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In this work we show the step by step calculations needed to quantify thecontribution of a three-loop order diagram with dihedral symmetry to theradiative corrections of the pressure in SU(2) thermal Yang-Mills theory indeconfining phase. We surveyed past developments, and performed computationsfor separate channel combinations, defined by Mandelstam variables which areconstrained by two 4-vertices. An analytically integrable approximation forhigh-temperature conditions was found, to verify the relevance of thecorrections for this diagram. A numerical analysis with Monte Carlo methods wascarried out to check the validity of such approximation, to compare it with thefull integral. A Dyson-Schwinger resummation had to be performed to alldihedral loop orders in order to control the temperature dependency found.

Pressure corrections in decoupling SU(2) Yang-Mills Theory: The case of dihedral diagrams involving both massive and massless modes