Related papers: Differential Equations for the 2-Loop Equal Mass S…

Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…

This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…

We consider electroweak radiative corrections to hard inclusive processes at the TeV scale, and we investigate how collinear logarithms factorize in a spontaneously broken gauge theory, similarly to the DGLAP analysis in QCD. Due to the…

We use mixed Hodge structures to investigate Feynman amplitudes as functions of external momenta and masses.

We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point. We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link…

This paper describes Sunrise, a parallel, free Monte-Carlo code for the calculation of radiation transfer through astronomical dust. Sunrise uses an adaptive-mesh refinement grid to describe arbitrary geometries of emitting and…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous…

We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…

We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…

To study the convergence of the loop expansion at the high-temperature electroweak phase transition, we calculate the 2-loop effective potential of the 3d SU(2)-Higgs model in a general covariant gauge. We find that the loop expansion…

We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…

We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of…

We present exact results, at next-to-leading order in renormalization-group improved perturbation theory, for the Wilson coefficients appearing at order 1/m_Q in the heavy-quark expansion of heavy-light current operators. To this end, we…

A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with…

We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…

A method is presented for using coherent vectors to calculate the explicit form of Schur polynomials which are the coefficients of Laurent expansion of a vertex operator.

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that…

For a three-dimensional higher-derivative scalar superfield model, and a four-dimensional higher-derivative chiral superfield model, where which the higher-derivative operators are described by polynomials of arbitrary degrees, we…