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Perturbative and Nonperturbative Effects in Transverse Momentum Generation

Erik Thomé

TL;DR

This thesis analyzes how perturbative parton branchings and nonperturbative primordial $k_{ obreakot}$ shape the transverse momentum $p_{ obreakot}$ of color-singlet states in hadronic collisions, focusing on Z$^0$ production. By testing corrections to pure DGLAP evolution in \\textsc{Pythia}—including angular ordering, the $\hat u<0$ constraint, and a shift to $\alpha_s(p_{ obreakot}^2)$—the study estimates how much $\Lambda_{ ext{QCD}}$ must be raised to compensate for slower evolution, and examines how this impacts $p_{ obreakot}$ spectra and primordial $k_{ obreakot}$. A new shower algorithm ordering branchings in $p_{ obreakot}^2$ is introduced, yielding spectra that are less sensitive to primordial $k_{ obreakot}$ and offering comparable fits to data under certain parameter choices ($\Lambda_{ ext{QCD}} \approx 0.19 ext{--}0.20$ GeV; $k_{ obreakot} \approx 1.4 ext{--}2$ GeV). The inclusion of heavy quarks in this framework is work in progress. Overall, the work clarifies how perturbative corrections and nonperturbative inputs combine to reproduce transverse-momentum spectra and guides improvements to event generators like \\textsc{Pythia}.

Abstract

The transverse momentum of a colour-singlet massive particle in a hadronic collision is built up by two components, the perturbative effect of parton branchings and the nonperturbative effect of primordial kT. In previous studies of transverse momentum spectra for Z0 production at the Tevatron, the best fit to the experimental data are given when the primordial kT is set to a much higher value than what is expected considering the confinement of partons in the proton. We here investigate the possibility that the reason for this is that too few branchings are generated in showers, compared to the evolution used in the tuning of parton densities. This could then be compensated by increasing the value of Lambda_QCD. The study is done using the regular Pythia showering routines and a new algorithm where the branchings are ordered in transverse momentum pT^2 instead of virtuality Q^2.

Perturbative and Nonperturbative Effects in Transverse Momentum Generation

TL;DR

This thesis analyzes how perturbative parton branchings and nonperturbative primordial shape the transverse momentum of color-singlet states in hadronic collisions, focusing on Z production. By testing corrections to pure DGLAP evolution in \\textsc{Pythia}—including angular ordering, the constraint, and a shift to —the study estimates how much must be raised to compensate for slower evolution, and examines how this impacts spectra and primordial . A new shower algorithm ordering branchings in is introduced, yielding spectra that are less sensitive to primordial and offering comparable fits to data under certain parameter choices ( GeV; GeV). The inclusion of heavy quarks in this framework is work in progress. Overall, the work clarifies how perturbative corrections and nonperturbative inputs combine to reproduce transverse-momentum spectra and guides improvements to event generators like \\textsc{Pythia}.

Abstract

The transverse momentum of a colour-singlet massive particle in a hadronic collision is built up by two components, the perturbative effect of parton branchings and the nonperturbative effect of primordial kT. In previous studies of transverse momentum spectra for Z0 production at the Tevatron, the best fit to the experimental data are given when the primordial kT is set to a much higher value than what is expected considering the confinement of partons in the proton. We here investigate the possibility that the reason for this is that too few branchings are generated in showers, compared to the evolution used in the tuning of parton densities. This could then be compensated by increasing the value of Lambda_QCD. The study is done using the regular Pythia showering routines and a new algorithm where the branchings are ordered in transverse momentum pT^2 instead of virtuality Q^2.

Paper Structure

This paper contains 25 sections, 35 equations, 18 figures, 1 table.

Table of Contents

  1. Introduction
  2. Parton showers
  3. General concepts of parton showers
  4. DGLAP equations
  5. Initial-state showers in $\textsc{Pythia}$
  6. Primordial $k_{\perp}$
  7. Corrections to pure DGLAP evolution in $\textsc{Pythia}$
  8. Angular ordering
  9. The condition that $\hat{u}\,<\,0$
  10. Evolution with $\alpha_{\mathrm{s}}$($p_{\perp}^2$) instead of $\alpha_{\mathrm{s}}$($Q^2$)
  11. Final-state showers of emitted particles with timelike virtuality
  12. Other corrections
  13. Study of $\Lambda_{\mathrm{QCD}}$ values, $p_{\perp}$-spectra and primordial $k_{\perp}$
  14. Study of the increase in $\Lambda_{\mathrm{QCD}}$ needed to compensate for the corrections to DGLAP
  15. Toy model studies
  16. ...and 10 more sections

Figures (18)

  • Figure 1: From the three processes q $\rightarrow$ qg, g $\rightarrow$ gg and g $\rightarrow$ q$\mathrm{\overline{q}}$ it is possible to build up complicated showers. The emissions are ordered in $Q^2$.
  • Figure 2: Production of a $\mathrm{Z}^0$-boson in a parton shower model. At each branching the accumulated $p_{\perp}$ is split between the particles in $z$ vs. $1 - z$ fractions. New $p_{\perp}$ values for the partons after the branching are generated, and the shower continues. This means that showers with many branchings are not very sensitive to the value of primordial $k_{\perp}$.
  • Figure 3: Emissions in $\textsc{Pythia}$ are angular ordered: $\theta_\mathrm{1}\,<\,\theta_\mathrm{2}\,<\,\theta_\mathrm{3}$.
  • Figure 4: The emission of a gluon by one of the quarks at $\mathrm{Z}^0$-production seen a) in a parton shower model and b) as a 2 $\rightarrow$ 2 process.
  • Figure 5: Emission of a gluon by a massless quark.
  • ...and 13 more figures