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arXiv · hep-ph/9811340

$k_T$ and threshold resummations

Hsiang-nan Li
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Abstract

We demonstrate that both the $k_T$ and threshold resummations can be performed in the Collins-Soper resummation formalism by evaluating soft gluon emissions with infrared cutoffs for the longitudinal and transverse loop momenta, respectively. The reason the $k_T$ resummation for a parton distribution function leads to suppression in the large $b$ region, $b$ being the conjugate variable of parton transverse momentum $k_T$, and the threshold resummation leads to enhancement in the large $N$ limit, $N$ being the moment of a distribution function, is a consequence of opposite directions of double-logarithm evolutions. The $k_T$ and threshold resummations for an energetic final-state jet give suppression. The switch of the threshold resummation from enhancement to suppression is attributed to a nonvanishing jet invariant mass. In the same framework we derive a unification of the $k_T$ and threshold resummations for a parton distribution function by requiring infrared cutoffs for both longitudinal and transverse loop momenta. This unified resummation exhibits suppression at large $b$, similar to the $k_T$ resummation, and exhibits enhancement at small $b$, similar to the threshold resummation.

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Hsiang-nan Li. 1999-07-08. $k_T$ and threshold resummations. https://arxiv.org/abs/hep-ph/9811340

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