Nonrelativistic effective field theory of unstable top

We develop a new nonrelativistic effective field theory of $ρ$NRQCD [1] to describe the finite lifetime effects in the threshold production of top quark-antiquark pairs. The theory is based on the expansion in a parameter $ρ=1-m_W/m_t$ characterizing the dynamics of the top-quark decay. Within this framework we compute the nonresonant contribution to the total cross section of the top quark-antiquark threshold production in electron-positron annihilation up to the next-to-next-to-leading order. Our method naturally resolves the problem of spurious divergences in the analysis of the unstable top production.

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