We investigate the invariant-mass distribution of top-quark pairs near the $2m_t$ threshold, which has strong impact on the determination of the top-quark mass $m_t$. We show that higher-order non-relativistic corrections lead to large contributions which are not included in the state-of-the-art theoretical predictions. We derive a factorization formula to resum such corrections to all orders in the strong-coupling, and calculate necessary ingredients to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numeric results. We find that the resummation effect significantly enhances the differential cross section in the threshold region, and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of $m_t$ will lead to a value closer to the result of direct measurement.

中文翻译：

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顶夸克对的不变质量分布和顶夸克质量测定

我们研究了接近 $2m_t$ 阈值的顶夸克对的不变质量分布，这对顶夸克质量 $m_t$ 的确定有很大影响。我们表明，高阶非相对论校正会导致大量贡献，而这些贡献并未包含在最先进的理论预测中。我们推导出一个分解公式来恢复对强耦合中所有阶的这种修正，并计算必要的成分以在次领先的功率下执行恢复。我们将求和与固定顺序结果相结合，并呈现与现象学相关的数值结果。我们发现求和效应显着增强了阈值区域的微分截面，使理论预测与实验数据更加兼容。