Related papers: Evaluating double and triple (?) boxes
We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this…
We present a map between the tree-level Standard Model Effective Theory (SMEFT) in the Warsaw basis and massive on-shell amplitudes. As a first step, we focus on the electroweak sector without fermions. We describe the Feynman rules for a…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…
We evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus…
We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…
The parametric representation has been used since a long time for the evaluation of Feynman diagrams. As a dimension independent intermediate representation, it allows a clear description of singularities. Recently, it has become a choice…
Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the…
We study one and two-loop triangle integrals with massless propagators and all external legs off shell. We show that there is a kinematic region where the results can be expressed in terms of a basis of single-valued polylogarithms in one…
We show some examples of calculations of massless and massive Feynman integrals.
A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our…
Evaluation of a wide variety of Feynman diagrams with multi-loop integrals and physical parameters and its comparison with high energy experiments are expected to investigate new physics beyond the Standard Model. We have been developing a…
We express a toy model of the ten-point elliptic double-box, first characterized in arXiv:1712.02785, in terms of elliptic polylogarithms. This toy model corresponds to a particular unphysical limit of the elliptic double-box in which it…
Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid state physics, asymptotic theory, etc. Although MB…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…
In the current paper, we construct a Lorentz-violating electrodynamics in (1+2) spacetime dimensions from the electromagnetic sector of the nonminimal Standard-Model Extension (SME) in (1+3) dimensions. Subsequently, we study some of the…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
The well-known $D$-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be…