Related papers: Methods to calculate scalar two-loop vertex diagra…
The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one- and two-loop diagrams in dimensional regularization, MSbar and on-shell renormalization schemes, decoupling of…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree…
We present the ultraviolet poles and finite terms of two-loop vertex corrections for diagrams with massive partons in the eikonal approximation. We discover and prove that the results for a set of the corrections generalize to n-loop…
We use the worldline path integral approach to the Bern-Kosower formalism for extending this formalism to the calculation of higher order corrections to N - photon scattering. The case of the two-loop QED beta-function is considered in…
In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…
We systematically analyze the $d=5$ Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop…
Two methods to reduce the CPU time needed for the numerical evaluation of cross-sections and similar quantities are discussed.
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
We introduce in typical examples new methods for the calculation of massive loop integrals appearing in the radiative correction calculations of the Standard Model.
The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a…
We present a brief review of current methods for the calculation of multi-loop amplitudes including recent developments. As an example we present the calculation of the second moment of the heavy quark current correlator and the extraction…
We present results for two-loop diagrams with massive quarks in the eikonal approximation. Explicit expressions are given for the UV poles in dimensional regularization of several of the required integrals.
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…
I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to 3 loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations…
Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The…
We present an overview of techniques developed in recent years for the efficient calculation of one-loop multiparton amplitudes, in particular those relying on unitarity and collinear factorization.
I discuss recent progress in the calculation of two-loop QCD corrections in the eikonal approximation. I present specific results for the UV structure of the corrections.
We present the first numerical computation of two-loop amplitudes based on the unitarity method. As a proof of principle, we compute the four-gluon process. We discuss the new method, analyze its numerical properties and apply it to…
We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…