Related papers: Evaluating massive planar two-loop tensor vertex i…
We consider two-loop corrections to $2\to 2$ scattering processes with massive particles in the final state and massive particles in the loop. We discuss the combination of analytic expansions in the high-energy limit and for small…
We present a method to calculate to very high precision the coefficients of the divergences occuring in two-loop diagrams for a massive scalar field on the lattice. The approach is based on coordinate space techniques and extensive use of…
We report on the three-loop unpolarized and polarized massive operator matrix elements, with single- and two-mass corrections, and the associated deep-inelastic massive Wilson coefficients in the region $Q^2 \gg m_Q^2$, the calculation of…
Two-loop electroweak corrections to the muon anomalous magnetic moment are automatically calculated by using GRACE-FORM system, as a trial to extend our system for two-loop calculation. We adopt the non-linear gauge (NLG) to check the…
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 discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…
In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate…
Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented, concerning the evaluation of the…
Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop…
We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop…
We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…
An automatic system to calculate two loop weak corrections to muon anomalous magnetic moment is discussed. Diagrams are classified into eight types, according to their topology. Adopting Civitanovi\'c-Kinoshita representation of Feynman…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
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…
In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless…
Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large…
We consider the three-loop mixed strong-electroweak (${\mathcal{O}}(\alpha \alpha_s^2)$) corrections to the quark form factor. We compute the master integrals which are appearing in the Feynman diagrams containing a single massive boson in…
Multi-loop scattering amplitudes are difficult to evaluate due to singularities of the integrals involved, especially with increasing number of loops, external legs, and mass scales. For the first time for hadronic collisions at two loops,…