Related papers: One loop integration with hypergeometric series by…

We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$ between its three propagator masses, corresponding to zeros of the associated…

We discuss topological Landau-Ginzburg theories coupled to the 2-dimensional topological gravity. We point out that the basic recursion relations for correlation functions of the 2-dimesional gravity have exactly the same form as the…

OneLOop is a program to evaluate the one-loop scalar 1-point, 2-point, 3-point and 4-point functions, for all kinematical configurations relevant for collider-physics, and for any non-positive imaginary parts of the internal squared masses.…

Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…

This paper is a review of the relationship between the metric formulation of (2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the geometry, via the theory of geometric…

We compare several parametrized analytic expressions for an arbitrary off-shell one-loop $n$-point function in scalar field theory in $D$-dimensional space-time, and show their equivalence both directly and through path-integral methods.

The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman…

A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is…

We present compact formulas for the box coefficients of the six-point NMHV one-loop amplitudes in N=8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR…

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the…

We derive the one-loop perturbative formula of the redshift-space matter power spectrum after density field reconstruction in the Zeldovich approximation. We find that the reconstruction reduces the amplitudes of nonlinear one-loop…

We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as…

In this note we consider several kind of partition functions of one-dimensional models with nearest - neighbor interactions $I_n, n\in \mathbf{Z}$ and spin values $\pm 1$. We derive systems of recursive equations for each kind of such…

We present formulas for the coefficients of 2-, 3-, 4- and 5-point master integrals for one-loop massive amplitudes. The coefficients are derived from unitarity cuts in D dimensions. The input parameters can be read off from any…

We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…

We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of…

For $a,b,p\in \mathbb{R}$, $-c\notin \mathbb{N\cup }\left\{ 0\right\} $ and $ \theta \in \left[ -1,1\right] $, let \begin{equation*} U_{\theta }\left( x\right) =\left( 1-\theta x\right) ^{p}F\left( a,b;c;x\right) =\sum_{n=0}^{\infty…

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…

We present a review of the one-loop photon ($\Pi$) and neutrino ($\Sigma$) two-point functions in a covariant and deformed $\rm U(1)$ gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor…

We analyze the one-loop correction to the three-point function coefficient of scalar primary operators in N=4 SYM theory. By applying constraints from the superconformal symmetry, we demonstrate that the type of Feynman diagrams that…