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Role of the nonperturbative input in QCD resummed Drell-Yan $Q_T$-distributions

Jianwei Qiu, Xiaofei Zhang

TL;DR

This work analyzes how nonperturbative input affects Collins–Soper–Sterman $b$-space resummation for Drell–Yan $Q_T$ distributions and quantifies the predictive power across energies. It introduces a dynamical power-correction extrapolation that preserves perturbative small-$b$ physics while modeling large-$b$ nonperturbative effects, and shows that collider energies (via small-$x$ evolution) greatly enhance predictive power for $W/Z$ production with $Q_T\le Q$. At fixed-target energies, power corrections become crucial to describe data, and a two-parameter fit to low-energy Drell–Yan data demonstrates the necessity and significance of these nonperturbative contributions. The framework yields excellent agreement with collider data and provides a robust, physically interpretable description that extends to Higgs production at the LHC.

Abstract

We analyze the role of the nonperturbative input in the Collins, Soper, and Sterman (CSS)'s $b$-space QCD resummation formalism for Drell-Yan transverse momentum ($Q_T$) distributions, and investigate the predictive power of the CSS formalism. We find that the predictive power of the CSS formalism has a strong dependence on the collision energy $\sqrt{S}$ in addition to its well-known $Q^2$ dependence, and the $\sqrt{S}$ dependence improves the predictive power at collider energies. We show that a reliable extrapolation from perturbatively resummed $b$-space distributions to the nonperturbative large $b$ region is necessary to ensure the correct $Q_T$ distributions. By adding power corrections to the renormalization group equations in the CSS formalism, we derive a new extrapolation formalism. We demonstrate that at collider energies, the CSS resummation formalism plus our extrapolation has an excellent predictive power for $W$ and $Z$ production at all transverse momenta $Q_T\le Q$. We also show that the $b$-space resummed $Q_T$ distributions provide a good description of Drell-Yan data at fixed target energies.

Role of the nonperturbative input in QCD resummed Drell-Yan $Q_T$-distributions

TL;DR

This work analyzes how nonperturbative input affects Collins–Soper–Sterman -space resummation for Drell–Yan distributions and quantifies the predictive power across energies. It introduces a dynamical power-correction extrapolation that preserves perturbative small- physics while modeling large- nonperturbative effects, and shows that collider energies (via small- evolution) greatly enhance predictive power for production with . At fixed-target energies, power corrections become crucial to describe data, and a two-parameter fit to low-energy Drell–Yan data demonstrates the necessity and significance of these nonperturbative contributions. The framework yields excellent agreement with collider data and provides a robust, physically interpretable description that extends to Higgs production at the LHC.

Abstract

We analyze the role of the nonperturbative input in the Collins, Soper, and Sterman (CSS)'s -space QCD resummation formalism for Drell-Yan transverse momentum () distributions, and investigate the predictive power of the CSS formalism. We find that the predictive power of the CSS formalism has a strong dependence on the collision energy in addition to its well-known dependence, and the dependence improves the predictive power at collider energies. We show that a reliable extrapolation from perturbatively resummed -space distributions to the nonperturbative large region is necessary to ensure the correct distributions. By adding power corrections to the renormalization group equations in the CSS formalism, we derive a new extrapolation formalism. We demonstrate that at collider energies, the CSS resummation formalism plus our extrapolation has an excellent predictive power for and production at all transverse momenta . We also show that the -space resummed distributions provide a good description of Drell-Yan data at fixed target energies.

Paper Structure

This paper contains 12 sections, 41 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Collins-Soper-Sterman Formalism
  3. Extrapolation to the Large $b$ Region
  4. Extrapolation proposed by Collins, Soper, and Sterman
  5. Extrapolation with dynamical power corrections
  6. Corrections from parton's intrinsic transverse momentum
  7. Extrapolation to low $Q^2$
  8. Numerical Results and Conclusions
  9. Numerical accuracy
  10. $Q_T$ distributions of $W$ and $Z$ production
  11. Drell-Yan $Q_T$ distributions at low energies
  12. Conclusions

Figures (15)

  • Figure 1: (a) Integrand of the $b$-integration in Eq. (\ref{['css-W-F']}) at $Q_T=0$ and $Q=6$ GeV as a function of $b$ with an arbitrary normalization at Tevatron energy; (b) the first (solid) and second (dashed) terms in Eq. (\ref{['saddle']}) as a function of $b$ at the same $Q$ and $\sqrt{S}$.
  • Figure 2: (a) Integrand of the $b$-integration in Eq. (\ref{['css-W-F']}) at $Q_T=0$ and $Q=M_Z$ as a function of $b$ with an arbitrary normalization at Tevatron energy ($\sqrt{S}=1.8$ TeV); (b) the first (solid) and second (dashed) terms in Eq. (\ref{['saddle']}) as a function of $b$ at the same $Q$ and $\sqrt{S}$.
  • Figure 3: (a) Integrand of the $b$-integration in Eq. (\ref{['css-W-F']}) at $Q_T=0$ and $Q=M_Z$ as a function of $b$ with an arbitrary normalization at the LHC energy ($\sqrt{S}=14$ TeV); (b) the first (solid) and second (dashed) terms in Eq. (\ref{['saddle']}) as a function of $b$ at the same $Q$ and $\sqrt{S}$.
  • Figure 4: (a) Integrand of the $b$-integration in Eq. (\ref{['css-W-F']}) at $Q_T=0$ and $Q=6$ GeV as a function of $b$ with an arbitrary normalization at E288 energy ($\sqrt{S}=27.4$ GeV); (b) the first (solid) and second (dashed) terms in Eq. (\ref{['saddle']}) as a function of $b$ at the same $Q$ and $\sqrt{S}$.
  • Figure 5: Integrand of the $b$-integration in Eq. (\ref{['css-W-F']}) at $Q_T=1$ GeV (solid line) and $Q_T=2$ GeV (dashed line) as a function of $b$ with an arbitrary normalization. The $Q$ and $\sqrt{S}$ are the same as those in Fig. \ref{['fig4']}(a).
  • ...and 10 more figures