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arXiv · 2506.23791

Analytic NNLO transverse-momentum-dependent soft function for heavy quark pair hadroproduction at threshold

Hua-Sheng Shao·Guoxing Wang
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Abstract

The transverse-momentum-dependent (TMD) soft function for non-relativistic heavy quark pair production at hadron colliders is analytically computed at next-to-next-to-leading order (NNLO) in the strong coupling expansion. We present the details of our computational approach and analyze the general two-loop structure of the soft function. The final result, which takes a particularly simple form, provides the last missing ingredient for a complete NNLO calculation of color-octet $S$-wave quarkonium hadroproduction--including charmonium, bottomonium, and toponium--using the $q_T$-slicing formalism. It also enables next-to-next-to-next-to-leading-logarithmic (N$^3$LL) resummation at small transverse momentum for the same process.

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Hua-Sheng Shao, Guoxing Wang. 2025-06-30. Analytic NNLO transverse-momentum-dependent soft function for heavy quark pair hadroproduction at threshold. https://doi.org/10.1007/jhep10(2025)164

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