[{"file":[{"checksum":"badaaa36fa4d9a8c38ee5bed4f246a23","file_id":"2776014","file_name":"Diss.pdf","date_updated":"2019-09-06T09:18:33Z","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"1970-01-01T00:00:00Z"}],"ddc":["530"],"email":"tluthe@physik.uni-bielefeld.de","place":"Bielefeld","date_created":"2015-09-21T08:06:05Z","supervisor":[{"first_name":"York","last_name":"Schröder","full_name":"Schröder, York"},{"last_name":"Borghini","first_name":"Nicolas","full_name":"Borghini, Nicolas","id":"189816"}],"abstract":[{"lang":"eng","text":"Massive vacuum integrals with a single mass scale are a class of Feynman integrals that appear in many precision calculations within the Standard Model of particle physics and have been calculated to the 4-loop level. In this thesis I start pushing this limit to 5 loops by considering the subclass of fully massive vacuum integrals, which can be used to determine the β-function of Quantum Chromodynamics (QCD). To this end I employ a method devised by Laporta for the evaluation of multi-loop Feynman integrals based on difference equations and factorial series. Significant improvements to this method are introduced to account for the great increase in complexity when going from 4 to 5 loops. An implementation of the improved approach in C ++ is then used to obtain high-precision numerical results for the integrals needed for the 5-loop correction to the QCD β-function."}],"year":"2015","author":[{"first_name":"Thomas","last_name":"Luthe","full_name":"Luthe, Thomas"}],"type":"bi_dissertation","page":"140","publisher":"Universität Bielefeld","citation":{"ieee":" T. Luthe, *Fully massive vacuum integrals at 5 loops*, Bielefeld: Universität Bielefeld, 2015.","frontiers":"Luthe, T. (2015). Fully massive vacuum integrals at 5 loops. Bielefeld: Universität Bielefeld.","apa":"Luthe, T. (2015). *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld.","bio1":"Luthe T (2015)

*Fully massive vacuum integrals at 5 loops*.

Bielefeld: Universität Bielefeld.","mla":"Luthe, Thomas. *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld, 2015.","harvard1":"Luthe, T., 2015. *Fully massive vacuum integrals at 5 loops*, Bielefeld: Universität Bielefeld.","chicago":"Luthe, Thomas. 2015. *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld.

","dgps":"Luthe, T. (2015). *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld.

","ama":"Luthe T. *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld; 2015.","lncs":" Luthe, T.: Fully massive vacuum integrals at 5 loops. Universität Bielefeld, Bielefeld (2015).","default":"Luthe T (2015)

Bielefeld: Universität Bielefeld.","angewandte-chemie":"T. Luthe, *Fully massive vacuum integrals at 5 loops*, Universität Bielefeld, Bielefeld, **2015**.","apa_indent":"Luthe, T. (2015). *Fully massive vacuum integrals at 5 loops*. Bielefeld: Universität Bielefeld.

","wels":"Luthe, T. (2015): Fully massive vacuum integrals at 5 loops. Bielefeld: Universität Bielefeld."},"file_date_updated":"2019-09-06T09:18:33Z","has_accepted_license":"1","defense_date":"2015-09-18","oa":1,"_id":"2776013","language":[{"iso":"eng"}],"title":"Fully massive vacuum integrals at 5 loops","urn":"urn:nbn:de:hbz:361-27760133","date_updated":"2018-07-24T13:01:33Z","status":"public","department":[{"_id":"10028"}]}]