W and Z transverse momentum distributions: resummation in qT-space

TL;DR

The paper develops a resummation framework for $W$ and $Z$ transverse momentum distributions directly in $q_T$-space using an extended DDT formula, aiming to unify small- and large-$q_T$ behavior while avoiding $b$-space pathologies. By carefully choosing the $q_T$-space Sudakov coefficients, the method matches the conventional $b$-space results up to ${\cal O}(\alpha_S^2)$ and provides a practical non-perturbative extension via $q_T^*$ and $\tilde F^{NP}$. It demonstrates close agreement with $b$-space predictions in the perturbative region, and introduces flexible modeling (non-perturbative and optional smearing) to describe the low-$q_T$ regime. The approach offers a robust, perturbatively consistent alternative to the $b$-space formalism with explicit matching to fixed-order results and a straightforward numerical implementation.

Abstract

We describe an alternative approach to the prediction of W and Z transverse momentum distributions based on an extended version of the DDT formula. The resummation of large logarithms, mandatory at small qT, is performed in qT-space, rather than in the impact parameter b. The leading, next-to-leading and next-to-next-to-leading towers of logarithms are identical in the b-space and qT-space approaches. We argue that these terms are sufficient for W and Z production in the region in which perturbation theory can be trusted. Direct resummation in qT-space provides a unified description of vector boson transverse momentum distributions valid at both large and small qT.

Figures (10)

• Figure 1: Comparison of the $b$-space $d\sigma /d q_{\hbox{\tiny T}}$ distribution for $W^++W^-$ production at $\sqrt{S}=1.8{\;\rm TeV}$ with ${\cal O}(\alpha_S)$ perturbative calculation. The resummation results were obtained with pure gaussian ($g= 3.0{\;\rm GeV}^2,b_{\;\rm lim}= 0.5{\;\rm GeV}^{-1}$) form of $F^{NP}$. We assumed $BR(W\rightarrow e\nu) = 0.111$.
• Figure 2: $F^{(b)}(q_{\hbox{\tiny T}})$ for the two different choices of the non-perturbative function.
• Figure 3: Form factors $F^{(b)}$, $F^{(q_{\hbox{\tiny T}})}$ and $F^{(p)}$. The $b$-space results were obtained with an effective gaussian form of $F^{NP}$ ($g = 3.0{\;\rm GeV}^2,b_{\;\rm lim}=0.5{\;\rm GeV}^{-1}$).
• Figure 4: The $q_{\hbox{\tiny T}}$-space form factor $F^{(q_{\hbox{\tiny T}})}$ calculated with $B^{(2)}$ and $\tilde{B}^{(2)}$.
• Figure 5: Comparison of various theoretical predictions for $W^++W^-$$d\sigma /d q_{\hbox{\tiny T}}$ with CDF data CDFW. The $b$-space results were obtained with an effective gaussian form of $F^{NP}$ ($g = 3.0{\;\rm GeV}^2,b_{\;\rm lim}=0.5{\;\rm GeV}^{-1}$). We assumed $BR(W\rightarrow e\nu) = 0.111$.