Related papers: Hyperspherical Integration and the Triple-Cross Ve…
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 have calculated the one-loop supersymmetric corrections to the 2 to 2 parton scattering subprocesses antiq q to antiq q, antiq q to g g, g q to g q and g g to g g, including form-factor corrections and box diagrams with internal squarks…
We review a new technique for the calculation of two-loop amplitudes and discuss as an example the fermionic contributions to e+ e- --> q qbar g.
Trivalent plane graphs are used in various areas of mathematics which relate for instance to the colored Jones polynomial, invariants of 3-manifolds and quantum computation. Their evaluation is based on computations in the Temperley-Lieb…
We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are…
We evaluate the two-photon box contribution to heavy fermion production in electron positron annihilation, that provides O(alpha^2) electromagnetic corrections to the Born cross section. The study of its non-relativistic expansion, relevant…
We present some techniques which have been developed recently or in the recent past to compute Feynman graphs beyond one-loop order. These techniques are useful to compute the three-loop splitting functions in QCD and to obtain the complete…
Hypergeometric function method is proposed to calculate the scalar integrals of Feynman diagrams. For the scalar integral of three-loop vacuum diagram with four-propagator, we verify the equivalency of Feynman parametrization and the…
The possibility of treating colour in one-loop amplitude calculations alike the other quantum numbers is briefly discussed for semi-numerical algorithms based on generalized unitarity and parametric integration techniques. Numerical results…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the…
We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the $p$-adic approximation…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to…
The elemental composition and electronic structure of materials analyzed by electron energy loss spectroscopy (EELS) are probed by the inner-shell ionization of atoms. This is a localized process that can be approximated by the scattering…
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
We extend the study of integrable structures and analyticity of the spectrum in large $N_c$ QCD$_2$ to a broad class of theories called the generalized QCD, which are given by the Lagrangian $\mathcal{L}\propto {\rm tr}\,B\wedge F- {\rm…
An algorithm for calculation of three-loop propagator diagrams in HQET, based on integration-by-parts recurrence relations, is constructed and implemented as a REDUCE package Grinder, and in Axiom.
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…