[{"status":"public","year":"2005","date_created":"2011-01-11T18:00:18Z","doi":"10.1088/1126-6708/2005/06/051","issue":"06","arxiv":"1","keyword":["numerical calculations","Phenomenology-HEP","Feynman graph: higher-order","Laplace transformation","epsilon expansion"],"intvolume":" 2005","abstract":[{"text":"In this article we present a high-precision evaluation of the expansions in $\\e=(4-d)/2$ of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of `QED-type' master integrals, i.e. those with a single mass scale only (i.e. $m_i\\in\\{0,m\\}$) and an even number of massive lines at each vertex. Furthermore, we collect all that is known analytically about four-loop `QED-type' masters, as well as about {\\em all} single-mass-scale vacuum integrals at one-, two- and three-loop order.","lang":"eng"}],"publication_status":"published","quality_controlled":"1","author":[{"first_name":"York","orcid":"0000-0003-3535-4194","id":"138494","last_name":"Schroeder","full_name":"Schroeder, York"},{"last_name":"Vuorinen","id":"16080719","first_name":"Aleksi","full_name":"Vuorinen, Aleksi"}],"language":[{"iso":"eng"}],"document_type":"journalArticle","article_type":"original","inspire":"1","first_author":"Schroeder, York","publication_identifier":{"eissn":["1029-8479"]},"publication":"Journal of High Energy Physics","department":[{"_id":"23381619"},{"_id":"23470443"}],"volume":"2005","title":"High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles","edit_mode":"expert","citation":{"bio1":"Schroeder Y, Vuorinen A (2005)

High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles.

Journal of High Energy Physics 2005(06): 051.","chicago":"Schroeder, York, and Vuorinen, Aleksi. 2005. “High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles”. *Journal of High Energy Physics* 2005 (06): 051.

","ieee":" Y. Schroeder and A. Vuorinen, “High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles”, *Journal of High Energy Physics*, vol. 2005, 2005, : 051.","ama":"Schroeder Y, Vuorinen A. High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics*. 2005;2005(06): 051.","apa_indent":"Schroeder, Y., & Vuorinen, A. (2005). High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics*, *2005*(06), 051. doi:10.1088/1126-6708/2005/06/051

","default":"Schroeder Y, Vuorinen A (2005)

*Journal of High Energy Physics* 2005(06): 051.","dgps":"Schroeder, Y. & Vuorinen, A. (2005). High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics*, *2005*(06): 051. doi:10.1088/1126-6708/2005/06/051.

","mla":"Schroeder, York, and Vuorinen, Aleksi. “High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles”. *Journal of High Energy Physics* 2005.06 (2005): 051.","angewandte-chemie":"Y. Schroeder, and A. Vuorinen, “High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles”, *Journal of High Energy Physics*, **2005**, *2005*, : 051.","apa":"Schroeder, Y., & Vuorinen, A. (2005). High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics*, *2005*(06), 051. doi:10.1088/1126-6708/2005/06/051","wels":"Schroeder, Y.; Vuorinen, A. (2005): High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles *Journal of High Energy Physics*,2005:(06):051","harvard1":"Schroeder, Y., & Vuorinen, A., 2005. High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics*, 2005(06): 051.","aps":" Y. Schroeder and A. Vuorinen, High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles, Journal of High Energy Physics **2005**, (2005).","frontiers":"Schroeder, Y., and Vuorinen, A. (2005). High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. *Journal of High Energy Physics* 2005:051.","lncs":" Schroeder, Y., Vuorinen, A.: High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. Journal of High Energy Physics. 2005, : 051 (2005)."},"isi":"1","type":"journal_article","external_id":{"inspire":["678772"],"isi":["000230409600034"],"arxiv":["hep-ph/0503209"]},"article_number":"051","_id":"1963813","date_updated":"2018-07-24T12:57:47Z"}]