Related papers: On a procedure to derive $\epsilon$-factorised dif…
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then,…
In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the…
In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by…
In this talk, we review a loop-by-loop approach used to generate differential equations for multi-scale (dual) Feynman integrals. We illustrate the method on a well-established example: the unequal mass elliptic sunrise.
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…
Differential equations are a powerful tool to tackle Feynman integrals. In this talk we discuss recent progress, where the method of differential equations has been applied to Feynman integrals which are not expressible in terms of multiple…
In this talk, we discuss how ideas from geometry help to improve Feynman integral reduction and the construction of $\varepsilon$-factorised differential equations. In particular, we outline a systematic procedure to obtain an…
Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic curves and Calabi-Yau varieties, are increasingly relevant in modern precision calculations. They arise not only in collider cross-section…
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…
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the…
We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with…
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently,…
Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach,…
Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the…
Feynman integrals are very often computed from their differential equations. It is not uncommon that the $\varepsilon$-factorised differential equation contains only dlog-forms with algebraic arguments, where the algebraic part is given by…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
In this talk we discuss the construction of a basis of master integrals for the family of the $l$-loop equal-mass banana integrals, such that the differential equation is in an $\varepsilon$-factorised form. As the $l$-loop banana integral…
In this talk we discuss how ideas from the theory of mixed Hodge structures can be used to find differential equations for Feynman integrals. In particular we discuss the two-loop sunrise graph in two dimensions and show that these methods…