Four loop vacuum energy density of the SU(N(c)) + adjoint Higgs theory

Kajantie K, Laine M, Rummukainen K, Schroeder Y. Four loop vacuum energy density of the SU(N(c)) + adjoint Higgs theory. JHEP. 2003;304:036: 036.We compute the dimensionally regularised four-loop vacuum energy density of the SU(N_c) gauge + adjoint Higgs theory, in the disordered phase. ``Scalarisation'', or reduction to a small set of master integrals of the type appearing in scalar field theories, is carried out in d dimensions, employing general partial integration identities through an algorithm developed by Laporta, while the remaining scalar integrals are evaluated in d = 3 - 2\epsilon dimensions, by expanding in \epsilon << 1 and evaluating a number of coefficients. The results have implications for the thermodynamics of finite temperature QCD, allowing to determine perturbative contributions of orders O(g^6 ln(1/g)), O(g^6) to the pressure, while the general methods are applicable also to studies of critical phenomena in QED-like statistical physics systems