On the Renormalization of Heavy Quark Effective Field Theory

The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach correctly reproduces the infrared behaviour of full QCD. Choosing a renormalization scheme in the full theory fixes the renormalization scheme in the effective theory except for the scale of the heavy quark field. Explicit formulae are given for the effective Lagrangian, and one--loop matching renormalization constants are computed for the operators of order $1/m$. Finally, the multiparticle sector of HqEFT is considered.