Related papers: New representation of the two-loop crossed vertex …
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with…
In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…
I present calculations of two-loop vertex corrections with massive and massless partons in the eikonal approximation. I show that the $n$-loop result for the UV poles can be given in terms of the one-loop calculation.
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…
The one-loop HQET heavy-heavy vertex diagram with arbitrary powers of all three denominators and arbitrary residual energies is investigated. Various particular cases in which the result becomes simpler are considered.
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the…
The method introduced in a previous paper to simplify the tensorial reduction in multi-leg loop calculations is extended to generic one-loop integrals, with arbitrary internal masses and external momenta.
Lax representation in terms of $2\times 2$ matrices is constructed for a separable multiply--periodic system splitting on two tori. Hyperelliptic Kleinian functions and their reduction to elliptic functions are used.
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric…
Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…
We present results for two-loop diagrams with massive quarks in the eikonal approximation. Explicit expressions are given for the UV poles in dimensional regularization of several of the required integrals.
We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions…
Partition functions of some two-dimensional statistical models can be represented by means of Grassmann integrals over loops living on two-dimensional torus. It is shown that those Grassmann integrals are topological invariants, which…