Related papers: Massive One-loop Conformal Feynman Integrals and Q…
We compute the complete set of two-loop master integrals for the scattering of four massless particles and a massive one. Our results are ready for phenomenological applications, removing a major obstacle to the computation of complete…
We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an…
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…
In this sequel calculation of the one-loop Feynman integral pertaining to a massive box diagram contributing to the photon-photon scattering amplitude in quantum electrodynamics, we present the six solutions as yet unknown in the…
We study the differential equations that follow from Yangian symmetry which was recently observed for a large class of conformal Feynman graphs, originating from integrable `fishnet' theories. We derive, for the first time, the explicit…
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…
This review covers a number of applications of conformal field theory methods for perturbative calculations in N=4 Super Yang-Mills and ABJM theory. After motivating the role of superconformal symmetry for elementary particle physics…
We propose a bootstrap program for the {\it form factor squared} with operator ${\rm tr}(\phi^2)$ in maximally supersymmetric Yang-Mills theory in the planar limit, which plays a central role for perturbative calculations of important…
We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria…
We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…
Within the non-perturbative 1/N expansion, we discuss numerical methods for calculating multi-loop Feynman graph needed to derive physical scattering amplitudes. We apply higher order 1/N methods to the scalar sector of the standard model,…
We present significant evidence that the powerful property of Yangian invariance extends to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an…
Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The…
We present analytic techniques for parametric integrations of massive two-loop four-point Feynman integrals at high energies, and their implementation in the toolbox AsyInt. In the high-energy region, the Feynman integrals involving…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (aka the ``Operatope''). We derive a…
We consider super Yang-Mills Theory in $N=1$ conformal supergravity. Using the background field method and the Feddeev-Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat…
Building upon the algebraic consistency construction of one-loop Bern-Carrasco-Johansson (BCJ) numerators for Yang-Mills (YM) and Yang-Mills-scalar (YMS) theories, we explore the expansion formula of one-loop Einstein-Yang-Mills (EYM)…
The "old" conformal bootstrap was originally formulated by Migdal and Polyakov (MP) as a method for calculating conformal dimensions self-consistently. In this work we revisit the MP bootstrap and apply efficient multi-loop Feynman integral…