FMFT: Fully Massive Four-loop Tadpoles

We present FMFT - a package written in FORM that evaluates four-loop fully massive tadpole Feynman diagrams. It is a successor of the MATAD package that has been successfully used to calculate many renormalization group functions at three-loop order in a wide range of quantum field theories especially in the Standard Model. We describe an internal structure of the package and provide some examples of its usage.Comment: Available for download from https://github.com/apik/fmft

Three-loop SM beta-functions for matrix Yukawa couplings

We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken phase of the SM with the help of the MINCER program in a general linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition, ambiguities in Yukawa matrix beta-functions are studied.Comment: 9 pages, references added, version accepted by PL

Three-loop vertex integrals at symmetric point

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 $\varepsilon$-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.Comment: 14 pages, many figure

Three-loop Higgs self-coupling beta-function in the Standard Model with complex Yukawa matrices

Three-loop renormalization group equations for the Higgs self-coupling and Higgs mass parameter are recalculated in the case of complex Yukawa matrices, which encompass general flavour structure of the Standard Model. In addition, the anomalous dimensions both for the quantum Higgs field and its vacuum expectation value are presented in the $\overline{MS}$-scheme. A numerical study of the latter quantities is carried out for a certain set of initial parameters.Comment: 14 pages, 2 figures, report numbers added, figures redraw

Three-loop massive tadpoles and polylogarithms through weight six

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.Comment: 26 pages, 4 ancillary files, v3: version published in JHEP: minor additions, file with results for massive three-loop form-factor integrals adde