Quark effective theory at large orders in 1/m

The existing derivations of a heavy quark effective theory (HQET) are presented from a unified point of view. It is shown that a correct normalization of the heavy quark field in the effective theory is crucial for making explicit the mass dependence of the matrix elements. A possible variant of HQET which satisfies this requirement and which is constructed from a sequence of Foldy-Wouthuysen transformations is presented. The renormalization of the resulting effective Lagrangian to order 1/m² is performed including also effects arising from vacuum polarization.