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<p>The transverse-momentum-dependent (TMD) soft function for a generic hadroproduction process involving massive colored particles is analytically calculated at the one-loop level, extended to higher orders in the dimensional regulator <i>ϵ</i>. We present both the azimuthal-angle-averaged and azimuthal-angle-dependent soft functions in impact-parameter space, making them suitable for small <i>q</i><sub><i>T</i></sub> resummation calculations. Their analytic expressions are provided in terms of multiple polylogarithms. Our results offer essential ingredients for a complete higher-order perturbative calculation of the TMD soft function.</p>

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One-loop transverse-momentum-dependent soft function at higher orders in the dimensional regulator

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  • 发表日期：

    2025年6月26日

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  • Hua-Sheng Shao,
  • Guoxing Wang

摘要

The transverse-momentum-dependent (TMD) soft function for a generic hadroproduction process involving massive colored particles is analytically calculated at the one-loop level, extended to higher orders in the dimensional regulator ϵ. We present both the azimuthal-angle-averaged and azimuthal-angle-dependent soft functions in impact-parameter space, making them suitable for small qT resummation calculations. Their analytic expressions are provided in terms of multiple polylogarithms. Our results offer essential ingredients for a complete higher-order perturbative calculation of the TMD soft function.