Related papers: Rational terms in two-loop calculations
When using dimensional regularization/reduction the epsilon-dimensional numerator of the 1-loop Feynman diagrams gives rise to rational contributions. I list the set of fundamental rules that allow the extraction of such terms at the…
One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
We present a new algorithm for the reduction of one-loop \emph{tensor} Feynman integrals with $n\leq 4$ external legs to \emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l \geq 0$ and…
For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…
We study quantum loop corrections to two-point functions and extraction of physical quantities in a five-dimensional $\phi^4$ theory on an orbifold. At two-loop level, we find that divergence for quartic derivative terms of $(p^2)^2$ appear…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…
We compute radiative corrections in five and six dimensional field theories, using winding modes in mixed momentum-coordinate space. This method provides a simple way of finding UV divergencies, finite corrections and localized terms when…
We extend the method of differential renormalization to massive quantum field theories treating in particular $\ph4$-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in…
We consider large-order perturbative expansions in QED and QCD. The coefficients of the expansions are known to be dominated by the so called ultraviolet (UV) renormalons which arise from inserting a chain of vacuum-polarization graphs into…
We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the…
The overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector \lambda \phi^4 Euclidean field theory are written down up…
We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each…
Analytical expressions for the tenth order electromagnetic corrections to the lepton ($L=e, ~\mu $ and $\tau$) anomaly $a_L$ are derived explicitly for a class of Feynman diagrams with insertions of the vacuum polarization operator…
I comment and summarize the principles underlying the Four Dimensional Regularization/Renormalization (FDR) approach to the UV and IR infinities. A few recent results are also reviewed.
We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
Numerical reconstruction techniques are widely employed in the calculation of multi-loop scattering amplitudes. In recent years, it has been observed that the rational functions in multi-loop calculations greatly simplify under partial…