Hadron properties in a generalized Nambu-- Jona-Lasinio model.
Item
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Title
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Hadron properties in a generalized Nambu-- Jona-Lasinio model.
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Identifier
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AAI9959199
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identifier
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9959199
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Creator
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Li, Xiangdong.
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Contributor
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Adviser: Carl Shakin
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Date
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2000
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Nuclear
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Abstract
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In this work we calculate the properties of the sigma meson using a generalized Nambu-Jona-Lasinio model that includes a model of confinement. We describe, in some detail, how the sigma. coupling to states in the two-pion continuum may be calculated, when using a Lorentz-vector confining interaction. We provide a general procedure for calculating various loop diagrams in Minkowski momentum space for quarks in the presence of the confining interaction. We study the properties of the Signa meson by considering t-channel scalar-isoscalar exchange between two quarks.;We study the pseudoscalar octet of Goldstone bosons as well as the eta '. We are particularly interested in the properties of the eta ' and in the mixing of eta0 (singlet) and eta 8 (octet) modes. It is found that the value of the vacuum-polarization integral in each mesonic channel increases rapidly as one approaches the qq continuum in a model without confinement, since there is cusp behavior at the qq thresholds. That is not a problem in the description of the low-mass mesons pi, kappa, eta), but makes the study of the eta' problematic in a theory without confinement. With our model of Lorentz-vector confinement, we have shown in an earlier work that the Goldstone theorem is satisfied. As usual, we found a relation between the Bethe-Salpeter equation and the Schwinger-Dyson equation for zero-energy modes. The approximation we adopt for our calculations, made in Minkowski momentum space, is to take the constituent masses of the up, down and strange quarks to be independent of momentum. Here, we present values for the meson masses and the meson decay constants. We also calculate the decay rates of the processes eta → gamma + gamma and eta' → gamma + gamma for one particular model of confinement. As part of our analysis, we describe how the triangle (anomaly) diagram, governing the process eta' → gamma + gamma, may be calculated when using one version of our confining interaction. Our calculated rates for the processes eta → gamma +gamma and eta' → gamma + gamma are in good agreement with the experimental values.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
