The Screening Mass Squared in Hot Scalar Theory to Order $g^5$ Using Effective Field Theory

We study massless $g^2{\mathrm{\Phi }}^4$-theory at high temperature and with zero chemical potential. Using modern effective field theory methods,% recently developed by Braaten and Nieto, we derive the screening mass squared to order $g^5$. It is demonstrated that the result is renormalization group invariant to this order in the coupling constant. Renormalization group methods are used to sum up leading logarithms of $g$.