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We study the role of the threshold variable in soft-gluon thresholdresummation. We focus on the computation of the resummed total cross section,the final-state invariant-mass distribution, and transverse-momentumdistribution of the Higgs boson when produced in association with atop-anti-top quark pair for the Large Hadron Collider operating at 13 TeV. Weshow that different choices for the threshold variable result in differences atnext-to-leading power, i.e. contributions that are down by one power of thethreshold variable. These contributions are noticeable numerically, althoughtheir effect on the resummed observables lies within the scale uncertainty ofthose observables. The average central results, obtained after combiningseveral central-scale choices, agree remarkably well for different choices ofthe threshold variable. However, different threshold choices do effect theresulting scale uncertainty. To compute our results, we introduce a novelnumerical method that we call the deformation method, which aids thestabilization of the inverse Mellin transform in cases where the analyticalMellin transform of the partonic cross section is unknown. We show that thismethod leads to a factor of 10 less function evaluations, while gaining afactor of 4-5 in numerical precision when compared to the standard method.

The role of the threshold variable in soft-gluon resummation of the $t\bar{t}h$ production process