Related papers: Three-loop vertex integrals at symmetric point
The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method a characteristic scale $\mu_{s}$ is introduced to regularize the divergent…
The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…
This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All…
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous…
We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…
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)…
The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.
As a generalization of a previous work [Phys. Rev. D. {\bf 59}, 105014 (1999)], we compute analytically a class of three-loop vacuum diagrams with two {\em arbitrarily} different mass scales. We use a decomposition algorithm in which the…
In this work we compute the most general massive one-loop off-shell three-point vertex in D-dimensions, where the masses, external momenta, and exponents of propagators are arbitrary. This follows our previous paper in which we have…
In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…
In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg…
We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…
We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an…
3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation…
We evaluate analytically the one-loop one-mass hexagon in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three.
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 propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and…
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…