Related papers: One loop integrals reduction
We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…
A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that…
Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products…
The soft and collinear singularities of general scalar and tensor one-loop N-point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
We introduce a novel structure for Feynman integrals, reformulating them as integrals over a small set of parameters with a fully controllable integrand. The integrand closely resembles one-loop Feynman integrals, and they are very easy to…
Feynman integral reduction based on intersection theory provides an alternative to the traditional integration-by-parts method, yet its practical application has been constrained by the large number of variables required in the computation.…
We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct…