Related papers: Scalar one-loop 4-point integrals
One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are…
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…
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…
The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this…
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the…
I describe a method for determining the coefficients of scalar integrals for one-loop amplitudes in quantum field theory. The method is based upon generalized unitarity and the behavior of amplitudes when the free parameters of the cut…
We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e+ e- -> 4 fermions. The described methods for 3-point and 4-point integrals…
We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…
We have computed the self-energies and a set of three-particle vertex functions for massless QCD at the four-loop level in the MSbar renormalization scheme. The vertex functions are evaluated at points where one of the momenta vanishes.…
In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established.…
The four-loop QCD corrections to the electroweak $\rho$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of…
We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward…
In this paper, we focus on both analytical expressions of three and four point integrals for the case of small Gram determinant and numerical improvement of $n$-point integrals for $n\ge5$. Explicit expressions of three and four-point…
Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…
We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation.…
We calculate four-loop QCD corrections to the electroweak $\rho$ parameter with a non-vanishing $b$ quark mass. At three loops, it was observed that elliptic integrals contribute to this observable. This prompts the question of which…
In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future…
We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…
We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…