Related papers: Factorizing two-loop vacuum sum-integrals
This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…
We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals…
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.…
We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each…
We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…
We develop a procedure for re-summing the large logarithms induced in gravity by loops of inflationary scalars. We first show how the scalar can be integrated out of the field equations in the presence of constant graviton field. We then…
General algorithms for tensor reduction of two-loop massive vacuum diagrams are discussed. Some explicit useful formulae are presented.
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…
This paper discusses the methods and the results used in an accompanying paper describing the matching of effective chiral Lagrangians in dimensional and lattice regularizations. We present methods to compute 2-loop massless sunset diagrams…
We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby…
The study of QCD scattering amplitudes in the collinear regime provides crucial insight into the factorization properties of hadronic cross sections. In this paper, we present the first complete results for two-loop spacelike splitting…
We discuss the two-loop integrals necessary for evaluating massless 2 to 2 scattering amplitudes. As a test process, we consider the leading colour two-loop contribution to qqbar to q'qbar'. We show that for physical scattering processes…
We complete the QCD sum rule analysis of the Isgur Wise form factor $\xi(v\cdot v')$ at next-to-leading order in renormalization-group improved perturbation theory. To this end, the exact result for the two-loop corrections to the…
The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small…
Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
We study the singularity structure of two-loop QED amplitudes for the production of multiple off-shell photons in massless electron-positron annihilation and develop counterterms that remove their infrared and ultraviolet divergences point…
We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…
We give technical details about the computational strategy employed in a recently completed investigation of the four-loop QCD free energy. In particular, the reduction step from generic vacuum bubbles to master integrals is described from…
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…