Related papers: New ideas for handling of loop and angular integra…
We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation.…
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
In this paper, I present a technique to simplify the tensorial reduction of one-loop integrals with arbitrary internal masses, but at least two massless external legs. By applying the method to rank l tensor integrals, one ends up with at…
In this letter, we generalize the recursion methods based on cut equations arXiv:2412.21027, originally developed for scalar theories, to gluons in pure Yang-Mills theory. In gauge theories, planar loop integrands are subtle to defined and…
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
Recent progress in the calculation of multi-loop, multi-scale diagrams is reviewed. Expansion techniques combined with new developments in Computer algebra allow to evaluate the R ratio for massive quarks up to order $\alpha_s^2$ and,…
The possibility of treating colour in one-loop amplitude calculations alike the other quantum numbers is briefly discussed for semi-numerical algorithms based on generalized unitarity and parametric integration techniques. Numerical results…
In this contribution three-loop QCD corrections to current correlators are considered. The application of the large momentum procedure, which provides a systematic expansion in $(m^2/q^2)^n$, allows the computation of terms up to $n=6$ for…
We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the…
We present the computer code RECOLA for the computation of EW and QCD amplitudes in the Standard Model at next-to-leading order. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are…
In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of $n$- and $(n-1)$-point scalar integrals that are finite in the limit of vanishing…
We construct the complete (planar and non-planar) integrand for the six-loop four-point amplitude in maximal $D\le10$ super-Yang-Mills. This construction employs new advances that combat the proliferation of diagram contributions and state…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…