## Three-loop vertex integrals at symmetric point.(English)Zbl 1466.81047

Summary: 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 level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the $$\epsilon$$-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

### MSC:

 81S40 Path integrals in quantum mechanics 81T17 Renormalization group methods applied to problems in quantum field theory 81T25 Quantum field theory on lattices 81V05 Strong interaction, including quantum chromodynamics

### Keywords:

lattice QCD; renormalization group

### Software:

Reduze; pySecDec; Mincer; epsilon; FORM ; HyperInt
Full Text:

### References:

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