The Gluon Propagator at High Temperature

We study the gluon propagator in Landau gauge in the deconfined phase of $SU(2)$ gauge theory. From the long-distance behaviour of correlation functions of temporal and spatial components of the gauge fields we extract electric ($m_e$) and magnetic ($m_m$) screening masses. For temperatures larger than twice $T_c$ we find no additional temperature dependence in $m_e(T)/T$, while $m_m(T)/T$ drops with increasing temperature. The decrease is consistent with the expected behaviour, $m_m(T) \sim g^2(T)T$. We find $m_e(T) = 2.484(52)T$ and $m_m(T) = 0.466(15) g^2(T) T$.