Universality of the Collins-Soper-Sterman nonperturbative function in gauge boson production

Abstract

We revise the $b_*$ model for the Collins-Soper-Sterman resummed form factor to improve description of the leading-power contribution at nearly nonperturbative impact parameters. This revision leads to excellent agreement of the transverse momentum resummation with the data in a global analysis of Drell-Yan lepton pair and Z boson production. The nonperturbative contributions are found to follow universal quasi-linear dependence on the logarithm of the heavy boson invariant mass, which closely agrees with an estimate from the infrared renormalon analysis.

Figures (4)

• Figure 1: The best-fit values of $a(Q)$ obtained in independent scans of $\chi^{2}$ for the contributing experiments. The vertical error bars correspond to the increase of $\chi^{2}$ by unity above its minimum in each $Q$ bin. The slope of the line is equal to the central-value prediction from the renormalon analysis Tafat.
• Figure 2: The best-fit $\chi^{2}$ and coefficients $a_{1}$, $a_{2}$, and $a_{3}$ in ${\mathcal{F}}_{NP}(b,Q)$ for different values of $b_{max}$, $C_{3}=b_{0}$ (stars) and $C_{3}=2b_{0}$ (squares). The size of the symbols approximately corresponds to $1\sigma$ errors for the shown parameters.
• Figure 3: Differences between the measured (Data) and theoretical (Theory) cross sections, divided by the experimental error $\delta_{exp}$ in each $(Q,q_T)$ bin. The values of $\chi^2$ for each experiment in the two fits are listed in the legend in the same order.
• Figure 4: The best-fit form factors $b\widetilde{W}(b)$ in (a) Tevatron Run-2 $Z$ boson production; (b) E605 experiment. In the E605 case, $b\widetilde{W}(b)$ are divided by the best-fit normalizations $N_{fit}$ for the E605 data, and the form factor in the Qiu-Zhang parametrization QZ for $b_{max}^{QZ}=0.3\hbox{GeV}^{-1}$ is also shown.