Related papers: The massless higher-loop two-point function
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…
Several powerful techniques for evaluating massless scalar Feynman diagrams are developed, viz: the solution of recurrence relations to evaluate diagrams with arbitrary numbers of loops in $n=4-2\omega$ dimensions; the discovery and use of…
As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…
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…
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…
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…
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 propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The…
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…
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 consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…
Three-point vertex diagram plays a key role in the whole renormalization program of several QFT (quantum field theory) models such as QED, QCD, the Standard Model of eletroweak interactions and so forth. The exact analytic result for the…
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…