Quarkonia Production in Nonrelativistic Quantum Chromodynamics

Citation

Leibovich, Adam Keith (1998) Quarkonia Production in Nonrelativistic Quantum Chromodynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ezh4-nr37. https://resolver.caltech.edu/CaltechTHESIS:08072017-152935193

Abstract

Color-singlet production of quarkonia has failed to correctly predict the cross sections of ψ's produced at the Tevatron. Gluon fragmentation has been identified the dominant source of high energy prompt quarkonia at hadron colliders. Fragmentation approximations break down, however, when a quarkonium's transverse momentum becomes comparable to its mass. We review the NRQCD formalism, which is an effective field that improves upon the color-singlet calculations. As an example of color-singlet calculation, we calculate in closed form the complete O(α²_s) color-singlet differential cross section for e⁺e^- → γ^* → ψq + X scattering. The cross section reduces at high energies to a heavy quark fragmentation form. We find that the energy scale at which the approximate fragmentation result becomes reliable exceeds the ψq mass by more than an order of magnitude. We also discuss the color-singlet model's predictions for direct J/ψ angular and energy distributions at CLEO. For production at a pp collider, we identify a large class of color-octet diagrams that mediate quarkonia production at all energies and reduce to the dominant set of gluon fragmentation graphs in the high p⊥ limit. They contribute to quarkonia differential cross sections at the same order as color-singlet diagrams and bring theoretical predictions for γ and ψ production at the Tevatron into agreement with experimental measurements. Using recent CDF data, we extract numerical values for bottomonia and charmonia color-octet matrix elements which are consistent with NRQCD scaling rules. We calculated the polarization of ψ' due to pp → QQ[^2S+1L_J⁽⁸⁾]X → ψ^(λ)X color-octet quarkonia production at order α³_s which could be used as a test of NRQCD. We find that at low transverse momenta the ψ' is unpolarized due to the contributions proportional to the L = S = 0 and L = s = 1 color-octet matrix elements. As p⊥ increases, the ψ' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.

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