Hypergeometric representation of a four-loop vacuum bubble

2006/07/01 by E. Bejdakic, Ervin Bejdakic, York Schroder +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Bubble #Geometry and complex manifolds #Harmonic #Hypergeometric distribution #Representation (politics) #Vacuum state #hep-ph

paper · pdf · doi:10.1016/j.nuclphysbps.2006.09.040

5 pages, to appear in the proceedings of the conference "Loops and Legs", Eisenach, 2006

arxiv created 2006/07/01 · openalex publication_date 2006/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this article, we present a new analytic result for a certain single-mass-scale four-loop vacuum (bubble) integral. We also discuss its systematic \e-expansion in d=4-2\e as well as d=3-2\e dimensions, the coefficients of which are expressible in terms of harmonic sums at infinity.

Citations

• Four-loop singlet contribution to the electroweak ρ parameter
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Tuning FORM with large calculations
• Expansion around half-integer values, binomial sums, and inverse binomial sums
• Explicit solutions of the 3-loop vacuum integral recurrence relations
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles
• Pressure of hot QCD up tog6ln(1/g)
• Automatic reduction of four-loop bubbles
• Harmonic Polylogarithms