Related papers: Evaluating massive planar two-loop tensor vertex i…
I present calculations of two-loop vertex corrections with massive and massless partons in the eikonal approximation. I show that the $n$-loop result for the UV poles can be given in terms of the one-loop calculation.
We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine…
For Z -> b bbar, we calculate all the two-loop top dependent Feynman graphs, which have mixed QCD and electroweak contributions that are not factorizable. For evaluating the graphs, without resorting to a mass expansion, we apply a two-loop…
Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can…
In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…
We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals,…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…
We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All…
We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
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 determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard lines include an arbitrary mass scale. The…
Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…
New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various…
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, $d=d_\parallel+d_\perp$, being $d_\parallel$ the dimension of the parallel space spanned by the legs of the…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
We present GLoop, a Fortran90 computational framework that allows one to compute by Monte Carlo a certain class of higher-loop integrals in terms of lower-loop building blocks. This is based on a recently introduced method that enables the…