Related papers: A Short Note on Two-Loop Box Functions
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known…
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 discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals…
We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like $1\to 3$ decay to Minkowskian regions relevant to all $1\to 3$…
In the present paper the two and three point functions which occur at the study of the various physical processes are considered. The investigation has dan in the framework of the perturbative theory at the one loop level. The general and…
This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and…
We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…
We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All…
Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…
We show point processes generated in different ways and having different structure, presenting very similar power-law two--point correlation functions at small scales and quite different shapes at large scales.
The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The used algorithm is described and we present all results for Jordan-rank $r=2$ and $r=3$ where we make use of…
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…
We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…
We calculate the two-loop vertex function for the crossed topology, and for arbitrary masses and external momenta. We derive a double integral representation, suitable for a numerical evaluation by a Gaussian quadrature. Real and imaginary…
We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…
We investigate topological properties of simple Morse functions with 4 critical points on immersed 2-spheres. To classify such functions, dual graph of immersion and Reeb graphs is used. We have found all possible structures of the…
In two-dimensional critical loop models, including the $O(n)$ and Potts models, the spectrum is exactly known, as are a few structure constants or ratios thereof. Using numerical conformal bootstrap methods, we study $235$ of the simplest…