[Paper Review] The Unintegrated Gluon Density in the Photon and Heavy Quark Production

M. Hansson, H. Jung+1 more|ArXiv.org|Feb 2, 2004

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper presents the first full CCFM evolution of the unintegrated gluon density in the photon, implemented in the CASCADE Monte Carlo generator to calculate heavy quark production cross sections in $e^+e^-$ and $γ\u03b3$ collisions. The approach improves agreement with LEP charm data and provides predictions for TESLA energies, though it only partially resolves the $b\bar{b}$ cross section discrepancy.

ABSTRACT

The production cross section of heavy quarks in real and virtual photon-photon collisions has been studied. The unintegrated gluon density in the photon was obtained using the full CCFM evolution equation for the first time. The gluon density was implemented in the Monte Carlo generator CASCADE, and cross sections for heavy quark production in $e^+e^-$ collisions were calculated and compared to LEP data. Also, predictions for heavy quark cross sections in $e^+e^-$ and $γγ$ collisions at TESLA energies are given.

Motivation & Objective

• To investigate whether $k_t$-factorization with an unintegrated gluon density in the photon can explain the observed $b\bar{b}$ cross section in $γ\u03b3$ collisions.
• To implement the full CCFM evolution equations for the photon's gluon density, overcoming limitations of previous simplified models.
• To compare predictions for heavy quark production in $e^+e^-$ and $γ\u03b3$ collisions with LEP data and provide forecasts for TESLA.
• To assess uncertainties in the cross sections arising from parameters like $\Lambda$, $\mu^2$, and quark masses.

Proposed method

• Used the complete CCFM evolution equations to determine the unintegrated gluon density in the photon, replacing prior approximations.
• Implemented the CCFM-evolved gluon density into the CASCADE Monte Carlo event generator for parton-level simulation.
• Applied $k_t$-factorization to include transverse momentum dependence of partons, enabling off-shell initial states.
• Calculated cross sections for $c\bar{c}$ and $b\bar{b}$ production in $e^+e^-$ and $γ\u03b3$ collisions at LEP and TESLA energies.
• Varied key parameters ($\Lambda$, $\mu^2$, quark masses, input distributions) to estimate theoretical uncertainties.
• Used $m_c = 1.5$ GeV and $m_b = 4.75$ GeV as default masses, with ranges tested for uncertainty analysis.

Experimental results

Research questions

• RQ1 Can the full CCFM evolution of the photon's unintegrated gluon density improve the description of $b\bar{b}$ production in $γ\u03b3$ collisions?
• RQ2 How does the $k_t$-factorization approach with CCFM-evolved gluon densities compare to standard collinear DGLAP predictions for heavy quark production at LEP?
• RQ3 To what extent do uncertainties in $\Lambda$, $\mu^2$, and quark masses affect the predicted cross sections?
• RQ4 What are the expected cross sections for $c\bar{c}$ and $b\bar{b}$ production in $e^+e^-$ and $γ\u03b3$ collisions at TESLA energies?

Key findings

• The full CCFM evolution of the photon's unintegrated gluon density was implemented for the first time, replacing earlier simplified approximations.
• The CCFM approach improved agreement with LEP charm data compared to standard collinear DGLAP predictions, though the improvement was modest.
• For beauty quark production, the CCFM approach provided a slight improvement over DGLAP but still failed to fully resolve the observed $b\bar{b}$ cross section discrepancy at LEP.
• The largest source of uncertainty in the cross sections came from variations in the heavy quark masses, with $m_b$ varied between 4.5 and 5 GeV and $m_c$ between 1.3 and 1.7 GeV.
• Changing $\Lambda$ from 0.2 to 0.34 GeV produced the largest variation in cross sections, while changes in $\mu^2$ and gluon density inputs had smaller effects.
• Predictions for $c\bar{c}$ and $b\bar{b}$ production in $e^+e^-$ and $γ\u03b3$ collisions at TESLA energies were provided, offering benchmarks for future experiments.