Related papers: Banana integrals in configuration space
We describe a systematic approach to cast the differential equation for the $l$-loop equal mass banana integral into an $\varepsilon$-factorised form. With the known boundary value at a specific point we obtain systematically the term of…
It has recently been shown that two-loop kite-type diagrams can be computed analytically in terms of iterated integrals with algebraic kernels. This result was obtained using a new integral representation for two-loop sunset subgraphs. In…
We compute the three-loop banana integral with four unequal masses in dimensional regularisation. This integral is associated to a family of K3 surfaces, thus representing an example for Feynman integrals with geometries beyond elliptic…
We show that the differential equation for the three-loop equal-mass banana integral can be cast into an $\varepsilon$-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as…
We present a system of canonical differential equations satisfied by the three-loop banana integrals with four distinct non-zero masses in $D = 2-2\eps$ dimensions. Together with the initial condition in the small-mass limit, this provides…
Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose…
In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less…
We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the…
We discuss general one and two-loop banana diagrams and one-loop diagrams with external lines with arbitrary masses on the anti de Sitter spacetime by using methods of AdS quantum field theory in the dimensional regularization approach. The…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
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 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…
We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably simple and all integrals are expressed as linear combinations of iterated integrals…
We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under…
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…
In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an $\varepsilon $-factorised manner, regardless of their hidden geometric essence. In particular, some extra…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…
We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $\epsilon$-form, we manage to obtain a simple one-fold integral representation exact in…
We present for the first time fully analytic results for multi-loop equal-mass ice cone graphs in two dimensions. By analysing the leading singularities of these integrals, we find that the maximal cuts in two dimensions can be organised…