Related papers: Multiple Mellin-Barnes integrals with straight con…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes representations arising from massive loop integrals, by modifying the contours of integration. We implement an exact solution to the differential equation determining…
We present new closed-form expressions for certain improper integrals of Mathematical Physics such as certain Ising, Box, and Associated integrals. The techniques we employ here include (a) the Method of Brackets and its modifications and…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
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 compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…
The status of numerical evaluations of Mellin-Barnes integrals is discussed, in particular, the application of the quasi-Monte Carlo integration package QMC to the efficient calculation of multi-dimensional integrals.
One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The…
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…
Feynman integrals may be represented by the Mathematica packages AMBRE and MB as multiple Mellin-Barnes integrals. With the Mathematica package MBsums these Mellin-Barnes integrals are transformed into multiple sums.
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
In this paper we proceed to study properties of Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions. In our previous papers [Nuclear Physics B 870 (2013) 243], [Nuclear Physics B 876 (2013) 322] we showed that multi-fold…
When using the convex hull approach in the boundary modeling process, Model-Based Calibration (MBC) software suites -- such as Model-Based Calibration Toolbox from MathWorks -- can be computationally intensive depending on the amount of…
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to…
We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to…
The diagramatic Monte Carlo method has so far been primarily used in connection with the weak coupling expansion. Here we show that the strong coupling expansion offers a significant advantage: it can be efficiently implemented on both the…
Detecting the coalescences of massive black hole binaries (MBHBs) is one of the primary targets for space-based gravitational wave observatories such as LISA, Taiji, and Tianqin. The fast and accurate parameter estimation of merging MBHBs…
We observe a property of orthogonality of the Mellin-Barnes transformation of the triangle one-loop diagrams, which follows from our previous papers [JHEP {\bf 0808} (2008) 106, JHEP {\bf 1003} (2010) 051, JMP {\bf 51} (2010) 052304]. In…