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We develop a new nonrelativistic effective field theory of $\rho$NRQCD [1] todescribe the finite lifetime effects in the threshold production of topquark-antiquark pairs. The theory is based on the expansion in a parameter$\rho=1-m_W/m_t$ characterizing the dynamics of the top-quark decay. Withinthis framework we compute the nonresonant contribution to the total crosssection of the top quark-antiquark threshold production in electron-positronannihilation up to the next-to-next-to-leading order. Our method naturallyresolves the problem of spurious divergences in the analysis of the unstabletop production.

Nonrelativistic effective field theory of unstable top