Screening Masses and Improvement in Pure SU(2) Lattice Gauge Theory at High Temperatures

The high temperature plasma phase of QCD is characterized by the occurrence of chromoelectric and -magnetic screening masses (me and mm) which control the infrared behaviour of the theory [1]. It has been known for a long time that the lowest order perturbative result for the electric mass in pure gauge theory is me,0(T ) = √ Nc/3 g(T )T . This is sufficient to cure infrared divergences of O(gT ). The magnetic mass is known to be entirely of non-perturbative origin, as all orders in perturbation theory would contribute equally. However, a dependence of the form mm ∼ O(gT ) is widely believed and would cure the higher order infrared divergences of O(gT ). If one finds indeed mm 6= 0, than mm contributes in next-to-leading order perturbation theory to me [2], me(T ) = m 2 e,0 (1+ √ 6 2π g(T ) me me,0 [ log 2me mm − 1 2 ] +O(g) )