Related papers: Numerical integration of subtraction terms
In this thesis the two-particle-irreducible (2PI) formalism is investigated with several applications, particular emphasis on renormalizability. In the O(N) symmetric scalar quantum field theory formulated with auxiliary fields it is…
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss…
Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon…
For general two-electron two-centre integrals over Slater-type orbitals (STOs), the use of the Neumann expansion for the Coulomb interaction potential yields infinite series in terms of few basic functions. In many important cases the…
We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…
We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…
Experience with core-collapse supernova simulations shows that accurate accounting of total particle number and 4-momentum can be a challenge for computational radiative transfer. This accurate accounting would be facilitated by the use of…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
In this talk we describe a procedure for isolating the infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. We use the antenna subtraction framework which has been successfully applied to the…
We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
We report on our recent progress towards including the photon fragmentation contribution in next-to-next-to-leading order (NNLO) QCD predictions for photon production cross sections. This extension to previous NNLO calculations requires the…
We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the…
We suggest improvements for double counting subtraction scheme, which is needed for the consistent treatment of real corrections in the high-energy limit, and apply it to the single photon production at the NLO${}^\star$ approximation of…
In the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order, one approach is to perform all of the integrations, including the virtual loop integration numerically. One would use a…
Multi-loop scattering amplitudes are difficult to evaluate due to singularities of the integrals involved, especially with increasing number of loops, external legs, and mass scales. For the first time for hadronic collisions at two loops,…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…