A study of Feynman integrals with uniform transcendental weights and their symbology

One-loop hexagon integral to higher orders in the dimensional regulator

Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

A nice two-loop next-to-next-to-MHV amplitude in N = 4 super-Yang-Mills

Evaluating master integrals in non-factorizable corrections to t-channel single-top production at NNLO QCD

https://link.springer.com/content/pdf/10.1007/JHEP10(2022)165.pdf

I and J

This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some algebraic properties of Hopf π-algebras as well.

Hopf π- Algebras

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and propose criteria for finding an optimal basis. This builds on experience obtained in supersymmetric field theories that can be applied successfully to generic quantum field theory integrals. It involves studying leading singularities and explicit integral representations. When the differential equations are cast into canonical form, their solution becomes elementary. The class of functions involved is easily identified, and the solution can be written down to any desired order in ϵ within dimensional regularization. Results obtained in this way are particularly simple and compact. In this Letter, we outline the general ideas of the method and apply them to a two-loop example.

/pdf/multiloop-integrals-in-dimensional-regularization-made-1vvlfm5tmq.pdf

A study of Feynman integrals with uniform transcendental weights and their symbology

Citations

One-loop hexagon integral to higher orders in the dimensional regulator

Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

A nice two-loop next-to-next-to-MHV amplitude in N = 4 super-Yang-Mills

Evaluating master integrals in non-factorizable corrections to t-channel single-top production at NNLO QCD

References

I and J

Hopf π- Algebras

Multiloop integrals in dimensional regularization made simple

Differential equations method. New technique for massive Feynman diagram calculation

Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory