlin.de/dissertationen/garcia-ramos-elena-2013-12-16/PDF/garcia-ramos.pdf |
| Alternate Webpage(s) | https://bib-pubdb1.desy.de/record/401574/files/garcia-ramos.pdf |
| Alternate Webpage(s) | https://bib-pubdb1.desy.de/record/401574/files/garcia-ramos.pdf?subformat=pdfa |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Adjudication Algorithmic efficiency Analysis of algorithms Anomaly detection Autocorrelation Chirality (chemistry) Computation (action) Extrapolation Ian H. Witten Indirect Treatment Lattice QCD Lattice field theory Maximal set Mesons Movie projector Numerical analysis Observable Path integral formulation Perturbation theory (quantum mechanics) Population Parameter Simulation Spinor Spontaneous order Statistical Mechanics Stellar classification Symmetry breaking Triune continuum paradigm Twisted Video projector |
| Content Type | Text |
| Resource Type | Article |
