相关论文: New representation of the two-loop crossed vertex …

In this work, we study a mathematically rigorous metric of a graph visualization quality under conditions that relate to visualizing a bipartite graph. Namely we study rectilinear crossing number in a special arrangement of the complete…

The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak…

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with…

We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…

Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…

In the present paper the two and three point functions which occur at the study of the various physical processes are considered. The investigation has dan in the framework of the perturbative theory at the one loop level. The general and…

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…

We briefly discuss an algorithm for the tensor reduction of the two-loop massless crossed boxes, with light-like external legs, and the computation of the relative master integrals.

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally…

We compute the Schroedinger functional (SF) for the case of pure SU(3) gauge theory at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to…

I present the two-loop self-energy functions for scalar bosons in a general renormalizable theory, within the approximation that vector bosons are treated as massless or equivalently that gauge symmetries are unbroken. This enables the…

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.

We calculate the two-loop flavor-singlet axial-vector and gluon transversity coefficient functions for deeply virtual Compton scattering in QCD. We observe interesting properties regarding the transcendentality of the transversity…

For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the…

We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

We evaluated all two-loop conformal integrals of scalar half-BPS six-point functions in $\mathcal{N} = 4$ SYM restricted to a configuration where all points lie on a line. Moreover, we also computed some of these integrals in the…