Six-loop renormalization-group equations for the 22 basis invariants of the 2HDM scalar potential are derived with invariant theory and Groebner bases, including the 63 minimal syzygies.
General Quartic $\beta$-Function at Three Loops
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abstract
We determine the three-loop $\overline{\text{MS}}$ quartic $ \beta $-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ \beta $-function is compared to known $ \beta $-functions for specific theories to fix all coefficients. Three-loop $ \beta $-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.
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On the scalar sector of 2HDM: ring of basis invariants, syzygies, and six-loop renormalization-group equations
Six-loop renormalization-group equations for the 22 basis invariants of the 2HDM scalar potential are derived with invariant theory and Groebner bases, including the 63 minimal syzygies.