New Fits for the Non-Perturbative Parameters in the CSS Resummation Formalism

TL;DR

This work refines the Collins–Soper–Sterman non-perturbative component in the CSS resummation formalism by fitting two- and three-parameter models to low-energy Drell–Yan data, extracting $g_1$, $g_2$, and $g_3$ with quantified uncertainties. The study demonstrates that both parametrizations provide good descriptions of existing data and emphasizes the potential of Tevatron Run 1 $Z$ data to test universality and constrain the $Q$- and $x$-dependence of the non-perturbative function. It also shows that a single effective parameter can describe the $W$ transverse momentum at low $Q_T$, but universality tests and future collider predictions require the full $Q$ and possibly $x$ dependence. The results advance precision predictions for $W/Z$ $Q_T$ spectra and offer a pathway to validate the universal non-perturbative input in hadron collider phenomenology.

Abstract

We update the non-perturbative function of the Collins-Soper- Sterman resummation formalism in hadron collisions. Two functional forms in impact parameter space are considered, one with a pure Gaussian form with two parameters and the other with an additional linear term. The results for the two parameter fit are found to be g1=0.24+0.08-0.07 GeV^2, g2=0.34+0.07-0.08 GeV^2. The results for the three parameter fit are g1=0.15+004-0.03 GeV^2, g2=0.48+0.07-0.05 GeV^2, and g3=-0.58+0.26-0.20 GeV^-1. We discuss the potential for the full Tevatron Run I Z boson data for further testing of the universality of the non-perturbative function.

Figures (10)

• Figure 1: R209 data, from $p+p \rightarrow \mu^+ \mu^- +X$ at $\sqrt{S}=62$ GeV, with an overall systematic normalization error of $10\%$. The curves are the results of Fit $A_2$ and $A_3$ and are multiplied by the value of NORM, as shown in the figure and described in the text.
• Figure 2: Comparison of $4\,{\rm pb}^{-1}$ CDF-$Z$ data at the Tevatron with two different theory model predictions. The dots correspond to the results of Fit $A_2$ and $A_3$.
• Figure 3: E605 data, from $p+Cu \rightarrow \mu^+ \mu^- +X$ at $\sqrt{S}=38.8$ GeV, with an overall systematic normalization error of $15\%$. The curves are the results of Fit $A_2$ and $A_3$ and are multiplied by the value of NORM, as shown in the figure and described in the text.
• Figure 4: The error ellipse on the $g_1$ and $g_2$ plane from which the errors of the 2-parameter fit $A_2$ were interpreted.
• Figure 5: The error ellipse projections from which the errors of the 3-parameter fit $A_3$ were interpreted. (a) $g_1$ and $g_2$ plane, (b) $g_2$ and $g_3$ plane, and (c) $g_1$ and $g_3$ plane.