We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-particle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of $Gamma_X/m_X$, with $Gamma_X$ and $m_X$ the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the $q bar{q}$ partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the na ive counting $sim Gamma_t/m_t sim 1%$. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.
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