Related papers: 2-loop Integrals in the Standard Model
We present a review of the Bielefeld-Dubna activities on multiloop calculations.
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
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 obtain a closed form effective potential at the one-loop level of a Two Higgs Doublet Model. Through the loop expansion we reproduce the expression presented by Weinberg and Coleman, showing explicitly every step involved in the…
We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.
Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal…
We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $\gamma_5$ and derive results in the M-scheme.10
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
We review algorithmic methods for two-loop calculations in HQET, and the analogous methods for on-shell QCD, needed for matching HQET to QCD.
We transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (1e-15). We also use the…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…
The integral of an arbitrary two-loop modular graph function over the fundamental domain for $SL(2,Z)$ in the upper half plane is evaluated using recent results on the Poincar\'e series for these functions.
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 calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are…
We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations…
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the…
We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to $\Pep\Pem\to4 $fermions. In particular, the…