Related papers: The on-shell massless planar double box diagram wi…
The method of Mellin-Barnes representation is used to calculate dimensionally regularized massive on-shell double box Feynman diagrams contributing to Bhabha scattering at two loops.
We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations…
The dimensionally regularized massless on-shell double box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t. An explicit result is expressed either in…
The non-planar Feynman diagram with seven massless, scalar propagators and four on-shell legs (the crossed double box) is calculated analytically in dimensional regularization. The non-planar diagram with six propagators is also discussed.
The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the…
Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle…
A brief review of recent results on analytical evaluation of double-box Feynman integrals is presented. First steps towards evaluation of massless on-shell triple-box Feynman integrals within dimensional regularization are described. The…
The dimensionally regularized master planar double box Feynman diagram with four massive and three massless lines, powers of propagators equal to one, all four legs on the mass shell, i.e. with p_i^2=m^2, i=1,2,3,4, is analytically…
The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically…
A method is presented for obtaining the $\epsilon$-expansion for on-shell massless scalar double-box diagram.
A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations…
The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive…
The dimensionally regularized massless double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with non-zero q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for…
The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic propagator powers are expressed in terms of linear combinations of multiple hypergeometric series of the generalized Horn type. These results…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to…