Related papers: Massless scalar Feynman diagrams: five loops and b…
It is found that the number, $M_n$, of irreducible multiple zeta values (MZVs) of weight $n$, is generated by $1-x^2-x^3=\prod_n (1-x^n)^{M_n}$. For $9\ge n\ge3$, $M_n$ enumerates positive knots with $n$ crossings. Positive knots to which…
Inspired by the corresponding problem in QCD, we determine the pressure of massless O(N) scalar field theory up to order g^6 in the weak-coupling expansion, where g^2 denotes the quartic coupling constant. This necessitates the computation…
For Z -> b bbar, we calculate all the two-loop top dependent Feynman graphs, which have mixed QCD and electroweak contributions that are not factorizable. For evaluating the graphs, without resorting to a mass expansion, we apply a two-loop…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this…
Two-loop massive Feynman integrals for $\phi^4$ field-theoretical model with long-range correlated disorder are considered. Massive integrals for the vertex function $\Gamma^{(4)}$ including two or three massless propagators for generic…
Extending an argument of [Baikov:2010hf] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic \MSbar\ anomalous dimensions…
In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…
We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…
Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the ${O}(n)$-symmetric $\phi^4$-theory in $D=4-\ep$ dimensions we present the…
In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial…
A dimensionally continued background-field method makes the rationality of the 4-loop quenched QED beta function far more reasonable than had previously appeared. After 33 years of quest, dating from Rosner's discovery of 3-loop…
We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension…
The well-known $D$-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be…
In this work, we analyze vanishing cycles of Feynman loop integrals by means of the Mayer-Vietoris spectral sequence. A complete classification of possible vanishing geometries are obtained. We employ this result for establishing an…
We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass…
We apply the analytic conformal bootstrap method to study weakly coupled conformal gauge theories in four dimensions. We employ twist conformal blocks to find the most general form of the one-loop four-point correlation function of…
Dyson-Schwinger equations are used to evaluate the 4-loop anomalous dimensions of quenched QED in terms of finite, scheme-independent, 3-loop integrals. Three of the results serve as strong checks of terms from scheme-dependent 4-loop QCD…
We review an approach for the computation of Feynman integrals by use of multiple polylogarithms, with an emphasis on the related criterion of linear reducibility of the graph. We show that the set of graphs which satisfies the linear…
A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…