Third-order correction to top-quark pair production near threshold. Part I. Effective theory set-up and matching coefficients

This is the first in a series of two papers, in which we compute the third-order QCD corrections to top-antitop production near threshold in e⁺e⁻ collisions. The present paper provides a detailed outline of the strategy of computation in the framework of non-relativistic effective theory and the threshold expansion, applicable more generally to heavy-quark pair production near threshold. It summarizes matching coefficients and potentials relevant to the next-to-next-to-next-to-leading order and ends with the master formula for the computation of the third-order Green function. The master formula is evaluated in part II of the series.