Related papers: A Numerical Routine for the Crossed Vertex Diagram…
We present the master integrals relevant for computing the complete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two-loops in QCD. We include corrections due to massive fermion loops…
We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum…
We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique…
We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…
We present a novel framework for computing differential cross-sections in quantum field theory using the optical theorem and loop amplitudes, circumventing the traditional method of squaring scattering amplitudes. This approach addresses…
This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…
The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman…
We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
In the paper, we obtain an expression for a two-loop master-diagram by using the Mellin$-$Barnes transformation. In the two-dimensional case we managed to factorize the answer and write it as a bilinear combination of hypergeometric…
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to…
We consider the full set of master integrals with internal top-and $W$-propagators contributing to the three-loop Higgs self-energy diagrams of order ${\mathcal O}(\alpha^2 \alpha_s)$. We split the master integrals into a system relevant to…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…