Configuration mixing of quark states in nucleons and other baryons in the MIT bag model

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Configuration mixing of quark states in nucleons and other baryons in the MIT bag model

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Title: Configuration mixing of quark states in nucleons and other baryons in the MIT bag model
Author: Hazelton, William Donald
Abstract: The MIT bag model incorporates two of the main features of Quantum Chromodynamics (QCD), confinement of quarks in color singlet states, and asymptotic freedom. Most prior studies using this model have been perturbative, and have considered limited subsets of possible excitations, such as pair creation from the three quark ground state. However, there are many three quark excitations lower in energy than the five particle states. We calculate the ground state configuration of baryons, including all quark states up to a consistent energy cutoff, using the one gluon exchange (OGE) interaction. We study the p, n, $\Sigma\sp+,\ \Sigma\sp-,\ \Xi\sp-,$ and $\Xi\sp0$ in a spherical bag with a Fock space truncated at a succession of cutoffs, with the maximum cutoff at 1.5 GeV above the three quark ground state. This allows many qqq (three quark) and qqqqq (four quark plus anti-quark) states in the basis. As we raise the cutoff, the strength of the strong coupling constant necessary to fit the $\Delta-N$ splitting decreases from a value of $\alpha\sb{s} = 2.2$ with three valence quarks to a value of about $\alpha\sb{s} = 1.4$ at the 1.5 GeV cutoff. We require a positive Casimir energy for stability, in agreement with theoretical studies. This is opposite to the sign assumed for the original MIT bag model.Part of the motivation for this study stems from experiments at the Electron Muon Collaboration (EMC), Stanford Linear Accelerator (SLAC), and the Spin Muon Collaboration (SMC) that indicate the nucleon spin attributable to the spin of quarks is small. We find that configuration mixing may provide a partial explanation. Configuration mixing leads to substantial probabilities for states with two $p\sb{3/2}$ quark excitations, as well as for various other basis states. This allows much of the nucleon spin to be carried by quark orbital angular momentum. We calculate the spin fractions carried by u, d, and s quarks. We find reasonable agreement with the experimental measurements of the nucleon spin structure functions and the Bjorken sum rule. For the MIT bag with configuration mixing, we find $\Gamma\sbsp{1}{p}\approx 0.141{-}0.148$ and $\Gamma\sbsp{1}{p}{-}\Gamma\sbsp{1}{n}\approx 0.141{-}0.147.$
Description: Thesis (Ph. D.)--University of Washington, 1997

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