# Master integrals for four-loop massless propagators up to weight twelve

@article{Lee2011MasterIF, title={Master integrals for four-loop massless propagators up to weight twelve}, author={R. N. Lee and Alexander Valeryevich Smirnov and Vladimir A. Smirnov}, journal={Nuclear Physics}, year={2011}, volume={856}, pages={95-110} }

## 92 Citations

### Glue-and-cut at five loops

- MathematicsJournal of High Energy Physics
- 2021

We compute ε-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the…

### Recursion-free solution for two-loop vacuum integrals with “collinear” masses

- Physics, MathematicsJournal of High Energy Physics
- 2022

Abstract
We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation m1 + m2 = m3 between its three propagator masses,…

### Computation of form factors in massless QCD with finite master integrals

- Mathematics
- 2016

We present the bare one-, two-, and three-loop form factors in massless quantum chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their…

### Master integrals for all unitarity cuts of massless 4-loop propagators

- MathematicsProceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)
- 2019

Among the unitarity cuts of massless 4-loop propagators two classes have remained unknown until recently: 2-loop 3-particle cuts, and 1-loop 4-particle cuts. In this article we shall discuss the…

### Three-loop vertex integrals at symmetric point

- MathematicsJournal of High Energy Physics
- 2021

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop…

### Cutting massless four-loop propagators

- MathematicsJournal of High Energy Physics
- 2019

Among the unitarity cuts of 4-loop massless propagators two kinds are currently fully known: the 2-particle cuts with 3 loops corresponding to form-factors, and the 5-particle phase-space integrals.…

### Planar master integrals for four-loop form factors

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe present the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric…

### Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

- Physics
- 2017

A bstractWe extend the Oαs5$$ \mathcal{O}\left({\alpha}_s^5\right) $$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We…

### Forcer: a FORM program for 4-loop massless propagators

- Computer Science
- 2016

The program FORCER implements parametric reductions of the aforementioned class of Feynman integrals into a set of master integrals and can be considered as a four-loop extension of the three-loop MINCER program.

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