相关论文: Evaluation of two-loop self-energy basis integrals…

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…

A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon…

We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…

In this thesis, major developments in the publicly available program SecDec are presented, extending the numerical evaluation of multi-loop multi-scale integrals from Euclidean to physical kinematics. The power of this new feature is shown…

We studied the two-loop non-factorizable Feynman diagrams for the $t$-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one…

We discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals…

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of…

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…

We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical…

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…

The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method, whose…

New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…

It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…

In the paper, we study the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for the contribution in terms of three functions, formed from the Green's function expansion…

Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal…

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

The higher-order corrections become increasingly important with experiments reaching sub-percent level of uncertainty as they look for physics beyond the Standard Model. Our goal is to address the full set of two-loop electroweak…

We study one and two-loop triangle integrals with massless propagators and all external legs off shell. We show that there is a kinematic region where the results can be expressed in terms of a basis of single-valued polylogarithms in one…

I present the two-loop self-energy functions and pole masses for fermions in an arbitrary renormalizable field theory, in the approximation that vector bosons are treated as massless. The calculations are done simultaneously in the…