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In this talk we show that dual conformal symmetry has unexpected applications to Feynman integrals in dimensional regularization. Outside $4$ dimensions, the symmetry is anomalous, but still preserves the unitarity cut surfaces. This…
We present analytic results on physical kinematics for four integral families that are relevant to the production of two off-shell vector bosons with different masses. Our study consists of a ladder-box, a tennis-court, and two reducible…
The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…
In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…
Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…
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 report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD…
We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…
This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on…
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…
We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal massive fermion loop and is known to contain…
We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop 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…
Singularities hidden in the collinear region around an external massless leg may lead to conformal symmetry breaking in otherwise conformally invariant finite loop momentum integrals. For an $\ell$-loop integral, this mechanism leads to a…
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 report on the three-loop unpolarized and polarized massive operator matrix elements, with single- and two-mass corrections, and the associated deep-inelastic massive Wilson coefficients in the region $Q^2 \gg m_Q^2$, the calculation of…
We provide a complete classification of the Feynman-integral geometries at two-loop order in four-dimensional Quantum Field Theory with standard quadratic propagators. Concretely, we consider a finite basis of integrals in the 't…
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…
Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle,…