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

Schroeder Y, Vuorinen A (2005)
Journal of High Energy Physics 2005(06): 051.

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Journal Article | Original Article | Published | English

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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.
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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.
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
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.
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.
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.
Schroeder, Y., Vuorinen, A.: High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. Journal of High Energy Physics. 2005, : 051 (2005).
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.
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arXiv hep-ph/0503209

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