# Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion

@inproceedings{JFleischer1999SingleMS,
title={Single mass scale diagrams: construction of a basis for the \$\epsilon\$-expansion},
author={J.Fleischer and M.Yu.Kalmykov},
year={1999}
}
• Published 4 October 1999
• Physics
Exploring the idea of Broadhurst on the sixth root of unity'' we present an ansatz for construction of a basis of transcendental numbers for the epsilon-expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.
8 Citations
Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
Loop diagram calculations typically rely on reduction to a finite set of master integrals in 4− 2ǫ dimensions. It has been shown that for any problem, the masters can be chosen so that their
On a two-loop crossed six-line master integral with two massive lines
We compute the two-loop crossed six-line vertex master integral with two massive lines in dimensional regularisation, and give the result up to the finite part in D−4. We apply the differential
Effective potential at three loops
I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of
Evaluation of the general three-loop vacuum Feynman integral
• Physics
• 2017
We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis
Standard model parameters in the tadpole-free pure MS¯ scheme
• Physics
Physical Review D
• 2019
We present an implementation and numerical study of the Standard Model couplings, masses, and vacuum expectation value (VEV), using the pure $\overline{\rm{MS}}$ renormalization scheme based on
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter
• Physics, Mathematics
• 2007
We continue the study of the construction of analytical coefficients of the ?-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following
Hypergeometric Functions and Feynman Diagrams
• Physics, Mathematics
Texts & Monographs in Symbolic Computation
• 2021
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the constructionof the Y-expansion. As an example, we
Subleading power resummation of rapidity logarithms: the energy-energy correlator in $$\mathcal{N}$$ = 4 SYM
• Physics
• 2019
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which